 Mauro Maggioni, Professor of Mathematics
Harmonic analysis, spectral graph theory, multiscale analysis, stochastic dynamical systems, signal processing, applications to machine learning, Markov decision processes, imaging.
 Contact Info:
Teaching (Spring 2015):
 MATH 69040.01, TOPICS IN PROBABILITY
Synopsis
 Physics 119, MW 10:05 AM11:20 AM
 Education:
PhD  Washington University, St. Louis  2002 
MS  Washington University, St. Louis  2000 
Laurea in Matematica  Universita' degli Studi di Milano, Italy  1999 
 Specialties:

Applied Math
Analysis Probability
 Research Interests: Harmonic analysis, with applications to statistical analysis of highdimensional data, machine learning, imaging.
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
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.
 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
 Keywords:
Harmonic • Multiscale • Spectral graph theory • Multiscale Dynamical systems • Laplacian • Hyperspectral • Imaging
 Curriculum Vitae
 Current Ph.D. Students
(Former Students)
 Postdocs Mentored
 Wenjing Liao (August, 2013  present)
 David Lawlor (2012/10present)
 Joshua Vogelstein (2012/10present)
 Samuel Gerber (2012/10present)
 Grace Yi Wang (September, 2012  present)
 Nate Strawn (2011  present)
 Mark Iwen (2010  2013)
 Guangliang Chen (2009  2012)
 Jake Bouvrie (2009  2012)
 YoonMo Jung (2007  2009)
 Undergraduate Research Supervised
 Jason Lee (May, 2009  May, 2010)
 Representative Publications
(More Publications)
 W.K. Allard, G. Chen, M. Maggioni, Multiscale Geometric Methods for Data Sets II: Geometric Wavelets,
Appl. Comp. Harm. Anal., vol. 32 no. 3
(2012)
 M. Iwen, M. Maggioni, Approximation of Points on LowDimensional Manifolds Via Random Linear Projections,
Inference & Information, vol. 2
(February, 2013) [doi]
 M. Maggioni, Geometric Estimation of Probability Measures in HighDimensions,
Proc. IEEE Asilomar Conference
(November, 2013)
 S. Gerber, M. Maggioni, Multiscale dictionaries, transforms, and learning in highdimensions,
Proc. SPIE 8858, Wavelets and Sparsity XV
(2013) [doi]
 Mauro Maggioni and Gustave L. Davis and Frederick J. Warner and Frank B. Geshwind and Andreas C. Coppi and Richard A. DeVerse and Ronald R. Coifman, Hyperspectral microscopic analysis of normal, benign and carcinoma microarray tissue sections, edited by Robert R. Alfano and Alvin Katz,
Optical Biopsy VI, vol. 6091 no. 1
(2006),
pp. 60910I, SPIE [1]
 Ronald R Coifman and Mauro Maggioni, Diffusion Wavelets,
Appl. Comp. Harm. Anal., vol. 21 no. 1
(2006),
pp. 5394
 J. Bouvrie, M. Maggioni, Efficient Solution of Markov Decision Problems with Multiscale Representations,
Proc. 50th Annual Allerton Conference on Communication, Control, and Computing
(2012)
 Sridhar Mahadevan and Mauro Maggioni, Protovalue Functions: A Spectral Framework for Solving Markov Decision Processes,
submitted
(2006)
 J. Bouvrie, M. Maggioni, Geometric Multiscale Reduction for Autonomous and Controlled Nonlinear Systems,
in Proc. IEEE Conference on Decision and Control (CDC)
(2012) [pdf]
 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)
 Mary A. Rohrdanz, Wenwei Zheng, Mauro Maggioni,Cecilia Clementi, Determination of reaction coordinates via locally scaled diffusion map,
JCP, vol. 134 no. 12
(2011),
pp. 124116
 G. Chen, M. Maggioni, Multiscale Geometric Dictionaries for pointcloud data,
Proc. SampTA 2011
(2011)
 Wenwei Zheng,Mary A. Rohrdanz,Mauro Maggioni, Cecilia Clementi, Polymer reversal rate calculated via locally scaled diffusion map,
JCP, vol. 134 no. 14
(2011),
pp. 144109
 G. Chen, M. Maggioni, Multiscale Geometric Wavelets for the Analysis of Point Clouds,
Proc. CISS
(February, 2010)
 P.W. Jones, M. Maggioni, R. Schul, Universal local parametrizations via heat kernels and eigenfunctions of the Laplacian,
Ann. Acad. Scient. Fen., vol. 35
(January, 2010),
pp. 144 [1975] [abs]
 J. Lee, M. Maggioni, Multiscale Analysis of Time Series of Graphs,
Proc. SampTA 2011
(2010)
 P.W. Jones, M. Maggioni, R. Schul, Manifold parametrizations by eigenfunctions of the Laplacian and heat kernels,
Proc. Nat. Acad. Sci., vol. 105 no. 6
(2008)
 R R Coifman, I G Kevrekidis, S Lafon, M Maggioni, B. Nadler, Diffusion Maps, reduction coordinates and low dimensional representation of stochastic systems,
J.M.M.S., vol. 7
(2008),
pp. 842864
 S. Mahadevan, M. Maggioni, Protovalue Functions: A Laplacian Framework for Learning Representation and Control,
Journ. Mach. Learn. Res. no. 8
(September, 2007)
 G. Chen, A.V. Little, M. Maggioni, MultiResolution Geometric Analysis for Data in High Dimensions,
in Excursions in Harmonic Analysis, vol. 1
(2013), Birkhaüser Boston, ISBN 9780817683757 [doi]
 Sridhar Mahadevan and Mauro Maggioni, Value Function Approximation with Diffusion Wavelets and Laplacian Eigenfunctions,
in University of Massachusetts, Department of Computer Science Technical Report TR200538; Proc. NIPS 2005
(2005)
 Nets Hawk Katz and Elliot Krop and Mauro Maggioni, On the box problem,
Math. Research Letters, vol. 4
(2002),
pp. 515519
 Ronald R Coifman and Stephane Lafon and Ann Lee and Mauro Maggioni and Boaz Nadler and Frederick Warner and Steven Zucker, Geometric Diffusions as a tool for Harmonic Analysis and structure definition of data. Part II: Multiscale methods,
Proc. of Nat. Acad. Sci. no. 102
(2005),
pp. 74327438
 Ronald R Coifman and Stephane Lafon and Ann Lee and Mauro Maggioni and Boaz Nadler and Frederick Warner and Steven Zucker, Geometric Diffusions as a tool for Harmonic Analysis and structure definition of data. Part I: Diffusion maps,
Proc. of Nat. Acad. Sci. no. 102
(2005),
pp. 74267431
 J. Bouvrie, M. Maggioni, Multiscale Markov Decision Problems: Compression, Solution, and Transfer Learning
(Submitted, 2012) [1212.1143]
