Research Interests for Mauro Maggioni
Research Interests: Harmonic analysis, with applications to statistical analysis of highdimensional data, machine learning, imaging.
I am interested in novel constructions inspired by classical harmonic analysis that allow to analyse the geometry of manifolds and graphs and functions on such structures. These constructions are motivated by several important applications across many fields. In many situations we are confronted with large amounts of apparently unstructured highdimensional data. I find fascinating to study the intrinsic geometry of such data, and exploiting in order to study, explore, visualize, characterize statistical properties of the data. Oftentimes such data is modeled as a manifold (or something "close to a manifold") or a graph, and functions on these spaces need to approximated or "learned" from the data and experiments on the data. For example each data point could be a document, a graph associated with the documents could be given by for example hyperlinks, or by similarity of word frequencies, and a function on the set of documents would be how interesting I personally score a document. One may wish to learn how to predict how much I would score documents I have not seen yet. This can be cast as an approximation problem on the graph of documents, and it turns out that one can generalize Euclideantype approximation techniques (in particular multiscale regression techniques) to tackle this problem. An application of the above techniques that I find particularly interesting is Markov Decision Processes and Reinforcement Learning, where the problem of learning a behaviour from experience is cast in a rather general optimization and learning framework that involves approximations of functions and operators on graphs and manifolds. I am also interested in imaging, in particular I am working on novel classes of nonlinear denoising algorithms, based on diffusion processes on graphs of features built from images. Another interest is in the geometry of multiscale dynamical systems, and the construction of algorithms for the empirical construction of approximate equations for such systems. I also work on hyperspectral imaging, in particular in building automatic classifiers for discriminating normal from cancerous biopsies, for automated diagnostics and pathology.  Keywords:
 Algorithms, Amino Acids, BranchedChain, Animals, Anxiety, Base Sequence, Behavior, Animal, Brain, Chemistry, Physical, Chromosome Mapping, Diet, Diet, HighFat, Dietary Sucrose, Diffusion, Exploratory Behavior, Face, Harmonic, Hyperspectral, Imaging, Imaging, ThreeDimensional, Kinetics, Kynurenic Acid, Laplacian, Male, Models, Neurological, Models, Theoretical, Molecular Conformation, Molecular Dynamics Simulation, Mood Disorders, Multiscale, Multiscale Dynamical systems, Nanopores, Neural Networks (Computer), Neurons, Obesity, Polymers, Rats, Rats, Wistar, Serotonin, Spectral graph theory, Thermodynamics, Time Factors, Tryptophan, Weight Gain
 Current projects:
 Multiscale analysis on graphs and manifolds
 Nonlinear image denoising
 Compressed imaging and hyperspectral imaging
 Supervised and semisupervised learning on manifolds and graphs
 Universal mappings via the eigenfunctions of the Laplacian
 Perturbation of eigenfunctions of the Laplacian on graphs
 Multiscale manifolds methods for Markov Decision Processes
 Areas of Interest:
Harmonic analysis Multiscale analysis Markov decision processes Machine learning Highdimensional data analysis Stochastic dynamical systems Signal processing Imaging (e.g. hyperspectral) Geometric measure theory
 Representative Publications
 Allard, WK; Chen, G; Maggioni, M, Multiscale Geometric Methods for Data Sets II: Geometric Wavelets,
CoRR, vol. abs/1105.4924 no. 3
(2012)
 Iwen, MA; Maggioni, M, Approximation of Points on LowDimensional Manifolds Via Random Linear
Projections, vol. 2
(February, 2013) [1204.3337v1], [doi] [abs]
 M. Maggioni, Geometric Estimation of Probability Measures in HighDimensions,
Proc. IEEE Asilomar Conference
(November, 2013)
 Gerber, S; Maggioni, M, Multiscale dictionaries, transforms, and learning in highdimensions,
Smart Structures and Materials 2005: Active Materials: Behavior and Mechanics, vol. 8858
(2013), ISSN 0277786X [Gateway.cgi], [doi]
 Maggioni, M; Davis, GL; Warner, FJ; Geshwind, FB; Coppi, AC; DeVerse, RA; Coifman, RR, Hyperspectral microscopic analysis of normal, benign and carcinoma microarray tissue sections, edited by Robert R. Alfano and Alvin Katz,
Progress in Biomedical Optics and Imaging Proceedings of Spie, vol. 6091 no. 1
(2006),
pp. 60910I, SPIE, ISSN 16057422 [1], [doi] [abs]
 Coifman, RR; Maggioni, M, Diffusion wavelets,
Applied and Computational Harmonic Analysis, vol. 21 no. 1
(July, 2006),
pp. 5394, ISSN 10635203 [doi] [abs]
 Bouvrie, J; Maggioni, M, Efficient solution of Markov decision problems with multiscale representations,
2012 50th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2012
(December, 2012),
pp. 474481 [doi] [abs]
 Sridhar Mahadevan and Mauro Maggioni, Protovalue Functions: A Spectral Framework for Solving Markov Decision Processes,
submitted
(2006)
 Bouvrie, JV; Maggioni, M, Geometric multiscale reduction for autonomous and controlled nonlinear systems.,
in Proc. IEEE Conference on Decision and Control (CDC),
CDC
(2012),
pp. 43204327, IEEE, ISBN 9781467320658 [mostRecentIssue.jsp], [doi]
 Mauro Maggioni and Sridhar Mahadevan, Multiscale Diffusion Bases for Policy Iteration in Markov Decision Processes,
submitted
(Submitted, 2006)
 G. Chen, A.V. Little, M. Maggioni, L. Rosasco, Some recent advances in multiscale geometric analysis of point clouds,
in Wavelets and Multiscale Analysis: Theory and Applications
(March, 2011), Springer
 G. Chen, M. Maggioni, Multiscale Analysis of Plane Arrangements,
in Proc. C.V.P.R.
(2011)
 Rohrdanz, MA; Zheng, W; Maggioni, M; Clementi, C, Determination of reaction coordinates via locally scaled diffusion map.,
The Journal of Chemical Physics, vol. 134 no. 12
(2011),
pp. 124116 [21456654], [doi] [abs]
 G. Chen, M. Maggioni, Multiscale Geometric Dictionaries for pointcloud data,
Proc. SampTA 2011
(2011)
 Zheng, W; Rohrdanz, MA; Maggioni, M; Clementi, C, Polymer reversal rate calculated via locally scaled diffusion map.,
The Journal of Chemical Physics, vol. 134 no. 14
(2011),
pp. 144109 [21495744], [doi] [abs]
 Chen, G; Maggioni, M, Multiscale geometric wavelets for the analysis of point clouds,
2010 44th Annual Conference on Information Sciences and Systems, CISS 2010
(February, 2010) [doi] [abs]
 Jones, PW; Maggioni, M; Schul, R, Universal local parametrizations via heat kernels and eigenfunctions of the laplacian,
Annales Academiae Scientiarum Fennicae Mathematica, vol. 35 no. 1
(January, 2010),
pp. 131174, ISSN 1239629X [0709.1975v4], [doi] [abs]
 J. Lee, M. Maggioni, Multiscale Analysis of Time Series of Graphs,
Proc. SampTA 2011
(2010)
 Jones, PW; Maggioni, M; Schul, R, Manifold parametrizations by eigenfunctions of the Laplacian and heat kernels.,
Proceedings of the National Academy of Sciences of the United States of America, vol. 105 no. 6
(2008),
pp. 18031808 [18258744], [doi] [abs]
 Coifman, RR; Kevrekidis, IG; Lafon, S; Maggioni, M; Nadler, B, Diffusion Maps, Reduction Coordinates, and Low Dimensional Representation of Stochastic Systems,
Multiscale Modeling & Simulation, vol. 7 no. 2
(2008),
pp. 842864, ISSN 15403459 [doi] [abs]
 Mahadevan, S; Maggioni, M, Protovalue Functions: A Laplacian Framework for Learning Representation and Control,
Journ. Mach. Learn. Res. no. 8
(September, 2007)
 Chen, G; Little, AV; Maggioni, M, Multiresolution geometric analysis for data in high dimensions,
in Excursions in Harmonic Analysis: The February Fourier Talks at the Norbert Wiener Center, vol. 1
(January, 2013),
pp. 259285, Birkhaüser Boston, ISBN 9780817683764 [doi] [abs]
 Mahadevan, S; Maggioni, M, Value function approximation with diffusion wavelets and Laplacian eigenfunctions,
in University of Massachusetts, Department of Computer Science Technical Report TR200538; Proc. NIPS 2005,
Advances in Neural Information Processing Systems
(December, 2005),
pp. 843850, ISSN 10495258 [abs]
 Katz, NH; Krop, E; Maggioni, M, On the box problem,
Math. Research Letters, vol. 4
(2002),
pp. 515519
 Coifman, RR; Lafon, S; Lee, AB; Maggioni, M; Nadler, B; Warner, F; Zucker, SW, Geometric diffusions as a tool for harmonic analysis and structure definition of data: multiscale methods.,
Proceedings of the National Academy of Sciences of the United States of America, vol. 102 no. 21
(May, 2005),
pp. 74327437, ISSN 00278424 [15899969], [doi] [abs]
 Coifman, RR; Lafon, S; Lee, AB; Maggioni, M; Nadler, B; Warner, F; Zucker, SW, Geometric diffusions as a tool for harmonic analysis and structure definition of data: diffusion maps.,
Proceedings of the National Academy of Sciences of the United States of America, vol. 102 no. 21
(May, 2005),
pp. 74267431, ISSN 00278424 [15899970], [doi] [abs]
 J. Bouvrie, M. Maggioni, Multiscale Markov Decision Problems: Compression, Solution, and Transfer Learning
(Submitted, 2012) [1212.1143]
