 Mauro Maggioni, Professor of Mathematics and Electrical and Computer Engineering and Computer Science
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.
 Contact Info:
Teaching (Fall 2015):
 MATH 561.01, SCIENTIFIC COMPUTING
Synopsis
 Gross Hall 304B, MW 01:25 PM02:40 PM
Teaching (Spring 2016):
 MATH 431.01, ADVANCED CALCULUS I
Synopsis
 Physics 235, MW 10:05 AM11:20 AM
 Education:
Ph.D.  Washington University  2002 
M.S.  Washington University  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:
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
 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)
 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)
 Sridhar Mahadevan and Mauro Maggioni, Protovalue Functions: A Spectral Framework for Solving Markov Decision Processes,
submitted
(2006)
 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)
 G. Chen, M. Maggioni, Multiscale Geometric Dictionaries for pointcloud data,
Proc. SampTA 2011
(2011)
 J. Lee, M. Maggioni, Multiscale Analysis of Time Series of Graphs,
Proc. SampTA 2011
(2010)
 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]
 J. Bouvrie, M. Maggioni, Multiscale Markov Decision Problems: Compression, Solution, and Transfer Learning
(Submitted, 2012) [1212.1143]
