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@article{fds339291,
Author = {Murphy, JM and Maggioni, M},
Title = {Unsupervised Clustering and Active Learning of Hyperspectral
Images with Nonlinear Diffusion},
Journal = {Ieee Transactions on Geoscience and Remote
Sensing},
Volume = {57},
Number = {3},
Pages = {1829-1845},
Publisher = {Institute of Electrical and Electronics Engineers
(IEEE)},
Year = {2019},
Month = {March},
url = {http://dx.doi.org/10.1109/TGRS.2018.2869723},
Abstract = {© 1980-2012 IEEE. The problem of unsupervised learning and
segmentation of hyperspectral images is a significant
challenge in remote sensing. The high dimensionality of
hyperspectral data, presence of substantial noise, and
overlap of classes all contribute to the difficulty of
automatically clustering and segmenting hyperspectral
images. We propose an unsupervised learning technique called
spectral-spatial diffusion learning (DLSS) that combines a
geometric estimation of class modes with a
diffusion-inspired labeling that incorporates both spectral
and spatial information. The mode estimation incorporates
the geometry of the hyperspectral data by using diffusion
distance to promote learning a unique mode from each class.
These class modes are then used to label all the points by a
joint spectral-spatial nonlinear diffusion process. A
related variation of DLSS is also discussed, which enables
active learning by requesting labels for a very small number
of well-chosen pixels, dramatically boosting overall
clustering results. Extensive experimental analysis
demonstrates the efficacy of the proposed methods against
benchmark and state-of-the-art hyperspectral analysis
techniques on a variety of real data sets, their robustness
to choices of parameters, and their low computational
complexity.},
Doi = {10.1109/TGRS.2018.2869723},
Key = {fds339291}
}
@article{fds341876,
Author = {Vogelstein, JT and Bridgeford, EW and Wang, Q and Priebe, CE and Maggioni, M and Shen, C},
Title = {Discovering and deciphering relationships across disparate
data modalities.},
Journal = {Elife},
Volume = {8},
Year = {2019},
Month = {January},
url = {http://dx.doi.org/10.7554/eLife.41690},
Abstract = {Understanding the relationships between different properties
of data, such as whether a genome or connectome has
information about disease status, is increasingly important.
While existing approaches can test whether two properties
are related, they may require unfeasibly large sample sizes
and often are not interpretable. Our approach, 'Multiscale
Graph Correlation' (MGC), is a dependence test that
juxtaposes disparate data science techniques, including
k-nearest neighbors, kernel methods, and multiscale
analysis. Other methods may require double or triple the
number of samples to achieve the same statistical power as
MGC in a benchmark suite including high-dimensional and
nonlinear relationships, with dimensionality ranging from 1
to 1000. Moreover, MGC uniquely characterizes the latent
geometry underlying the relationship, while maintaining
computational efficiency. In real data, including brain
imaging and cancer genetics, MGC detects the presence of a
dependency and provides guidance for the next experiments to
conduct.},
Doi = {10.7554/eLife.41690},
Key = {fds341876}
}
@article{fds337334,
Author = {Escande, P and Debarnot, V and Maggioni, M and Mangeat, T and Weiss,
P},
Title = {Learning and exploiting physics of degradations},
Journal = {Optics Infobase Conference Papers},
Volume = {Part F105-MATH 2018},
Publisher = {OSA},
Year = {2018},
Month = {January},
ISBN = {9781557528209},
url = {http://dx.doi.org/10.1364/MATH.2018.MTu2D.4},
Abstract = {© 2018 The Author(s). Even though physics of degradations
of an acquisition system might be complex, it often relies
on a small number of parameters. We present a methodology to
learn this physics and exploit it for restoration
purposes.},
Doi = {10.1364/MATH.2018.MTu2D.4},
Key = {fds337334}
}
@article{fds337145,
Author = {Murphy, JM and Maggioni, M},
Title = {Diffusion geometric methods for fusion of remotely sensed
data},
Journal = {Smart Structures and Materials 2005: Active Materials:
Behavior and Mechanics},
Volume = {10644},
Publisher = {SPIE},
Year = {2018},
Month = {January},
ISBN = {9781510617995},
url = {http://dx.doi.org/10.1117/12.2305274},
Abstract = {© COPYRIGHT SPIE. Downloading of the abstract is permitted
for personal use only. We propose a novel unsupervised
learning algorithm that makes use of image fusion to
efficiently cluster remote sensing data. Exploiting
nonlinear structures in multimodal data, we devise a
clustering algorithm based on a random walk in a fused
feature space. Constructing the random walk on the fused
space enforces that pixels are considered close only if they
are close in both sensing modalities. The structure learned
by this random walk is combined with density estimation to
label all pixels. Spatial information may also be used to
regularize the resulting clusterings. We compare the
proposed method with several spectral methods for image
fusion on both synthetic and real data.},
Doi = {10.1117/12.2305274},
Key = {fds337145}
}
@article{fds320928,
Author = {Little, AV and Maggioni, M and Rosasco, L},
Title = {Multiscale geometric methods for data sets I: Multiscale
SVD, noise and curvature},
Journal = {Applied and Computational Harmonic Analysis},
Volume = {43},
Number = {3},
Pages = {504-567},
Publisher = {Elsevier BV},
Year = {2017},
Month = {November},
url = {http://dx.doi.org/10.1016/j.acha.2015.09.009},
Abstract = {© 2015 Elsevier Inc. Large data sets are often modeled as
being noisy samples from probability distributions μ in RD,
with D large. It has been noticed that oftentimes the
support M of these probability distributions seems to be
well-approximated by low-dimensional sets, perhaps even by
manifolds. We shall consider sets that are locally
well-approximated by k-dimensional planes, with k≪D, with
k-dimensional manifolds isometrically embedded in RD being a
special case. Samples from μ are furthermore corrupted by
D-dimensional noise. Certain tools from multiscale geometric
measure theory and harmonic analysis seem well-suited to be
adapted to the study of samples from such probability
distributions, in order to yield quantitative geometric
information about them. In this paper we introduce and study
multiscale covariance matrices, i.e. covariances
corresponding to the distribution restricted to a ball of
radius r, with a fixed center and varying r, and under
rather general geometric assumptions we study how their
empirical, noisy counterparts behave. We prove that in the
range of scales where these covariance matrices are most
informative, the empirical, noisy covariances are close to
their expected, noiseless counterparts. In fact, this is
true as soon as the number of samples in the balls where the
covariance matrices are computed is linear in the intrinsic
dimension of M. As an application, we present an algorithm
for estimating the intrinsic dimension of
M.},
Doi = {10.1016/j.acha.2015.09.009},
Key = {fds320928}
}
@article{fds331595,
Author = {Wang, YG and Maggioni, M and Chen, G},
Title = {Enhanced detection of chemical plumes in hyperspectral
images and movies throughimproved backgroundmodeling},
Journal = {Workshop on Hyperspectral Image and Signal Processing,
Evolution in Remote Sensing},
Volume = {2015-June},
Publisher = {IEEE},
Year = {2017},
Month = {October},
ISBN = {9781467390156},
url = {http://dx.doi.org/10.1109/WHISPERS.2015.8075369},
Abstract = {© 2015 IEEE. We extend recent work that models the
background in hyperspectral images by a single distribution
(Gaussian or subspace) to use a mixture of such
distributions. This seems to better capture the complexity
of the background, which often consists of heterogeneous
regions (e.g., sky, mountain and ground). We derive mixture
versions of the previous estimators and apply them to
benchmark data sets for detecting chemical plumes of known
chemicals in hyperspectral images and movies. Our
experiments show that the mixture background models
consistently outperform their counterparts with a single
distribution.},
Doi = {10.1109/WHISPERS.2015.8075369},
Key = {fds331595}
}
@article{fds329467,
Author = {Gerber, S and Maggioni, M},
Title = {Multiscale strategies for computing optimal
transport},
Journal = {Journal of Machine Learning Research},
Volume = {18},
Pages = {1-32},
Year = {2017},
Month = {August},
Abstract = {©2017 Samuel Gerber and Mauro Maggioni. This paper presents
a multiscale approach to efficiently compute approximate
optimal transport plans between point sets. It is
particularly well-suited for point sets that are in
high-dimensions, but are close to being intrinsically
low-dimensional. The approach is based on an adaptive
multiscale decomposition of the point sets. The multiscale
decomposition yields a sequence of optimal transport
problems, that are solved in a top-to-bottom fashion from
the coarsest to the finest scale. We provide numerical
evidence that this multiscale approach scales approximately
linearly, in time and memory, in the number of nodes,
instead of quadratically or worse for a direct solution.
Empirically, the multiscale approach results in less than
one percent relative error in the objective function.
Furthermore, the multiscale plans constructed are of
interest by themselves as they may be used to introduce
novel features and notions of distances between point sets.
An analysis of sets of brain MRI based on optimal transport
distances illustrates the effectiveness of the proposed
method on a real world data set. The application
demonstrates that multiscale optimal transport distances
have the potential to improve on state-of-the-art metrics
currently used in computational anatomy.},
Key = {fds329467}
}
@article{fds325965,
Author = {Bongini, M and Fornasier, M and Hansen, M and Maggioni,
M},
Title = {Inferring interaction rules from observations of evolutive
systems I: The variational approach},
Journal = {Mathematical Models and Methods in Applied
Sciences},
Volume = {27},
Number = {5},
Pages = {909-951},
Publisher = {World Scientific Pub Co Pte Lt},
Year = {2017},
Month = {May},
url = {http://dx.doi.org/10.1142/S0218202517500208},
Abstract = {© 2017 World Scientific Publishing Company. In this paper,
we are concerned with the learnability of nonlocal
interaction kernels for first-order systems modeling certain
social interactions, from observations of realizations of
their dynamics. This paper is the first of a series on
learnability of nonlocal interaction kernels and presents a
variational approach to the problem. In particular, we
assume here that the kernel to be learned is bounded and
locally Lipschitz continuous and that the initial conditions
of the systems are drawn identically and independently at
random according to a given initial probability
distribution. Then the minimization over a rather arbitrary
sequence of (finite-dimensional) subspaces of a least square
functional measuring the discrepancy from observed
trajectories produces uniform approximations to the kernel
on compact sets. The convergence result is obtained by
combining mean-field limits, transport methods, and a
Γ-convergence argument. A crucial condition for the
learnability is a certain coercivity property of the least
square functional, defined by the majorization of an L2-norm
discrepancy to the kernel with respect to a probability
measure, depending on the given initial probability
distribution by suitable push forwards and transport maps.
We illustrate the convergence result by means of several
numerical experiments.},
Doi = {10.1142/S0218202517500208},
Key = {fds325965}
}
@article{fds328806,
Author = {Tomita, TM and Maggioni, M and Vogelstein, JT},
Title = {ROFLMAO: Robust oblique forests with linear MAtrix
operations},
Journal = {Proceedings of the 17th Siam International Conference on
Data Mining, Sdm 2017},
Pages = {498-506},
Year = {2017},
Month = {January},
ISBN = {9781611974874},
Abstract = {Copyright © by SIAM. Random Forest (RF) remains one of the
most widely used general purpose classification methods. Two
recent largescale empirical studies demonstrated it to be
the best overall classification method among a variety of
methods evaluated. One of its main limitations, however, is
that it is restricted to only axis-aligned recursive
partitions of the feature space. Consequently, RF is
particularly sensitive to the orientation of the data.
Several studies have proposed "oblique" decision forest
methods to address this limitation. However, these methods
either have a time and space complexity significantly
greater than RF, are sensitive to unit and scale, or
empirically do not perform as well as RF on real data. One
promising oblique method that was proposed alongside the
canonical RF method, called Forest-RC (F-RC), has not
received as much attention by the community. Despite it
being just as old as RF, virtually no studies exist
investigating its theoretical or empirical performance. In
this work, we demonstrate that F-RC empirically outperforms
RF and another recently proposed oblique method called
Random Rotation Random Forest, while approximately
maintaining the same computational complexity. Furthermore,
a variant of F-RC which rank transforms the data prior to
learning is especially invariant to affine transformations
and robust to data corruption. Open source code is
available.},
Key = {fds328806}
}
@article{fds325966,
Author = {Crosskey, M and Maggioni, M},
Title = {ATLAS: A geometric approach to learning high-dimensional
stochastic systems near manifolds},
Journal = {Multiscale Modeling & Simulation},
Volume = {15},
Number = {1},
Pages = {110-156},
Publisher = {Society for Industrial & Applied Mathematics
(SIAM)},
Year = {2017},
Month = {January},
url = {http://dx.doi.org/10.1137/140970951},
Abstract = {© 2017 Society for Industrial and Applied Mathematics. When
simulating multiscale stochastic differential equations
(SDEs) in highdimensions, separation of timescales,
stochastic noise, and high-dimensionality can make
simulations prohibitively expensive. The computational cost
is dictated by microscale properties and interactions of
many variables, while the behavior of interest often occurs
at the macroscale level and at large timescales, often
characterized by few important, but unknown, degrees of
freedom. For many problems bridging the gap between the
microscale and macroscale by direct simulation is
computationally infeasible. In this work we propose a novel
approach to automatically learn a reduced model with an
associated fast macroscale simulator. Our unsupervised
learning algorithm uses short parallelizable microscale
simulations to learn provably accurate macroscale SDE
models, which are continuous in space and time. The learning
algorithm takes as input the microscale simulator, a local
distance function, and a homogenization spatial or temporal
scale, which is the smallest time scale of interest in the
reduced system. The learned macroscale model can then be
used for fast computation and storage of long simulations.
We prove guarantees that relate the number of short paths
requested from the microscale simulator to the accuracy of
the learned macroscale simulator. We discuss various
examples, both low-and high-dimensional, as well as results
about the accuracy of the fast simulators we construct, and
the model's dependency on the number of short paths
requested from the microscale simulator.},
Doi = {10.1137/140970951},
Key = {fds325966}
}
@article{fds320927,
Author = {Liao, W and Maggioni, M and Vigogna, S},
Title = {Learning adaptive multiscale approximations to data and
functions near low-dimensional sets},
Journal = {2016 Ieee Information Theory Workshop, Itw
2016},
Pages = {226-230},
Publisher = {IEEE},
Year = {2016},
Month = {October},
ISBN = {9781509010905},
url = {http://dx.doi.org/10.1109/ITW.2016.7606829},
Abstract = {© 2016 IEEE. In the setting where a data set in D consists
of samples from a probability measure ρ concentrated on or
near an unknown d-dimensional set M, with D large but d ≪
D, we consider two sets of problems: geometric approximation
of M and regression of a function on M. In the first case we
construct multiscale low-dimensional empirical
approximations ofM, which are adaptive whenMhas geometric
regularity that may vary at different locations and scales,
and give performance guarantees. In the second case we
exploit these empirical geometric approximations to
construct multiscale approximations to on M, which adapt to
the unknown regularity of even when this varies at different
scales and locations. We prove guarantees showing that we
attain the same learning rates as if was defined on a
Euclidean domain of dimension d, instead of an unknown
manifold M. All algorithms have complexity O(n log n), with
constants scaling linearly in D and exponentially in
d.},
Doi = {10.1109/ITW.2016.7606829},
Key = {fds320927}
}
@article{fds318319,
Author = {Goetzmann, WN and Jones, PW and Maggioni, M and Walden,
J},
Title = {Beauty is in the bid of the beholder: An empirical basis for
style},
Journal = {Research in Economics},
Volume = {70},
Number = {3},
Pages = {388-402},
Publisher = {Elsevier BV},
Year = {2016},
Month = {September},
url = {http://dx.doi.org/10.1016/j.rie.2016.05.004},
Abstract = {© 2016 University of Venice We develop a method for
classification of works of art based on their price
dynamics. The method is in the same spirit as factor models
commonly used within financial economics. Factor models
assume that price dynamics of assets are related to
underlying fundamental characteristics. We assume that such
characteristics exist for works of art, and that they are
associated with what we intuitively think of as style. We
use a clustering algorithm to group artists that represent
similar styles. This algorithm is specifically well-suited
for situations where statistical distributions are far from
normal – a description we believe fits well with markets
for art. We test the method empirically on a ten-year sample
of price data for paintings by 58 artists. Even with this
limited data set, we clearly identify five groups and show
that these are related to a standard classification of
style.},
Doi = {10.1016/j.rie.2016.05.004},
Key = {fds318319}
}
@article{fds290935,
Author = {Maggioni, M},
Title = {Geometry of data and biology},
Journal = {Notices of the American Mathematical Society},
Volume = {62},
Number = {10},
Pages = {1185-1188},
Publisher = {American Mathematical Society (AMS)},
Year = {2015},
Month = {January},
ISSN = {0002-9920},
url = {http://dx.doi.org/10.1090/noti1289},
Doi = {10.1090/noti1289},
Key = {fds290935}
}
@article{fds313569,
Author = {Maggioni, M and Minsker, S and Strawn, N},
Title = {Geometric multi-resolution analysis for dictionary
learning},
Journal = {Smart Structures and Materials 2005: Active Materials:
Behavior and Mechanics},
Volume = {9597},
Publisher = {SPIE},
Year = {2015},
Month = {January},
ISBN = {9781628417630},
ISSN = {0277-786X},
url = {http://dx.doi.org/10.1117/12.2189594},
Abstract = {© 2015 SPIE. We present an efficient algorithm and theory
for Geometric Multi-Resolution Analysis (GMRA), a procedure
for dictionary learning. Sparse dictionary learning provides
the necessary complexity reduction for the critical
applications of compression, regression, and classification
in high-dimensional data analysis. As such, it is a critical
technique in data science and it is important to have
techniques that admit both efficient implementation and
strong theory for large classes of theoretical models. By
construction, GMRA is computationally efficient and in this
paper we describe how the GMRA correctly approximates a
large class of plausible models (namely, the noisy
manifolds).},
Doi = {10.1117/12.2189594},
Key = {fds313569}
}
@article{fds225842,
Author = {M. Maggioni and S. Minsker and N. Strawn},
Title = {Multiscale Dictionary and Manifold Learning: Non-Asymptotic
Bounds for the Geometric Multi-Resolution
Analysis},
Booktitle = {Proc. iTWIST’14: international - Traveling Workshop on
Interactions between Sparse models and Technology},
Year = {2014},
Month = {August},
Key = {fds225842}
}
@article{fds243780,
Author = {Altemose, N and Miga, KH and Maggioni, M and Willard,
HF},
Title = {Genomic characterization of large heterochromatic gaps in
the human genome assembly.},
Journal = {Plos Computational Biology},
Volume = {10},
Number = {5},
Pages = {e1003628},
Year = {2014},
Month = {May},
ISSN = {1553-734X},
url = {http://dx.doi.org/10.1371/journal.pcbi.1003628},
Abstract = {The largest gaps in the human genome assembly correspond to
multi-megabase heterochromatic regions composed primarily of
two related families of tandem repeats, Human Satellites 2
and 3 (HSat2,3). The abundance of repetitive DNA in these
regions challenges standard mapping and assembly algorithms,
and as a result, the sequence composition and potential
biological functions of these regions remain largely
unexplored. Furthermore, existing genomic tools designed to
predict consensus-based descriptions of repeat families
cannot be readily applied to complex satellite repeats such
as HSat2,3, which lack a consistent repeat unit reference
sequence. Here we present an alignment-free method to
characterize complex satellites using whole-genome shotgun
read datasets. Utilizing this approach, we classify HSat2,3
sequences into fourteen subfamilies and predict their
chromosomal distributions, resulting in a comprehensive
satellite reference database to further enable genomic
studies of heterochromatic regions. We also identify 1.3 Mb
of non-repetitive sequence interspersed with HSat2,3 across
17 unmapped assembly scaffolds, including eight annotated
gene predictions. Finally, we apply our satellite reference
database to high-throughput sequence data from 396 males to
estimate array size variation of the predominant HSat3 array
on the Y chromosome, confirming that satellite array sizes
can vary between individuals over an order of magnitude (7
to 98 Mb) and further demonstrating that array sizes are
distributed differently within distinct Y haplogroups. In
summary, we present a novel framework for generating initial
reference databases for unassembled genomic regions enriched
with complex satellite DNA, and we further demonstrate the
utility of these reference databases for studying patterns
of sequence variation within human populations.},
Doi = {10.1371/journal.pcbi.1003628},
Key = {fds243780}
}
@article{fds243782,
Author = {Gerber, S and Maggioni, M},
Title = {Multiscale dictionaries, transforms, and learning in
high-dimensions},
Journal = {Smart Structures and Materials 2005: Active Materials:
Behavior and Mechanics},
Volume = {8858},
Publisher = {SPIE},
Year = {2013},
Month = {December},
ISBN = {9780819497086},
ISSN = {0277-786X},
url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000326764600047&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92},
Abstract = {Mapping images to a high-dimensional feature space, either
by considering patches of images or other features, has lead
to state-of-art results in signal processing tasks such as
image denoising and imprinting, and in various machine
learning and computer vision tasks on images. Understanding
the geometry of the embedding of images into
high-dimensional feature space is a challenging problem.
Finding efficient representations and learning dictionaries
for such embeddings is also problematic, often leading to
expensive optimization algorithms. Many such algorithms
scale poorly with the dimension of the feature space, for
example with the size of patches of images if these are
chosen as features. This is in contrast with the crucial
needs of using a multi-scale approach in the analysis of
images, as details at multiple scales are crucial in image
understanding, as well as in many signal processing tasks.
Here we exploit a recent dictionary learning algorithm based
on Geometric Wavelets, and we extend it to perform
multi-scale dictionary learning on image patches, with
efficient algorithms for both the learning of the
dictionary, and the computation of coefficients onto that
dictionary. We also discuss how invariances in images may be
introduced in the dictionary learning phase, by generalizing
the construction of such dictionaries to non-Euclidean
spaces. © 2013 SPIE.},
Doi = {10.1117/12.2021984},
Key = {fds243782}
}
@article{fds221112,
Author = {M. Maggioni},
Title = {Geometric Estimation of Probability Measures in
High-Dimensions},
Journal = {Proc. IEEE Asilomar Conference},
Year = {2013},
Month = {November},
Key = {fds221112}
}
@article{fds243813,
Author = {Coppola, A and Wenner, BR and Ilkayeva, O and Stevens, RD and Maggioni,
M and Slotkin, TA and Levin, ED and Newgard, CB},
Title = {Branched-chain amino acids alter neurobehavioral function in
rats.},
Journal = {American journal of physiology. Endocrinology and
metabolism},
Volume = {304},
Number = {4},
Pages = {E405-E413},
Year = {2013},
Month = {February},
url = {http://www.ncbi.nlm.nih.gov/pubmed/23249694},
Abstract = {Recently, we have described a strong association of
branched-chain amino acids (BCAA) and aromatic amino acids
(AAA) with obesity and insulin resistance. In the current
study, we have investigated the potential impact of BCAA on
behavioral functions. We demonstrate that supplementation of
either a high-sucrose or a high-fat diet with BCAA induces
anxiety-like behavior in rats compared with control groups
fed on unsupplemented diets. These behavioral changes are
associated with a significant decrease in the concentration
of tryptophan (Trp) in brain tissues and a consequent
decrease in serotonin but no difference in indices of
serotonin synaptic function. The anxiety-like behaviors and
decreased levels of Trp in the brain of BCAA-fed rats were
reversed by supplementation of Trp in the drinking water but
not by administration of fluoxetine, a selective serotonin
reuptake inhibitor, suggesting that the behavioral changes
are independent of the serotonergic pathway of Trp
metabolism. Instead, BCAA supplementation lowers the brain
levels of another Trp-derived metabolite, kynurenic acid,
and these levels are normalized by Trp supplementation. We
conclude that supplementation of high-energy diets with BCAA
causes neurobehavioral impairment. Since BCAA are elevated
spontaneously in human obesity, our studies suggest a
potential mechanism for explaining the strong association of
obesity and mood disorders.},
Doi = {10.1152/ajpendo.00373.2012},
Key = {fds243813}
}
@article{fds243779,
Author = {Maggioni, M},
Title = {Geometric estimation of probability measures in
high-dimensions},
Journal = {Conference Record Asilomar Conference on Signals, Systems
and Computers},
Pages = {1363-1367},
Publisher = {IEEE},
Year = {2013},
Month = {January},
ISSN = {1058-6393},
url = {http://dx.doi.org/10.1109/ACSSC.2013.6810517},
Abstract = {We are interested in constructing adaptive probability
models for high-dimensional data that is well-approximated
by low-dimensional geometric structures. We discuss a family
of estimators for probability distributions based on
data-adaptive multiscale geometric approximations. They are
particularly effective when the probability distribution
concentrates near low-dimensional sets, having sample and
computational complexity depending mildly (linearly in cases
of interest) in the ambient dimension, as well as in the
intrinsic dimension of the data, suitably defined. Moreover
the construction of these estimators may be performed, under
suitable assumptions, by fast algorithms, with cost O((cd;
d2)Dnlog n) where n is the number of samples, D the ambient
dimension, d is the intrinsic dimension of the data, and c a
small constant. © 2013 IEEE.},
Doi = {10.1109/ACSSC.2013.6810517},
Key = {fds243779}
}
@article{fds243781,
Author = {Krishnamurthy, K and Mrozack, A and Maggioni, M and Brady,
D},
Title = {Multiscale, dictionary-based speckle denoising},
Journal = {Optics Infobase Conference Papers},
Booktitle = {Proc. Computational Optical Sensing and Imaging},
Year = {2013},
Month = {January},
ISBN = {978-1-55752-975-6},
url = {http://dx.doi.org/http://dx.doi.org/10.1364/COSI.2013.CM2C.2},
Abstract = {We propose a multiscale, dictionary-based, data-adaptive
estimation method to recover intensities from
multiplicative, speckle data. The proposed method preserves
the edges and textures in the underlying image while
smoothing intensities in homogenous regions. © OSA
2013.},
Doi = {http://dx.doi.org/10.1364/COSI.2013.CM2C.2},
Key = {fds243781}
}
@article{fds327596,
Author = {Chen, G and Little, AV and Maggioni, M},
Title = {Multi-resolution geometric analysis for data in high
dimensions},
Volume = {1},
Pages = {259-285},
Booktitle = {Applied and Numerical Harmonic Analysis},
Publisher = {Birkhäuser Boston},
Year = {2013},
Month = {January},
ISBN = {9780817683757},
url = {http://dx.doi.org/10.1007/978-0-8176-8376-4_13},
Abstract = {© Springer Science+Business Media New York 2013. Large data
sets arise in a wide variety of applications and are often
modeled as samples from a probability distribution in
high-dimensional space. It is sometimes assumed that the
support of such probability distribution is well
approximated by a set of low intrinsic dimension, perhaps
even a low-dimensional smooth manifold. Samples are often
corrupted by high-dimensional noise. We are interested in
developing tools for studying the geometry of such
high-dimensional data sets. In particular, we present here a
multiscale transform that maps high-dimensional data as
above to a set of multiscale coefficients that are
compressible/sparse under suitable assumptions on the data.
We think of this as a geometric counterpart to
multi-resolution analysis in wavelet theory: whereas
wavelets map a signal (typically low dimensional, such as a
one-dimensional time series or a two-dimensional image) to a
set of multiscale coefficients, the geometric wavelets
discussed here map points in a high-dimensional point cloud
to a multiscale set of coefficients. The geometric
multi-resolution analysis (GMRA) we construct depends on the
support of the probability distribution, and in this sense
it fits with the paradigm of dictionary learning or
data-adaptive representations, albeit the type of
representation we construct is in fact mildly nonlinear, as
opposed to standard linear representations. Finally, we
apply the transform to a set of synthetic and real-world
data sets.},
Doi = {10.1007/978-0-8176-8376-4_13},
Key = {fds327596}
}
@article{fds243783,
Author = {Bouvrie, J and Maggioni, M},
Title = {Efficient solution of Markov decision problems with
multiscale representations},
Journal = {2012 50th Annual Allerton Conference on Communication,
Control, and Computing, Allerton 2012},
Pages = {474-481},
Publisher = {IEEE},
Year = {2012},
Month = {December},
url = {http://dx.doi.org/10.1109/Allerton.2012.6483256},
Abstract = {Many problems in sequential decision making and stochastic
control naturally enjoy strong multiscale structure:
sub-tasks are often assembled together to accomplish complex
goals. However, systematically inferring and leveraging
hierarchical structure has remained a longstanding
challenge. We describe a fast multiscale procedure for
repeatedly compressing or homogenizing Markov decision
processes (MDPs), wherein a hierarchy of sub-problems at
different scales is automatically determined. Coarsened MDPs
are themselves independent, deterministic MDPs, and may be
solved using any method. The multiscale representation
delivered by the algorithm decouples sub-tasks from each
other and improves conditioning. These advantages lead to
potentially significant computational savings when solving a
problem, as well as immediate transfer learning
opportunities across related tasks. © 2012
IEEE.},
Doi = {10.1109/Allerton.2012.6483256},
Key = {fds243783}
}
@article{fds243784,
Author = {Bouvrie, J and Maggioni, M},
Title = {Geometric multiscale reduction for autonomous and controlled
nonlinear systems},
Journal = {Proceedings of the Ieee Conference on Decision and
Control},
Pages = {4320-4327},
Booktitle = {Proc. IEEE Conference on Decision and Control
(CDC)},
Publisher = {IEEE},
Year = {2012},
Month = {December},
ISBN = {9781467320658},
url = {http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=6416474},
Abstract = {Most generic approaches to empirical reduction of dynamical
systems, controlled or otherwise, are global in nature. Yet
interesting systems often exhibit multiscale structure in
time or in space, suggesting that localized reduction
techniques which take advantage of this multiscale structure
might provide better approximations with lower complexity.
We introduce a snapshot-based framework for localized
analysis and reduction of nonlinear systems, based on a
systematic multiscale decomposition of the statespace
induced by the geometry of empirical trajectories. A given
system is approximated by a piecewise collection of
low-dimensional systems at different scales, each of which
is suited to and responsible for a particular region of the
statespace. Within this framework, we describe localized,
multiscale variants of the proper orthogonal decomposition
(POD) and empirical balanced truncation methods for model
order reduction of nonlinear systems. The inherent locality
of the treatment further motivates control strategies
involving collections of simple, local controllers and
raises decentralized control possibilities. We illustrate
the localized POD approach in the context of a
high-dimensional fluid mechanics problem involving
incompressible flow over a bluff body. © 2012
IEEE.},
Doi = {10.1109/CDC.2012.6425873},
Key = {fds243784}
}
@article{fds243785,
Author = {Chen, G and Iwen, M and Chin, S and Maggioni, M},
Title = {A fast multiscale framework for data in high-dimensions:
Measure estimation, anomaly detection, and compressive
measurements},
Journal = {2012 Ieee Visual Communications and Image Processing, Vcip
2012},
Pages = {1-6},
Publisher = {IEEE},
Year = {2012},
Month = {December},
ISBN = {9781467344050},
url = {http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=6393503},
Abstract = {Data sets are often modeled as samples from some probability
distribution lying in a very high dimensional space. In
practice, they tend to exhibit low intrinsic dimensionality,
which enables both fast construction of efficient data
representations and solving statistical tasks such as
regression of functions on the data, or even estimation of
the probability distribution from which the data is
generated. In this paper we introduce a novel multiscale
density estimator for high dimensional data and apply it to
the problem of detecting changes in the distribution of
dynamic data, or in a time series of data sets. We also show
that our data representations, which are not standard sparse
linear expansions, are amenable to compressed measurements.
Finally, we test our algorithms on both synthetic data and a
real data set consisting of a times series of hyperspectral
images, and demonstrate their high accuracy in the detection
of anomalies. © 2012 IEEE.},
Doi = {10.1109/VCIP.2012.6410789},
Key = {fds243785}
}
@article{fds243810,
Author = {Allard, WK and Chen, G and Maggioni, M},
Title = {Multi-scale geometric methods for data sets II: Geometric
Multi-Resolution Analysis},
Journal = {Applied and Computational Harmonic Analysis},
Volume = {32},
Number = {3},
Pages = {435-462},
Publisher = {Elsevier BV},
Year = {2012},
Month = {May},
ISSN = {1063-5203},
url = {http://dx.doi.org/10.1016/j.acha.2011.08.001},
Abstract = {Data sets are often modeled as samples from a probability
distribution in RD, for D large. It is often assumed that
the data has some interesting low-dimensional structure, for
example that of a d-dimensional manifold M, with d much
smaller than D. When M is simply a linear subspace, one may
exploit this assumption for encoding efficiently the data by
projecting onto a dictionary of d vectors in RD (for example
found by SVD), at a cost (n+D)d for n data points. When M is
nonlinear, there are no "explicit" and algorithmically
efficient constructions of dictionaries that achieve a
similar efficiency: typically one uses either random
dictionaries, or dictionaries obtained by black-box global
optimization. In this paper we construct data-dependent
multi-scale dictionaries that aim at efficiently encoding
and manipulating the data. Their construction is fast, and
so are the algorithms that map data points to dictionary
coefficients and vice versa, in contrast with L1-type
sparsity-seeking algorithms, but like adaptive nonlinear
approximation in classical multi-scale analysis. In
addition, data points are guaranteed to have a compressible
representation in terms of the dictionary, depending on the
assumptions on the geometry of the underlying probability
distribution. © 2011 Elsevier Inc. All rights
reserved.},
Doi = {10.1016/j.acha.2011.08.001},
Key = {fds243810}
}
@article{fds303547,
Author = {Iwen, MA and Maggioni, M},
Title = {Approximation of Points on Low-Dimensional Manifolds Via
Random Linear Projections},
Volume = {2},
Year = {2012},
Month = {April},
url = {http://arxiv.org/abs/1204.3337v1},
Abstract = {This paper considers the approximate reconstruction of
points, x \in R^D, which are close to a given compact
d-dimensional submanifold, M, of R^D using a small number of
linear measurements of x. In particular, it is shown that a
number of measurements of x which is independent of the
extrinsic dimension D suffices for highly accurate
reconstruction of a given x with high probability.
Furthermore, it is also proven that all vectors, x, which
are sufficiently close to M can be reconstructed with
uniform approximation guarantees when the number of linear
measurements of x depends logarithmically on D. Finally, the
proofs of these facts are constructive: A practical
algorithm for manifold-based signal recovery is presented in
the process of proving the two main results mentioned
above.},
Doi = {10.1093/imaiai/iat001},
Key = {fds303547}
}
@article{fds243811,
Author = {Maggioni, M},
Title = {What is...data mining?},
Journal = {A.M.S. Notices},
Year = {2012},
Month = {April},
url = {http://www.ams.org/notices/201204/rtx120400532p.pdf},
Key = {fds243811}
}
@article{fds243814,
Author = {Zheng, W and Rohrdanz, MA and Maggioni, M and Clementi,
C},
Title = {Polymer reversal rate calculated via locally scaled
diffusion map.},
Journal = {The Journal of Chemical Physics},
Volume = {134},
Number = {14},
Pages = {144109},
Year = {2011},
Month = {April},
url = {http://www.ncbi.nlm.nih.gov/pubmed/21495744},
Abstract = {A recent study on the dynamics of polymer reversal inside a
nanopore by Huang and Makarov [J. Chem. Phys. 128, 114903
(2008)] demonstrated that the reaction rate cannot be
reproduced by projecting the dynamics onto a single
empirical reaction coordinate, a result suggesting the
dynamics of this system cannot be correctly described by
using a single collective coordinate. To further investigate
this possibility we have applied our recently developed
multiscale framework, locally scaled diffusion map (LSDMap),
to obtain collective reaction coordinates for this system.
Using a single diffusion coordinate, we obtain a reversal
rate via Kramers expression that is in good agreement with
the exact rate obtained from the simulations. Our
mathematically rigorous approach accounts for the local
heterogeneity of molecular configuration space in
constructing a diffusion map, from which collective
coordinates emerge. We believe this approach can be applied
in general to characterize complex macromolecular dynamics
by providing an accurate definition of the collective
coordinates associated with processes at different time
scales.},
Doi = {10.1063/1.3575245},
Key = {fds243814}
}
@article{fds189285,
Author = {G. Chen and A.V. Little and M. Maggioni and L. Rosasco},
Title = {Some recent advances in multiscale geometric analysis of
point clouds},
Booktitle = {Wavelets and Multiscale Analysis: Theory and
Applications},
Publisher = {Springer},
Year = {2011},
Month = {March},
Key = {fds189285}
}
@article{fds243815,
Author = {Rohrdanz, MA and Zheng, W and Maggioni, M and Clementi,
C},
Title = {Determination of reaction coordinates via locally scaled
diffusion map.},
Journal = {The Journal of Chemical Physics},
Volume = {134},
Number = {12},
Pages = {124116},
Year = {2011},
Month = {March},
url = {http://www.ncbi.nlm.nih.gov/pubmed/21456654},
Abstract = {We present a multiscale method for the determination of
collective reaction coordinates for macromolecular dynamics
based on two recently developed mathematical techniques:
diffusion map and the determination of local intrinsic
dimensionality of large datasets. Our method accounts for
the local variation of molecular configuration space, and
the resulting global coordinates are correlated with the
time scales of the molecular motion. To illustrate the
approach, we present results for two model systems: all-atom
alanine dipeptide and coarse-grained src homology 3 protein
domain. We provide clear physical interpretation for the
emerging coordinates and use them to calculate transition
rates. The technique is general enough to be applied to any
system for which a Boltzmann-sampled set of molecular
configurations is available.},
Doi = {10.1063/1.3569857},
Key = {fds243815}
}
@article{fds243809,
Author = {Chen, G and Maggioni, M},
Title = {Multiscale geometric and spectral analysis of plane
arrangements},
Journal = {Proceedings of the Ieee Computer Society Conference on
Computer Vision and Pattern Recognition},
Pages = {2825-2832},
Publisher = {IEEE},
Year = {2011},
Month = {January},
ISSN = {1063-6919},
url = {http://dx.doi.org/10.1109/CVPR.2011.5995666},
Abstract = {Modeling data by multiple low-dimensional planes is an
important problem in many applications such as computer
vision and pattern recognition. In the most general setting
where only coordinates of the data are given, the problem
asks to determine the optimal model parameters (i.e., number
of planes and their dimensions), estimate the model planes,
and cluster the data accordingly. Though many algorithms
have been proposed, most of them need to assume prior
knowledge of the model parameters and thus address only the
last two components of the problem. In this paper we propose
an efficient algorithm based on multiscale SVD analysis and
spectral methods to tackle the problem in full generality.
We also demonstrate its state-of-the-art performance on both
synthetic and real data. © 2011 IEEE.},
Doi = {10.1109/CVPR.2011.5995666},
Key = {fds243809}
}
@article{fds335542,
Author = {Chen, G and Little, AV and Maggioni, M and Rosasco,
L},
Title = {Some recent advances in multiscale geometric analysis of
point clouds},
Pages = {199-225},
Booktitle = {Applied and Numerical Harmonic Analysis},
Publisher = {Birkhäuser Boston},
Year = {2011},
Month = {January},
ISBN = {9780817680947},
url = {http://dx.doi.org/10.1007/978-0-8176-8095-4_10},
Abstract = {© 2011, Springer Science+Business Media, LLC. We discuss
recent work based on multiscale geometric analyis for the
study of large data sets that lie in high-dimensional spaces
but have low-dimensional structure. We present three
applications: the first one to the estimation of intrinsic
dimension of sampled manifolds, the second one to the
construction of multiscale dictionaries, called Geometric
Wavelets, for the analysis of point clouds, and the third
one to the inference of point clouds modeled as unions of
multiple planes of varying dimensions.},
Doi = {10.1007/978-0-8176-8095-4_10},
Key = {fds335542}
}
@article{fds199203,
Author = {G. Chen and M. Maggioni},
Title = {Multiscale Analysis of Plane Arrangements},
Booktitle = {Proc. C.V.P.R.},
Year = {2011},
Key = {fds199203}
}
@article{fds189287,
Author = {G. Chen and M. Maggioni},
Title = {Multiscale Geometric Dictionaries for point-cloud
data},
Journal = {Proc. SampTA 2011},
Year = {2011},
Key = {fds189287}
}
@article{fds243812,
Author = {Allard, WK and Chen, G and Maggioni, M},
Title = {Multiscale Geometric Methods for Data Sets II: Geometric
Wavelets},
Journal = {CoRR},
Volume = {abs/1105.4924},
Number = {3},
Year = {2011},
Key = {fds243812}
}
@article{fds243808,
Author = {Monson, EE and Chen, G and Brady, R and Maggioni,
M},
Title = {Data representation and exploration with Geometric
Wavelets},
Journal = {2010 Ieee Symposium on Visual Analytics Science and
Technology},
Pages = {243-244},
Publisher = {IEEE},
Year = {2010},
Month = {October},
url = {http://dx.doi.org/10.1109/vast.2010.5653822},
Abstract = {Geometric Wavelets is a new multi-scale data representation
technique which is useful for a variety of applications such
as data compression, interpretation and anomaly detection.
We have developed an interactive visualization with multiple
linked views to help users quickly explore data sets and
understand this novel construction. Currently the interface
is being used by applied mathematicians to view results and
gain new insights, speeding methods development. ©2010
IEEE.},
Doi = {10.1109/vast.2010.5653822},
Key = {fds243808}
}
@article{fds243805,
Author = {Willinger, W and Rejaie, R and Torkjazi, M and Valafar, M and Maggioni,
M},
Title = {Research on online social networks: Time to face the real
challenges},
Journal = {Acm Sigmetrics Performance Evaluation Review},
Volume = {37},
Number = {3},
Pages = {49-54},
Publisher = {Association for Computing Machinery (ACM)},
Year = {2010},
Month = {August},
ISSN = {0163-5999},
url = {http://dx.doi.org/10.1145/1710115.1710125},
Abstract = {Online Social Networks (OSNs) provide a unique opportunity
for researchers to study how a combination of technological,
economical, and social forces have been conspiring to
provide a service that has attracted the largest user
population in the history of the Internet. With more than
half a billion of users and counting, OSNs have the
potential to impact almost every aspect of networking,
including measurement and performance modeling and analysis,
network architecture and system design, and privacy and user
behavior, to name just a few. However, much of the existing
OSN research literature seems to have lost sight of this
unique opportunity and has avoided dealing with the new
challenges posed by OSNs. We argue in this position paper
that it is high time for OSN researcher to exploit and face
these challenges to provide a basic understanding of the OSN
ecosystem as a whole. Such an understanding has to reflect
the key role users play in this system and must focus on the
system's dynamics, purpose and functionality when trying to
illuminate the main technological, economic, and social
forces at work in the current OSN revolution.},
Doi = {10.1145/1710115.1710125},
Key = {fds243805}
}
@article{fds243817,
Author = {Wu, Q and Guinney, J and Maggioni, M and Mukherjee,
S},
Title = {Learning gradients: Predictive models that infer geometry
and statistical dependence},
Journal = {Journal of Machine Learning Research},
Volume = {11},
Pages = {2175-2198},
Year = {2010},
Month = {August},
ISSN = {1532-4435},
url = {http://hdl.handle.net/10161/4634 Duke open
access},
Keywords = {Gradient estimates, manifold learning, graphical models,
inverse regression, dimension reduc- tion, gradient
diffusion maps},
Abstract = {The problems of dimension reduction and inference of
statistical dependence are addressed by the modeling
framework of learning gradients. The models we propose hold
for Euclidean spaces as well as the manifold setting. The
central quantity in this approach is an estimate of the
gradient of the regression or classification function. Two
quadratic forms are constructed from gradient estimates: the
gradient outer product and gradient based diffusion maps.
The first quantity can be used for supervised dimension
reduction on manifolds as well as inference of a graphical
model encoding dependencies that are predictive of a
response variable. The second quantity can be used for
nonlinear projections that incorporate both the geometric
structure of the manifold as well as variation of the
response variable on the manifold. We relate the gradient
outer product to standard statistical quantities such as
covariances and provide a simple and precise comparison of a
variety of supervised dimensionality reduction methods. We
provide rates of convergence for both inference of
informative directions as well as inference of a graphical
model of variable dependencies. © 2010.},
Key = {fds243817}
}
@article{fds243818,
Author = {Chen, G and Maggioni, M},
Title = {Multiscale geometric wavelets for the analysis of point
clouds},
Journal = {2010 44th Annual Conference on Information Sciences and
Systems, Ciss 2010},
Publisher = {IEEE},
Year = {2010},
Month = {June},
url = {http://dx.doi.org/10.1109/CISS.2010.5464843},
Abstract = {Data sets are often modeled as point clouds in RD, for D
large. It is often assumed that the data has some
interesting low-dimensional structure, for example that of
ad-dimensional manifold M, with d much smaller than D. When
M is simply a linear subspace, one may exploit this
assumption for encoding efficiently the data by projecting
onto a dictionary of d vectors in RD (for example found by
SVD), at a cost (d + n)D for n data points. When M is
nonlinear, there are no "explicit" constructions of
dictionaries that achieve a similar efficiency: typically
one uses either random dictionaries, or dictionaries
obtained by black-box optimization. In this paper we
construct data-dependent multiscale dictionaries that aim at
efficient encoding and manipulating of the data. Their
construction is fast, and so are the algorithms to map data
points to dictionary coefficients and vice versa. In
addition, data points are guaranteed to have a sparse
representation in terms of the dictionary. We think of
dictionaries as the analogue of wavelets, but for
approximating point clouds rather than functions. ©2010
IEEE.},
Doi = {10.1109/CISS.2010.5464843},
Key = {fds243818}
}
@article{fds243807,
Author = {Jones, PW and Maggioni, M and Schul, R},
Title = {Universal local parametrizations via heat kernels and
eigenfunctions of the Laplacian},
Journal = {Annales Academiae Scientiarum Fennicae Mathematica},
Volume = {35},
Number = {1},
Pages = {131-174},
Publisher = {Finnish Academy of Science and Letters},
Year = {2010},
Month = {March},
ISSN = {1239-629X},
url = {http://arxiv.org/abs/0709.1975v4},
Keywords = {Heat kernel bounds, eigenfunction bounds, local charts,
distortion estimates, bi- Lipschitz mappings, non-linear
dimension reduction},
Abstract = {We use heat kernels or eigenfunctions of the Laplacian to
construct local coordinates on large classes of Euclidean
domains and Riemannian manifolds (not necessarily smooth,
e.g. with ℒα metric). These coordinates are bi-Lipschitz
on embedded balls of the domain or manifold, with distortion
constants that depend only on natural geometric properties
of the domain or manifold. The proof of these results relies
on estimates, from above and below, for the heat kernel and
its gradient, as well as for the eigenfunctions of the
Laplacian and their gradient. These estimates hold in the
non-smooth category, and are stable with respect to
perturbations within this category. Finally, these
coordinate systems are intrinsic and efficiently computable,
and are of value in applications.},
Doi = {10.5186/aasfm.2010.3508},
Key = {fds243807}
}
@article{fds184928,
Author = {Eric E Monson and Rachael Brady and Guangliang Chen and Mauro
Maggioni},
Title = {Exploration & Representation of Data with Geometric
Wavelets},
Journal = {Poster and short paper at Visweek 2010},
Year = {2010},
Key = {fds184928}
}
@article{fds212851,
Author = {J. Lee and M. Maggioni},
Title = {Multiscale Analysis of Time Series of Graphs},
Journal = {Proc. SampTA 2011},
Year = {2010},
Key = {fds212851}
}
@article{fds212852,
Author = {A.V. Little and M. Maggioni and L. Rosasco},
Title = {Multiscale Geometric Methods for estimating intrinsic
dimension},
Journal = {Proc. SampTA 2011},
Year = {2010},
Key = {fds212852}
}
@article{fds243819,
Author = {Guinney, J and Febbo, P and Maggioni, M and Mukherjee,
S},
Title = {Multiscale factor models for molecular networks},
Journal = {JSM Proc.},
Pages = {4887-4901},
Publisher = {American Statistical Association},
Address = {Alexandria, VA},
Year = {2010},
Key = {fds243819}
}
@article{fds243804,
Author = {Little, AV and Lee, J and Jung, YM and Maggioni, M},
Title = {Estimation of intrinsic dimensionality of samples from noisy
low-dimensional manifolds in high dimensions with multiscale
SVD},
Journal = {Ieee Workshop on Statistical Signal Processing
Proceedings},
Pages = {85-88},
Publisher = {IEEE},
Year = {2009},
Month = {December},
url = {http://dx.doi.org/10.1109/SSP.2009.5278634},
Abstract = {The problem of estimating the intrinsic dimensionality of
certain point clouds is of interest in many applications in
statistics and analysis of high-dimensional data sets. Our
setting is the following: the points are sampled from a
manifold M of dimension k, embedded in ℝ D , with k < D,
and corrupted by D-dimensional noise. When M is a linear
manifold (hy-perplane), one may analyse this situation by
SVD, hoping the noise would perturb the rank k covariance
matrix. When M is a nonlinear manifold, SVD performed
globally may dramatically overestimate the intrinsic
dimensionality. We discuss a multiscale version SVD that is
useful in estimating the intrinsic dimensionality of
nonlinear manifolds. © 2009 IEEE.},
Doi = {10.1109/SSP.2009.5278634},
Key = {fds243804}
}
@article{fds243806,
Author = {Little, AV and Jung, YM and Maggioni, M},
Title = {Multiscale estimation of intrinsic dimensionality of data
sets},
Journal = {Aaai Fall Symposium Technical Report},
Volume = {FS-09-04},
Pages = {26-33},
Year = {2009},
Month = {December},
Abstract = {We present a novel approach for estimating the intrinsic
dimensionality of certain point clouds: we assume that the
points are sampled from a manifold M of dimension k, with k
≪ D, and corrupted by D-dimensional noise. When M is
linear, one may analyze this situation by SVD: with no noise
one would obtain a rank k matrix, and noise may be treated
as a perturbation of the covariance matrix. When M is a
nonlinear manifold, global SVD may dramatically overestimate
the intrinsic dimensionality. We introduce a multiscale
version SVD and discuss how one can extract estimators for
the intrinsic dimensionality that are highly robust to
noise, while require a smaller sample size than current
estimators. Copyright © 2009, Association for the
Advancement of Artificial Intelligence. All rights
reserved.},
Key = {fds243806}
}
@article{fds243801,
Author = {Mahoney, MW and Maggioni, M and Drineas, P},
Title = {Tensor-CUR decompositions for tensor-based
data},
Journal = {Siam Journal on Matrix Analysis and Applications},
Volume = {30},
Number = {3},
Pages = {957-987},
Publisher = {Society for Industrial & Applied Mathematics
(SIAM)},
Year = {2008},
Month = {December},
ISSN = {0895-4798},
url = {http://dx.doi.org/10.1137/060665336},
Abstract = {Motivated by numerous applications in which the data may be
modeled by a variable subscripted by three or more indices,
we develop a tensor-based extension of the matrix CUR
decomposition. The tensor-CUR decomposition is most relevant
as a data analysis tool when the data consist of one mode
that is qualitatively different from the others. In this
case, the tensor-CUR decomposition approximately expresses
the original data tensor in terms of a basis consisting of
underlying subtensors that are actual data elements and thus
that have a natural interpretation in terms of the processes
generating the data. Assume the data may be modeled as a (2
+ l)-tensor, i.e., an m × n × p tensor .A in which the
first two modes are similar and the third is qualitatively
different. We refer to each of the p different m × n
matrices as "slabs" and each of the mn different p-vectors
as "fibers." In this case, the tensor-CUR algorithm computes
an approximation to the data tensor A that is of the form
CWR., where C is an m × n × c tensor consisting of a small
number c of the slabs, R is an r × p matrix consisting of a
small number r of the fibers, and U is an appropriately
defined and easily computed c × r encoding matrix. Both C
and R may be chosen by randomly sampling either slabs or
fibers according to a judiciously chosen and data-dependent
probability distribution, and both c and r depend on a rank
parameter k, an error parameter ε, and a failure
probability δ. Under appropriate assumptions, provable
bounds on the Frobenius norm of the error tensor A - CUR are
obtained. In order to demonstrate the general applicability
of this tensor decomposition, we apply it to problems in two
diverse domains of data analysis: hyperspectral medical
image analysis and consumer recommendation system analysis.
In the hyperspectral data application, the tensor-CUR
decomposition is used to compress the data, and we show that
classification quality is not substantially reduced even
after substantial data compression. In the recommendation
system application, the tensor-CUR decomposition is used to
reconstruct missing entries in a user-product-product
preference tensor, and we show that high quality
recommendations can be made on the basis of a small number
of basis users and a small number of product-product
comparisons from a new user. © 2008 Society for Industrial
and Applied Mathematics.},
Doi = {10.1137/060665336},
Key = {fds243801}
}
@article{fds243816,
Author = {Coifman, RR and Lafon, S and Kevrekidis, IG and Maggioni, M and Nadler,
B},
Title = {Diffusion maps, reduction coordinates, and low dimensional
representation of stochastic systems},
Journal = {Multiscale Modeling & Simulation},
Volume = {7},
Number = {2},
Pages = {842-864},
Publisher = {Society for Industrial & Applied Mathematics
(SIAM)},
Year = {2008},
Month = {November},
ISSN = {1540-3459},
url = {http://dx.doi.org/10.1137/070696325},
Abstract = {The concise representation of complex high dimensional
stochastic systems via a few reduced coordinates is an
important problem in computational physics, chemistry, and
biology. In this paper we use the first few eigenfunctions
of the backward Fokker.Planck diffusion operator as a
coarse-grained low dimensional representation for the
long-term evolution of astochastic system and show that they
are optimal under a certain mean squared error criterion. We
denote the mapping from physical space to these
eigenfunctions as the diffusion map. While in high
dimensional systems these eigenfunctions are difficult to
compute numerically by conventional methods such as finite
differences or finite elements, we describe a simple
computational data-driven method to approximate them from a
large set of simulated data. Our method is based on defining
an appropriatelyweighted graph on the set of simulated data
and computing the first few eigenvectors and eigenvalues of
the corresponding random walk matrix on this graph. Thus,
our algorithm incorporates the local geometry and densityat
each point into a global picture that merges data from
different simulationruns in a natural way. Furthermore, we
describe lifting and restriction operators between the
diffusion map space and the original space. These operators
facilitate the description of the coarse-grained dynamics,
possibly in the form of a low dimensional effective free
energy surface parameterized by the diffusion map reduction
coordinates. They also enable a systematic exploration of
such effective free energy surfaces through the design of
additional intelligently biased computational experiments.
Weconclude by demonstrating our method in a few examples. ©
2008 Society for Industrial and applied Mathematics.},
Doi = {10.1137/070696325},
Key = {fds243816}
}
@article{fds243803,
Author = {Szlam, AD and Maggioni, M and Coifman, RR},
Title = {Regularization on graphs with function-adapted diffusion
processes},
Journal = {Journal of Machine Learning Research},
Volume = {9},
Pages = {1711-1739},
Year = {2008},
Month = {August},
ISSN = {1532-4435},
Abstract = {Harmonic analysis and diffusion on discrete data has been
shown to lead to state-of-the-art algorithms for machine
learning tasks, especially in the context of semi-supervised
and transductive learning. The success of these algorithms
rests on the assumption that the function(s) to be studied
(learned, interpolated, etc.) are smooth with respect to the
geometry of the data. In this paper we present a method for
modifying the given geometry so the function(s) to be
studied are smoother with respect to the modified geometry,
and thus more amenable to treatment using harmonic analysis
methods. Among the many possible applications, we consider
the problems of image denoising and transductive
classification. In both settings, our approach improves on
standard diffusion based methods.},
Key = {fds243803}
}
@article{fds243820,
Author = {Szlam, AD and Coifman, RR and Maggioni, M},
Title = {A general framework for adaptive regularization based on
diffusion processes},
Journal = {Journ. Mach. Learn. Res.},
Number = {9},
Pages = {1711-1739},
Year = {2008},
Month = {August},
Key = {fds243820}
}
@article{MM:DiffusionPolynomialFrames,
Author = {Maggioni, M and Mhaskar, HN},
Title = {Diffusion polynomial frames on metric measure
spaces},
Journal = {Applied and Computational Harmonic Analysis},
Volume = {24},
Number = {3},
Pages = {329-353},
Publisher = {Elsevier BV},
Year = {2008},
Month = {May},
ISSN = {1063-5203},
url = {http://dx.doi.org/10.1016/j.acha.2007.07.001},
Abstract = {We construct a multiscale tight frame based on an arbitrary
orthonormal basis for the L2 space of an arbitrary sigma
finite measure space. The approximation properties of the
resulting multiscale are studied in the context of Besov
approximation spaces, which are characterized both in terms
of suitable K-functionals and the frame transforms. The only
major condition required is the uniform boundedness of a
summability operator. We give sufficient conditions for this
to hold in the context of a very general class of metric
measure spaces. The theory is illustrated using the
approximation of characteristic functions of caps on a
dumbell manifold, and applied to the problem of recognition
of hand-written digits. Our methods outperforms comparable
methods for semi-supervised learning. © 2007 Elsevier Inc.
All rights reserved.},
Doi = {10.1016/j.acha.2007.07.001},
Key = {MM:DiffusionPolynomialFrames}
}
@article{fds243822,
Author = {Jones, PW and Maggioni, M and Schul, R},
Title = {Manifold parametrizations by eigenfunctions of the Laplacian
and heat kernels.},
Journal = {Proceedings of the National Academy of Sciences of the
United States of America},
Volume = {105},
Number = {6},
Pages = {1803-1808},
Year = {2008},
Month = {February},
url = {http://www.ncbi.nlm.nih.gov/pubmed/18258744},
Abstract = {We use heat kernels or eigenfunctions of the Laplacian to
construct local coordinates on large classes of Euclidean
domains and Riemannian manifolds (not necessarily smooth,
e.g., with (alpha) metric). These coordinates are
bi-Lipschitz on large neighborhoods of the domain or
manifold, with constants controlling the distortion and the
size of the neighborhoods that depend only on natural
geometric properties of the domain or manifold. The proof of
these results relies on novel estimates, from above and
below, for the heat kernel and its gradient, as well as for
the eigenfunctions of the Laplacian and their gradient, that
hold in the non-smooth category, and are stable with respect
to perturbations within this category. Finally, these
coordinate systems are intrinsic and efficiently computable,
and are of value in applications.},
Doi = {10.1073/pnas.0710175104},
Key = {fds243822}
}
@article{fds243802,
Author = {Mahadevan, S and Maggioni, M},
Title = {Proto-value functions: A Laplacian framework for learning
representation and control in Markov decision
processes},
Journal = {Journal of Machine Learning Research},
Volume = {8},
Pages = {2169-2231},
Year = {2007},
Month = {October},
ISSN = {1532-4435},
Abstract = {This paper introduces a novel spectral framework for solving
Markov decision processes (MDPs) by jointly learning
representations and optimal policies. The major components
of the framework described in this paper include: (i) A
general scheme for constructing representations or basis
functions by diagonalizing symmetric diffusion operators
(ii) A specific instantiation of this approach where global
basis functions calledproto-value functions (PVFs) are
formed using the eigenvectors of the graph Laplacian on an
undirected graph formed from state transitions induced by
the MDP (iii) A three-phased procedure called representation
policy iteration comprising of a sample collection phase, a
representation learning phase that constructs basis
functions from samples, and a final parameter estimation
phase that determines an (approximately) optimal policy
within the (linear) subspace spanned by the (current) basis
functions. (iv) A specific instantiation of the RPI
framework using least-squares policy iteration (LSPI) as the
parameter estimation method (v) Several strategies for
scaling the proposed approach to large discrete and
continuous state spaces, including the Nyström extension
for out-of-sample interpolation of eigenfunctions, and the
use of Kronecker sum factorization to construct compact
eigenfunctions in product spaces such as factored MDPs (vi)
Finally, a series of illustrative discrete and continuous
control tasks, which both illustrate the concepts and
provide a benchmark for evaluating the proposed approach.
Many challenges remain to be addressed in scaling the
proposed framework to large MDPs, and several elaboration of
the proposed framework are briefly summarized at the
end.},
Key = {fds243802}
}
@article{fds243821,
Author = {Mahadevan, S and Maggioni, M},
Title = {Proto-value Functions: A Laplacian Framework for Learning
Representation and Control},
Journal = {Journ. Mach. Learn. Res.},
Number = {8},
Year = {2007},
Month = {September},
Key = {fds243821}
}
@article{fds243798,
Author = {Prichep, LS and Causevic, E and Coifman, RR and Isenhart, R and Jacquin,
A and John, ER and Maggioni, M and Warner, FJ},
Title = {QEEG-based classification with wavelet packet and microstate
features for triage applications in the ER},
Journal = {2015 Ieee International Conference on Acoustics, Speech, and
Signal Processing (Icassp)},
Volume = {3},
Pages = {III1136-III1139},
Year = {2006},
Month = {December},
ISSN = {1520-6149},
Abstract = {We describe methods for the classification of brain state
using quantitative analysis of the EEG (QEEG). Neurometric
analysis of EEG collected from the 19 standard locations of
the International 10-20 System already provides such a tool.
In this work we demonstrate the effectiveness of this
approach when the available inputs are reduced to a set of
five frontal electrodes. This system has applications in
certain critical clinical care situations, such as emergency
room triage, when a full EEG might be unavailable,
inconvenient, or time-consuming. Additionally, we augment
the standard neurometric QEEG analysis with local
discriminant basis features of the power spectrum and
microstate-like features which exploit the rich temporal
structure of the EEG. These enhancements provide clear gains
in sensitivity and specificity on a representative database.
© 2006 IEEE.},
Key = {fds243798}
}
@inproceedings{smmm:FastDirectMDP,
Author = {Maggioni, M and Mahadevan, S},
Title = {Fast direct policy evaluation using multiscale analysis of
markov diffusion processes},
Journal = {Acm International Conference Proceeding Series},
Volume = {148},
Pages = {601-608},
Booktitle = {University of Massachusetts, Department of Computer Science
Technical Report TR-2005-39; accepted at ICML
2006},
Publisher = {ACM Press},
Year = {2006},
Month = {December},
url = {http://dx.doi.org/10.1145/1143844.1143920},
Abstract = {Policy evaluation is a critical step in the approximate
solution of large Markov decision processes (MDPs),
typically requiring O(|S|3) to directly solve the Bellman
system of |S| linear equations (where |S| is the state space
size in the discrete case, and the sample size in the
continuous case). In this paper we apply a recently
introduced multiscale framework for analysis on graphs to
design a faster algorithm for policy evaluation. For a fixed
policy π, this framework efficiently constructs a
multiscale decomposition of the random walk Pπ associated
with the policy π. This enables efficiently computing
medium and long term state distributions, approximation of
value functions, and the direct computation of the potential
operator (I - γPπ)~1 needed to solve Bellman's equation.
We show that even a preliminary nonoptimized version of the
solver competes with highly optimized iterative techniques,
requiring in many cases a complexity of O(|S|).},
Doi = {10.1145/1143844.1143920},
Key = {smmm:FastDirectMDP}
}
@article{fds243797,
Author = {Mahadevan, S and Maggioni, M and Ferguson, K and Osentoski,
S},
Title = {Learning representation and control in continuous Markov
decision processes},
Journal = {Proceedings of the National Conference on Artificial
Intelligence},
Volume = {2},
Pages = {1194-1199},
Year = {2006},
Month = {November},
Abstract = {This paper presents a novel framework for simultaneously
learning representation and control in continuous Markov
decision processes. Our approach builds on the framework of
proto-value functions, in which the underlying
representation or basis functions are automatically derived
from a spectral analysis of the state space manifold. The
proto-value functions correspond to the eigenfunctions of
the graph Laplacian. We describe an approach to extend the
eigenfunctions to novel states using the Nyström extension.
A least-squares policy iteration method is used to learn the
control policy, where the underlying subspace for
approximating the value function is spanned by the learned
proto-value functions. A detailed set of experiments is
presented using classic benchmark tasks, including the
inverted pendulum and the mountain car, showing the
sensitivity in performance to various parameters, and
including comparisons with a parametric radial basis
function method. Copyright © 2006, American Association for
Artificial Intelligence (www.aaai.org). All rights
reserved.},
Key = {fds243797}
}
@inproceedings{MMD:TensorCUR,
Author = {Mahoney, MW and Maggioni, M and Drineas, P},
Title = {Tensor-CUR decompositions for tensor-based
data},
Journal = {Proceedings of the Acm Sigkdd International Conference on
Knowledge Discovery and Data Mining},
Volume = {2006},
Pages = {327-336},
Booktitle = {Proc 12-th Annual SIGKDD},
Year = {2006},
Month = {October},
Abstract = {Motivated by numerous applications in which the data may be
modeled by a variable subscripted by three or more indices,
we develop a tensor-based extension of the matrix CUR
decomposition. The tensor-CUR decomposition is most relevant
as a data analysis tool when the data consist of one mode
that is qualitatively different than the others. In this
case, the tensor-CUR decomposition approximately expresses
the original data tensor in terms of a basis consisting of
underlying subtensors that are actual data elements and thus
that have natural interpretation in terms of the processes
generating the data. In order to demonstrate the general
applicability of this tensor decomposition, we apply it to
problems in two diverse domains of data analysis:
hyperspectral medical image analysis and consumer
recommendation system analysis. In the hyperspectral data
application, the tensor-CUR decomposition is used to
compress the data, and we show that classification quality
is not substantially reduced even after substantial data
compression. In the recommendation system application, the
tensor-CUR decomposition is used to reconstruct missing
entries in a user-product-product preference tensor, and we
show that high quality recommendations can be made on the
basis of a small number of basis users and a small number of
productproduct comparisons from a new user. Copyright 2006
ACM.},
Key = {MMD:TensorCUR}
}
@article{fds318320,
Author = {Maggioni, M and Mahadevan, S},
Title = {Fast direct policy evaluation using multiscale analysis of
Markov diffusion processes},
Journal = {Icml 2006 Proceedings of the 23rd International Conference
on Machine Learning},
Volume = {2006},
Pages = {601-608},
Year = {2006},
Month = {October},
Abstract = {Policy evaluation is a critical step in the approximate
solution of large Markov decision processes (MDPs),
typically requiring O(|S|3) to directly solve the Bellman
system of |S| linear equations (where |S| is the state space
size in the discrete case, and the sample size in the
continuous case). In this paper we apply a recently
introduced multiscale framework for analysis on graphs to
design a faster algorithm for policy evaluation. For a fixed
policy π, this framework efficiently constructs a
multiscale decomposition of the random walk Pπ associated
with the policy π. This enables efficiently computing
medium and long term state distributions, approximation of
value functions, and the direct computation of the potential
operator (I - γPπ)-1 needed to solve Bellman's equation.
We show that even a preliminary non-optimized version of the
solver competes with highly optimized iterative techniques,
requiring in many cases a complexity of O(|S|).},
Key = {fds318320}
}
@inproceedings{CLMKSWZ:GeometrySensorOutputs,
Author = {Coifman, RR and Lafon, S and Maggioni, M and Keller, Y and Szlam, AD and Warner, FJ and Zucker, SW},
Title = {Geometries of sensor outputs, inference and information
processing},
Journal = {Smart Structures and Materials 2005: Active Materials:
Behavior and Mechanics},
Volume = {6232},
Pages = {623209},
Booktitle = {Proc. SPIE},
Publisher = {SPIE},
Editor = {Intelligent Integrated Microsystems and Ravindra A. Athale,
John C. Zolper;},
Year = {2006},
Month = {September},
ISSN = {0277-786X},
url = {http://dx.doi.org/10.1117/12.669723},
Abstract = {We describe signal processing tools to extract structure and
information from arbitrary digital data sets. In particular
heterogeneous multi-sensor measurements which involve
corrupt data, either noisy or with missing entries present
formidable challenges. We sketch methodologies for using the
network of inferences and similarities between the data
points to create robust nonlinear estimators for missing or
noisy entries. These methods enable coherent fusion of data
from a multiplicity of sources, generalizing signal
processing to a non linear setting. Since they provide
empirical data models they could also potentially extend
analog to digital conversion schemes like "sigma
delta".},
Doi = {10.1117/12.669723},
Key = {CLMKSWZ:GeometrySensorOutputs}
}
@article{DiffusionWaveletPackets,
Author = {Bremer, JC and Coifman, RR and Maggioni, M and Szlam,
AD},
Title = {Diffusion wavelet packets},
Journal = {Applied and Computational Harmonic Analysis},
Volume = {21},
Number = {1},
Pages = {95-112},
Publisher = {Elsevier BV},
Year = {2006},
Month = {July},
ISSN = {1063-5203},
url = {http://dx.doi.org/10.1016/j.acha.2006.04.005},
Abstract = {Diffusion wavelets can be constructed on manifolds, graphs
and allow an efficient multiscale representation of powers
of the diffusion operator that generates them. In many
applications it is necessary to have time-frequency bases
that are more versatile than wavelets, for example for the
analysis, denoising and compression of a signal. In the
Euclidean setting, wavelet packets have been very successful
in many applications, ranging from image denoising, 2- and
3-dimensional compression of data (e.g., images, seismic
data, hyper-spectral data) and in discrimination tasks as
well. Till now these tools for signal processing have been
available mainly in Euclidean settings and in low
dimensions. Building upon the recent construction of
diffusion wavelets, we show how to construct diffusion
wavelet packets, generalizing the classical construction of
wavelet packets, and allowing the same algorithms existing
in the Euclidean setting to be lifted to rather general
geometric and anisotropic settings, in higher dimension, on
manifolds, graphs and even more general spaces. We show that
efficient algorithms exists for computations of diffusion
wavelet packets and discuss some applications and examples.
© 2006 Elsevier Inc. All rights reserved.},
Doi = {10.1016/j.acha.2006.04.005},
Key = {DiffusionWaveletPackets}
}
@article{CMDiffusionWavelets,
Author = {Coifman, RR and Maggioni, M},
Title = {Diffusion wavelets},
Journal = {Applied and Computational Harmonic Analysis},
Volume = {21},
Number = {1},
Pages = {53-94},
Publisher = {Elsevier BV},
Year = {2006},
Month = {July},
ISSN = {1063-5203},
url = {http://dx.doi.org/10.1016/j.acha.2006.04.004},
Abstract = {Our goal in this paper is to show that many of the tools of
signal processing, adapted Fourier and wavelet analysis can
be naturally lifted to the setting of digital data clouds,
graphs, and manifolds. We use diffusion as a smoothing and
scaling tool to enable coarse graining and multiscale
analysis. Given a diffusion operator T on a manifold or a
graph, with large powers of low rank, we present a general
multiresolution construction for efficiently computing,
representing and compressing Tt. This allows a direct
multiscale computation, to high precision, of functions of
the operator, notably the associated Green's function, in
compressed form, and their fast application. Classes of
operators for which these computations are fast include
certain diffusion-like operators, in any dimension, on
manifolds, graphs, and in non-homogeneous media. We use
ideas related to the Fast Multipole Methods and to the
wavelet analysis of Calderón-Zygmund and
pseudo-differential operators, to numerically enforce the
emergence of a natural hierarchical coarse graining of a
manifold, graph or data set. For example for a body of text
documents the construction leads to a directory structure at
different levels of generalization. The dyadic powers of an
operator can be used to induce a multiresolution analysis,
as in classical Littlewood-Paley and wavelet theory: we
construct, with efficient and stable algorithms, bases of
orthonormal scaling functions and wavelets associated to
this multiresolution analysis, together with the
corresponding downsampling operators, and use them to
compress the corresponding powers of the operator. While
most of our discussion deals with symmetric operators and
relates to localization to spectral bands, the symmetry of
the operators and their spectral theory need not be
considered, as the main assumption is reduction of the
numerical ranks as we take powers of the operator. © 2006
Elsevier Inc. All rights reserved.},
Doi = {10.1016/j.acha.2006.04.004},
Key = {CMDiffusionWavelets}
}
@conference{maggioni:60910I,
Author = {Maggioni, M and Davis, GL and Warner, FJ and Geshwind, FB and Coppi, AC and DeVerse, RA and Coifman, RR},
Title = {Hyperspectral microscopic analysis of normal, benign and
carcinoma microarray tissue sections},
Journal = {Progress in Biomedical Optics and Imaging Proceedings of
Spie},
Volume = {6091},
Number = {1},
Pages = {60910I},
Publisher = {SPIE},
Editor = {Robert R. Alfano and Alvin Katz},
Year = {2006},
Month = {May},
ISSN = {1605-7422},
url = {http://link.aip.org/link/?PSI/6091/60910I/1},
Abstract = {We apply a unique micro-optoelectromechanical tuned light
source & new algorithms to the hyper-spectral microscopic
analysis of human colon biopsies. The tuned light prototype
(Plain Sight Systems Inc.) transmits any combination of
light frequencies, range 440nm 700nm, trans-illuminating H &
E stained tissue sections of normal (N), benign adenoma (B)
and malignant carcinoma (M) colon biopsies, through a Nikon
Biophot microscope. Hyper-spectral photomicrographs,
randomly collected 400X magnication, are obtained with a CCD
camera (Sensovation) from 59 different patient biopsies (20
N, 19 B, 20 M) mounted as a microarray on a single glass
slide. The spectra of each pixel are normalized & analyzed
to discriminate among tissue features: gland nuclei, gland
cytoplasm & lamina propria/lumens. Spectral features permit
the automatic extraction of 3298 nuclei with classification
as N, B or M. When nuclei are extracted from each of the 59
biopsies the average classification among N, B and M nuclei
is 97.1%; classification of the biopsies, based on the
average nuclei classification, is 100%. However, when the
nuclei are extracted from a subset of biopsies, and the
prediction is made on nuclei in the remaining biopsies,
there is a marked decrement in performance to 60% across the
3 classes. Similarly the biopsy classification drops to 54%.
In spite of these classification differences, which we
believe are due to instrument & biopsy normalization issues,
hyper-spectral analysis has the potential to achieve
diagnostic efficiency needed for objective microscopic
diagnosis.},
Doi = {10.1117/12.646078},
Key = {maggioni:60910I}
}
@inproceedings{smkfsomm:SimLearningReprControlContinuou,
Author = {Sridhar Mahadevan and Kimberly Ferguson and Sarah Osentoski and Mauro Maggioni},
Title = {Simultaneous Learning of Representation and Control In
Continuous Domains},
Journal = {Proc. AAAI 2006},
Booktitle = {submitted},
Year = {2006},
Key = {smkfsomm:SimLearningReprControlContinuou}
}
@article{ImageDenoisingViaGraphDiffusion,
Author = {Arthur D Szlam and Yoel Shkolnisky and James C Bremer and Mauro Maggioni},
Title = {Image Denoising Via Graph Diffusions},
Journal = {in preparation},
Year = {2006},
Key = {ImageDenoisingViaGraphDiffusion}
}
@article{smmm:jmrl1,
Author = {Sridhar Mahadevan and Mauro Maggioni},
Title = {Proto-value Functions: A Spectral Framework for Solving
Markov Decision Processes},
Journal = {submitted},
Year = {2006},
Key = {smmm:jmrl1}
}
@article{jms:UniformizationEigenfunctions,
Author = {Peter W Jones and Mauro Maggioni and Raanan
Schul},
Title = {Universal parametrizations via Eigenfunctions of the
{L}aplacian},
Year = {2006},
Key = {jms:UniformizationEigenfunctions}
}
@conference{MSCB:MultiscaleManifoldMethods,
Author = {Szlam, AD and Maggioni, M and Coifman, RR and Bremer,
JC},
Title = {Diffusion-driven multiscale analysis on manifolds and
graphs: Top-down and bottom-up constructions},
Journal = {Smart Structures and Materials 2005: Active Materials:
Behavior and Mechanics},
Volume = {5914},
Number = {1},
Pages = {1-11},
Publisher = {SPIE},
Editor = {Manos Papadakis and Andrew F. Laine and Michael A.
Unser},
Year = {2005},
Month = {December},
ISSN = {0277-786X},
url = {http://link.aip.org/link/?PSI/5914/59141D/1},
Abstract = {Classically, analysis on manifolds and graphs has been based
on the study of the eigenfunctions of the Laplacian and its
generalizations. These objects from differential geometry
and analysis on manifolds have proven useful in applications
to partial differential equations, and their discrete
counterparts have been applied to optimization problems,
learning, clustering, routing and many other algorithms. 1-7
The eigenfunctions of the Laplacian are in general global:
their support often coincides with the whole manifold, and
they are affected by global properties of the manifold (for
example certain global topological invariants). Recently a
framework for building natural multiresolution structures on
manifolds and graphs was introduced, that greatly
generalizes, among other things, the construction of
wavelets and wavelet packets in Euclidean spaces. 8,9 This
allows the study of the manifold and of functions on it at
different scales, which are naturally induced by the
geometry of the manifold. This construction proceeds
bottom-up, from the finest scale to the coarsest scale,
using powers of a diffusion operator as dilations and a
numerical rank constraint to critically sample the
multiresolution subspaces. In this paper we introduce a
novel multiscale construction, based on a top-down recursive
partitioning induced by the eigenfunctions of the Laplacian.
This yields associated local cosine packets on manifolds,
generalizing local cosines in Euclidean spaces. 10 We
discuss some of the connections with the construction of
diffusion wavelets. These constructions have direct
applications to the approximation, denoising, compression
and learning of functions on a manifold and are promising in
view of applications to problems in manifold approximation,
learning, dimensionality reduction.},
Doi = {10.1117/12.616931},
Key = {MSCB:MultiscaleManifoldMethods}
}
@conference{MBCS:BiorthogonalDiffusionWavelets,
Author = {Maggioni, M and Bremer, JC and Coifman, RR and Szlam,
AD},
Title = {Biorthogonal diffusion wavelets for multiscale
representations on manifolds and graphs},
Journal = {Smart Structures and Materials 2005: Active Materials:
Behavior and Mechanics},
Volume = {5914},
Number = {1},
Pages = {1-13},
Publisher = {SPIE},
Editor = {Manos Papadakis and Andrew F. Laine and Michael A.
Unser},
Year = {2005},
Month = {December},
ISSN = {0277-786X},
url = {http://link.aip.org/link/?PSI/5914/59141M/1},
Abstract = {Recent work by some of the authors presented a novel
construction of a multiresolution analysis on manifolds and
graphs, acted upon by a given symmetric Markov semigroup {T
t} t≥o, for which T t has low rank for large t. 1 This
includes important classes of diffusion-like operators, in
any dimension, on manifolds, graphs, and in non-homogeneous
media. The dyadic powers of an operator are used to induce a
multiresolution analysis, analogous to classical
Littlewood-Paley 14 and wavelet theory, while associated
wavelet packets can also be constructed. 2 This extends
multiscale function and operator analysis and signal
processing to a large class of spaces, such as manifolds and
graphs, with efficient algorithms. Powers and functions of T
(notably its Green's function) are efficiently computed,
represented and compressed. This construction is related and
generalizes certain Fast Multipole Methods, 3 the wavelet
representation of Calderón-Zygmund and pseudo-differential
operators, 4 and also relates to algebraic multigrid
techniques. 5 The original diffusion wavelet construction
yields orthonormal bases for multiresolution spaces {V j}.
The orthogonality requirement has some advantages from the
numerical perspective, but several drawbacks in terms of the
space and frequency localization of the basis functions.
Here we show how to relax this requirement in order to
construct biorthogonal bases of diffusion scaling functions
and wavelets. This yields more compact representations of
the powers of the operator, better localized basis
functions. This new construction also applies to non
self-adjoint semigroups, arising in many
applications.},
Doi = {10.1117/12.616909},
Key = {MBCS:BiorthogonalDiffusionWavelets}
}
@inproceedings{smmm:ValueFunction,
Author = {Mahadevan, S and Maggioni, M},
Title = {Value function approximation with diffusion wavelets and
Laplacian eigenfunctions},
Journal = {Advances in Neural Information Processing
Systems},
Pages = {843-850},
Booktitle = {University of Massachusetts, Department of Computer Science
Technical Report TR-2005-38; Proc. NIPS 2005},
Year = {2005},
Month = {December},
ISSN = {1049-5258},
Abstract = {We investigate the problem of automatically constructing
efficient representations or basis functions for
approximating value functions based on analyzing the
structure and topology of the state space. In particular,
two novel approaches to value function approximation are
explored based on automatically constructing basis functions
on state spaces that can be represented as graphs or
manifolds: one approach uses the eigenfunctions of the
Laplacian, in effect performing a global Fourier analysis on
the graph; the second approach is based on diffusion
wavelets, which generalize classical wavelets to graphs
using multiscale dilations induced by powers of a diffusion
operator or random walk on the graph. Together, these
approaches form the foundation of a new generation of
methods for solving large Markov decision processes, in
which the underlying representation and policies are
simultaneously learned.},
Key = {smmm:ValueFunction}
}
@article{CMZK:CONB,
Author = {Coifman, RR and Maggioni, M and Zucker, SW and Kevrekidis,
IG},
Title = {Geometric diffusions for the analysis of data from sensor
networks.},
Journal = {Current Opinion in Neurobiology},
Volume = {15},
Number = {5},
Pages = {576-584},
Year = {2005},
Month = {October},
ISSN = {0959-4388},
url = {http://www.ncbi.nlm.nih.gov/pubmed/16150587},
Abstract = {Harmonic analysis on manifolds and graphs has recently led
to mathematical developments in the field of data analysis.
The resulting new tools can be used to compress and analyze
large and complex data sets, such as those derived from
sensor networks or neuronal activity datasets, obtained in
the laboratory or through computer modeling. The nature of
the algorithms (based on diffusion maps and connectivity
strengths on graphs) possesses a certain analogy with neural
information processing, and has the potential to provide
inspiration for modeling and understanding biological
organization in perception and memory formation.},
Doi = {10.1016/j.conb.2005.08.012},
Key = {CMZK:CONB}
}
@article{DiffusionPNAS,
Author = {Coifman, RR and Lafon, S and Lee, AB and Maggioni, M and Nadler, B and Warner, F and Zucker, SW},
Title = {Geometric diffusions as a tool for harmonic analysis and
structure definition of data: diffusion maps.},
Journal = {Proceedings of the National Academy of Sciences of the
United States of America},
Volume = {102},
Number = {21},
Pages = {7426-7431},
Year = {2005},
Month = {May},
ISSN = {0027-8424},
url = {http://www.ncbi.nlm.nih.gov/pubmed/15899970},
Abstract = {We provide a framework for structural multiscale geometric
organization of graphs and subsets of R(n). We use diffusion
semigroups to generate multiscale geometries in order to
organize and represent complex structures. We show that
appropriately selected eigenfunctions or scaling functions
of Markov matrices, which describe local transitions, lead
to macroscopic descriptions at different scales. The process
of iterating or diffusing the Markov matrix is seen as a
generalization of some aspects of the Newtonian paradigm, in
which local infinitesimal transitions of a system lead to
global macroscopic descriptions by integration. We provide a
unified view of ideas from data analysis, machine learning,
and numerical analysis.},
Doi = {10.1073/pnas.0500334102},
Key = {DiffusionPNAS}
}
@article{DiffusionPNAS2,
Author = {Coifman, RR and Lafon, S and Lee, AB and Maggioni, M and Nadler, B and Warner, F and Zucker, SW},
Title = {Geometric diffusions as a tool for harmonic analysis and
structure definition of data: multiscale
methods.},
Journal = {Proceedings of the National Academy of Sciences of the
United States of America},
Volume = {102},
Number = {21},
Pages = {7432-7437},
Year = {2005},
Month = {May},
ISSN = {0027-8424},
url = {http://www.ncbi.nlm.nih.gov/pubmed/15899969},
Abstract = {In the companion article, a framework for structural
multiscale geometric organization of subsets of R(n) and of
graphs was introduced. Here, diffusion semigroups are used
to generate multiscale analyses in order to organize and
represent complex structures. We emphasize the multiscale
nature of these problems and build scaling functions of
Markov matrices (describing local transitions) that lead to
macroscopic descriptions at different scales. The process of
iterating or diffusing the Markov matrix is seen as a
generalization of some aspects of the Newtonian paradigm, in
which local infinitesimal transitions of a system lead to
global macroscopic descriptions by integration. This article
deals with the construction of fast-order N algorithms for
data representation and for homogenization of heterogeneous
structures.},
Doi = {10.1073/pnas.0500896102},
Key = {DiffusionPNAS2}
}
@inproceedings{MM:EEG,
Author = {E Causevic and R~R Coifman and R Isenhart and A Jacquin and E~R John and M Maggioni and L~S Prichep and F~J
Warner},
Title = {{QEEG}-based classification with wavelet packets and
microstate features for triage applications in the
{ER}},
Year = {2005},
Key = {MM:EEG}
}
@article{fds243789,
Author = {Cassidy, RJ and Berger, J and Lee, K and Maggioni, M and Coifman,
RR},
Title = {Analysis of hyperspectral colon tissue images using vocal
synthesis models},
Journal = {Conference Record Asilomar Conference on Signals, Systems
and Computers},
Volume = {2},
Pages = {1611-1615},
Year = {2004},
Month = {December},
ISSN = {1058-6393},
Abstract = {In prior work, we examined the possibility of sound
generation from colon tissue scan data using vocal synthesis
models. In this work, we review key results and present
extensions to the prior work. Sonification entails the
mapping of data values to sound synthesis parameters such
that informative sounds are produced by the chosen sound
synthesis model. We review the physical equations and
technical highlights of a vocal synthesis model developed by
Cook. Next we present the colon tissue scan data gathered,
and discuss processing steps applied to the data. Finally,
we review preliminary results from a simple sonification
map. New findings regarding perceptual distance of vowel
sounds are presented1,2. ©2004 IEEE.},
Key = {fds243789}
}
@article{MM_WaveletFrames,
Author = {Maggioni, M},
Title = {Wavelet frames on groups and hypergroups via discretization
of calderón formulas},
Journal = {Monatshefte F�R Mathematik},
Volume = {143},
Number = {4},
Pages = {299-331},
Publisher = {Springer Nature},
Year = {2004},
Month = {December},
url = {http://dx.doi.org/10.1007/s00605-004-0282-z},
Abstract = {Continuous wavelets are often studied in the general
framework of representation theory of square-integrable
representations, or by using convolution relations and
Fourier transforms. We consider the well-known problem
whether these continuous wavelets can be discretized to
yield wavelet frames. In this paper we use Calderón-Zygmund
singular integral operators and atomic decompositions on
spaces of homogeneous type, endowed with families of general
translations and dilations, to attack this problem, and
obtain strong convergence results for wavelets expansions in
a variety of classical functional spaces and smooth molecule
spaces. This approach is powerful enough to yield, in a
uniform way, for example, frames of smooth wavelets for
matrix dilations in ℝn, for an affine extension of the
Heisenberg group, and on many commutative hypergroups. ©
Springer-Verlag 2004.},
Doi = {10.1007/s00605-004-0282-z},
Key = {MM_WaveletFrames}
}
@article{MRA_HRBF2004,
Author = {Ferrari, S and Maggioni, M and Borghese, NA},
Title = {Multiscale approximation with hierarchical radial basis
functions networks.},
Journal = {Ieee Transactions on Neural Networks},
Volume = {15},
Number = {1},
Pages = {178-188},
Year = {2004},
Month = {January},
ISSN = {1045-9227},
url = {http://www.ncbi.nlm.nih.gov/pubmed/15387258},
Abstract = {An approximating neural model, called hierarchical radial
basis function (HRBF) network, is presented here. This is a
self-organizing (by growing) multiscale version of a radial
basis function (RBF) network. It is constituted of
hierarchical layers, each containing a Gaussian grid at a
decreasing scale. The grids are not completely filled, but
units are inserted only where the local error is over
threshold. This guarantees a uniform residual error and the
allocation of more units with smaller scales where the data
contain higher frequencies. Only local operations, which do
not require any iteration on the data, are required; this
allows to construct the network in quasi-real time. Through
harmonic analysis, it is demonstrated that, although a HRBF
cannot be reduced to a traditional wavelet-based
multiresolution analysis (MRA), it does employ Riesz bases
and enjoys asymptotic approximation properties for a very
large class of functions. HRBF networks have been
extensively applied to the reconstruction of
three-dimensional (3-D) models from noisy range data. The
results illustrate their power in denoising the original
data, obtaining an effective multiscale reconstruction of
better quality than that obtained by MRA.},
Doi = {10.1109/TNN.2003.811355},
Key = {MRA_HRBF2004}
}
@article{MMIEEEPath,
Author = {Mauro Maggioni and Frederick J Warner and Gustave L Davis and Ronald R Coifman and Frank B Geshwind and Andreas C
Coppi and Richard A DeVerse},
Title = {Algorithms from Signal and Data Processing Applied to
Hyperspectral Analysis: Application to Discriminating Normal
and Malignant Microarray Colon Tissue Sections},
Journal = {submitted},
Year = {2004},
Key = {MMIEEEPath}
}
@article{AuditoryDisplay,
Author = {RJ Cassidy and J Berger and Mauro Maggioni and RR
Coifman},
Title = {Auditory display of hyperspectral colon tissue images using
vocal synthesis models},
Journal = {Proc. 2004 Intern. Con. Auditory Display},
Year = {2004},
Key = {AuditoryDisplay}
}
@article{ModPath:2003,
Author = {Davis, GL and Maggioni, M and Coifman, RR and Levinson, R and Rimm,
D},
Title = {Spatial-Spectral Analysis of Colon Carcinoma},
Journal = {Mod. Path.},
Year = {2004},
Key = {ModPath:2003}
}
@article{ModPath:2004,
Author = {Davis, GL and Maggioni, M and Warner, FJ and Geshwind, FB and Coppi, AC and DeVerse, RA and Coifman, RR},
Title = {Spectral Analysis of normal and Malignant Microarray Tissue
Sections using a novel micro-optoelectrialmechanical
system},
Journal = {Mod Pathol},
Volume = {17},
Number = {1:358A},
Year = {2004},
Key = {ModPath:2004}
}
@article{CCMW,
Author = {Chui, CK and Czaja, W and Maggioni, M and Weiss, G},
Title = {Characterization of general tight wavelet frames with matrix
dilations and tightness preserving oversampling},
Journal = {Journal of Fourier Analysis and Applications},
Volume = {8},
Number = {2},
Pages = {173-200},
Publisher = {Springer Nature},
Year = {2002},
Month = {August},
ISSN = {1069-5869},
url = {http://dx.doi.org/10.1007/s00041-002-0007-4},
Abstract = {A characterization formula for tight frames of
matrix-dilated wavelets is developed. It is based on the
univariate formulation by Chui and Shi, and generalizes the
recent multivariate results of Bownik, Calogero, and Han
from (expanding) dilation matrices with integer entries to
arbitrary (expanding) dilation matrices. As an application,
the Second Oversampling Theorem (that addresses preservation
of frame bounds) is generalized to the multivariate matrix
dilation and matrix translation setting.},
Doi = {10.1007/s00041-002-0007-4},
Key = {CCMW}
}
@article{fds243787,
Author = {Katz, NH and Krop, E and Maggioni, M},
Title = {Remarks on the box problem},
Journal = {Mathematical Research Letters},
Volume = {9},
Number = {4},
Pages = {515-519},
Publisher = {International Press of Boston},
Year = {2002},
Month = {January},
url = {http://dx.doi.org/10.4310/MRL.2002.v9.n4.a11},
Doi = {10.4310/MRL.2002.v9.n4.a11},
Key = {fds243787}
}
@article{Box,
Author = {Katz, NH and Krop, E and Maggioni, M},
Title = {On the box problem},
Journal = {Math. Research Letters},
Volume = {4},
Pages = {515-519},
Year = {2002},
Key = {Box}
}
@article{fds243786,
Author = {Maggioni, M},
Title = {Critical Exponent of Short Even Filters andBurt-Adelson
Biorthogonal Wavelets},
Journal = {Monatshefte F�R Mathematik},
Volume = {131},
Number = {1},
Pages = {49-69},
Publisher = {Springer Nature},
Year = {2000},
Month = {November},
url = {http://dx.doi.org/10.1007/s006050070024},
Abstract = {We determine the critical exponent of all positive filters
having an even residual of degree two and present an
extension to the case of degree four. We apply these results
to Burt-Adelson filters, thus determining the critical
exponent of all the biorthogonal wavelets they generate.
After this, we consider the problem of smoothing the dual
wavelets by considering longer dual filters: we first create
new wavelets by imposing an extra zero at π on the new
filters and study their regularity by determining all the
critical exponents. Then we release this condition on the
filters and present the results of a numerical simulation
intended to maximize the Sobolev regularity.},
Doi = {10.1007/s006050070024},
Key = {fds243786}
}
@article{fds243788,
Author = {Maggioni, M},
Title = {M-Band Burt-Adelson Biorthogonal Wavelets},
Journal = {Applied and Computational Harmonic Analysis},
Volume = {9},
Number = {3},
Pages = {286-311},
Publisher = {Elsevier BV},
Year = {2000},
Month = {October},
url = {http://dx.doi.org/10.1006/acha.2000.0323},
Abstract = {For every integer M>2 we introduce a new family of
biorthogonal MRAs with dilation factor M, generated by
symmetric scaling functions with small support. This
construction generalizes Burt-Adelson biorthogonal 2-band
wavelets. For M∈{3,4} we are able to find simple explicit
expressions for two different families of wavelets
associated with these MRAs: one with better localization and
the other with interesting symmetry-antisymmetry properties.
We study the regularity of our scaling functions by
determining their Sobolev exponent, for every value of the
parameter and every M. We also study the critical exponent
when M=3. © 2000 Academic Press.},
Doi = {10.1006/acha.2000.0323},
Key = {fds243788}
}
@article{MBand,
Author = {Mauro Maggioni},
Title = {M-Band {B}urt-{A}delson Wavelets},
Journal = {Appl. Comput. Harm. Anal.},
Volume = {3},
Pages = {286-311},
Year = {2000},
Key = {MBand}
}
@article{CriticalExponent,
Author = {Mauro Maggioni},
Title = {Critical Exponent of Short Even Filters and Biorthogonal
Burt-Adelson Wavelets},
Journal = {Monats. Math.},
Volume = {131},
Number = {1},
Pages = {49-70},
Year = {2000},
Key = {CriticalExponent}
}
%% Papers Accepted
@article{fds317218,
Author = {Yin, R and Monson, E and Honig, E and Daubechies, I and Maggioni,
M},
Title = {Object recognition in art drawings: Transfer of a neural
network},
Journal = {2015 Ieee International Conference on Acoustics, Speech, and
Signal Processing (Icassp)},
Volume = {2016-May},
Pages = {2299-2303},
Publisher = {IEEE},
Year = {2016},
Month = {May},
ISBN = {9781479999880},
ISSN = {1520-6149},
url = {http://dx.doi.org/10.1109/ICASSP.2016.7472087},
Abstract = {© 2016 IEEE. We consider the problem of recognizing objects
in collections of art works, in view of automatically
labeling, searching and organizing databases of art works.
To avoid manually labelling objects, we introduce a
framework for transferring a convolutional neural network
(CNN), trained on available large collections of labelled
natural images, to the context of drawings. We retrain both
the top and the bottom layer of the network, responsible for
the high-level classiication output and the low-level
features detection respectively, by transforming natural
images into drawings. We apply this procedure to the
drawings in the Jan Brueghel Wiki, and show the transferred
CNN learns a discriminative metric on drawings and achieves
good recognition accuracy. We also discuss why standard
descriptor-based methods is problematic in the context of
drawings.},
Doi = {10.1109/ICASSP.2016.7472087},
Key = {fds317218}
}
@article{fds314792,
Author = {Maggioni, M and Minsker, S and Strawn, N},
Title = {Multiscale dictionary learning: Non-asymptotic bounds and
robustness},
Journal = {Journal of Machine Learning Research},
Volume = {17},
Year = {2016},
Month = {January},
ISSN = {1532-4435},
url = {http://arxiv.org/abs/1401.5833},
Abstract = {© 2016 Mauro Maggioni, Stanislav Minsker, and Nate Strawn.
High-dimensional datasets are well-approximated by
low-dimensional structures. Over the past decade, this
empirical observation motivated the investigation of
detection, measurement, and modeling techniques to exploit
these low-dimensional intrinsic structures, yielding
numerous implications for high-dimensional statistics,
machine learning, and signal processing. Manifold learning
(where the low-dimensional structure is a manifold) and
dictionary learning (where the low-dimensional structure is
the set of sparse linear combinations of vectors from a
finite dictionary) are two prominent theoretical and
computational frameworks in this area. Despite their
ostensible distinction, the recently-introduced Geometric
Multi-Resolution Analysis (GMRA) provides a robust,
computationally eficient, multiscale procedure for
simultaneously learning manifolds and dictionaries. In this
work, we prove non-asymptotic probabilistic bounds on the
approximation error of GMRA for a rich class of
data-generating statistical models that includes "noisy"
manifolds, thereby establishing the theoretical robustness
of the procedure and confirming empirical observations. In
particular, if a dataset aggregates near a low-dimensional
manifold, our results show that the approximation error of
the GMRA is completely independent of the ambient dimension.
Our work therefore establishes GMRA as a provably fast
algorithm for dictionary learning with approximation and
sparsity guarantees. We include several numerical
experiments confirming these theoretical results, and our
theoretical framework provides new tools for assessing the
behavior of manifold learning and dictionary learning
procedures on a large class of interesting
models.},
Key = {fds314792}
}
@article{fds300137,
Author = {M. Crosskey and M. Maggioni},
Title = {ATLAS: A geometric approach to learning high-dimensional
stochastic systems near manifolds},
Journal = {SIAM Journ. Mult. Model. Simul.},
Year = {2015},
Key = {fds300137}
}
@article{fds225833,
Author = {A.V. Little and M. Maggioni and L. Rosasco},
Title = {Multiscale Geometric Methods for Data Sets I: Multiscale
SVD, Noise and Curvature},
Year = {2012},
Key = {fds225833}
}
%% Papers Submitted
@article{fds316563,
Author = {Wang, Y and Chen, G and Maggioni, M},
Title = {High-Dimensional Data Modeling Techniques for Detection of
Chemical Plumes and Anomalies in Hyperspectral Images and
Movies},
Journal = {Ieee Journal of Selected Topics in Applied Earth
Observations and Remote Sensing},
Volume = {9},
Number = {9},
Pages = {4316-4324},
Publisher = {Institute of Electrical and Electronics Engineers
(IEEE)},
Year = {2016},
Month = {September},
ISSN = {1939-1404},
url = {http://dx.doi.org/10.1109/JSTARS.2016.2539968},
Abstract = {© 2016 IEEE. We briefly review recent progress in
techniques for modeling and analyzing hyperspectral images
and movies, in particular for detecting plumes of both known
and unknown chemicals. For detecting chemicals of known
spectrum, we extend the technique of using a single subspace
for modeling the background to a "mixture of subspaces"
model to tackle more complicated background. Furthermore, we
use partial least squares regression on a resampled training
set to boost performance. For the detection of unknown
chemicals, we view the problem as an anomaly detection
problem and use novel estimators with low-sampled complexity
for intrinsically low-dimensional data in high dimensions
that enable us to model the "normal" spectra and detect
anomalies. We apply these algorithms to benchmark datasets
made available by the Automated Target Detection program
cofunded by NSF, DTRA, and NGA, and compare, when
applicable, to current state-of-the-art algorithms, with
favorable results.},
Doi = {10.1109/JSTARS.2016.2539968},
Key = {fds316563}
}
@article{fds300142,
Author = {T. Tomita and J. Vogelstein and M. Maggioni},
Title = {Randomer Forests},
Year = {2015},
Key = {fds300142}
}
@article{fds225832,
Author = {M. Crosskey and M. Maggioni},
Title = {ATLAS: A geometric approach to learning high-dimensional
stochastic systems near manifolds},
Year = {2014},
url = {http://arxiv.org/abs/1404.0667},
Key = {fds225832}
}
@article{fds212847,
Author = {J. Bouvrie and M. Maggioni},
Title = {Multiscale Markov Decision Problems: Compression, Solution,
and Transfer Learning},
Year = {2012},
url = {http://arxiv.org/abs/1212.1143},
Key = {fds212847}
}
@inproceedings{MC:MultiscaleSpectralAnalysisDataSetsDif,
Author = {Mauro Maggioni and Ronald R Coifman},
Title = {Multiscale Spectral Analysis on Data Sets with Diffusion
Wavelets},
Booktitle = {submitted},
Year = {2006},
Key = {MC:MultiscaleSpectralAnalysisDataSetsDif}
}
@article{mmsm:jmrl2,
Author = {Mauro Maggioni and Sridhar Mahadevan},
Title = {Multiscale Diffusion Bases for Policy Iteration in Markov
Decision Processes},
Journal = {submitted},
Year = {2006},
Key = {mmsm:jmrl2}
}
@article{GoetzmannBeauty,
Author = {William Goetzmann and Peter W Jones and Mauro Maggioni and Johan Walden},
Title = {Beauty is in the eye of the beholder},
Journal = {submitted},
Year = {2004},
Key = {GoetzmannBeauty}
}
%% Preprints
@unpublished{CM:MultiscaleAnalysisOfDocumentCorpora,
Author = {Ronald Raphel Coifman and Mauro Maggioni},
Title = {Multiscale Analysis of Document Corpora},
Year = {2006},
Key = {CM:MultiscaleAnalysisOfDocumentCorpora}
}
@misc{PathNIH2004,
Author = {GL Davis and Mauro Maggioni and FJ Warner and FB Geshwind and AC Coppi and RA DeVerse and RR Coifman},
Title = {Hyper-spectral Analysis of normal and malignant colon tissue
microarray sections using a novel DMD system},
Year = {2004},
Key = {PathNIH2004}
}
@techreport{CMTech,
Author = {Ronald R Coifman and Mauro Maggioni},
Title = {Multiresolution Analysis associated to diffusion semigroups:
construction and fast algorithms},
Number = {YALE/DCS/TR-1289},
Organization = {Dept. Comp. Sci., Yale University},
Institution = {Dept. Comp. Sci., Yale University},
Year = {2004},
Key = {CMTech}
}
%% Other
@misc{fds139534,
Author = {E. Liberty and S. Zucker and Y. Keller and M. Maggioni and R.R. Coifman and F. Geshwind},
Title = {Methods for filtering data and filling in missing data using
nonlinear filtering},
Journal = {US Patent US2006/0214133 A1},
Year = {2007},
Month = {April},
Key = {fds139534}
}
@misc{fds139532,
Author = {M. Maggioni and R Coifman and AC Coppi and GL Davis and RA DeVerse and WG
Fately, F. Geshwind and FJ Warner},
Title = {System and method for hyperspectral analysis},
Journal = {US Patent US2006/0074835 A1},
Year = {2006},
Month = {April},
Key = {fds139532}
}
@misc{fds139531,
Author = {RR Coifman and A. Coppi and F. Geshwind and SS Lafon and AB Lee and M
Maggioni, FJ Warner and SW Zucker and WG Fately},
Title = {System and method for document analysis, processing and
information extraction},
Journal = {U.S. Patent US2006/0004753A1},
Year = {2006},
Month = {January},
Key = {fds139531}
}
|
