Mauro Maggioni, Professor of Mathematics and Computer Science and Electrical and Computer Engineering
Harmonic analysis, spectral graph theory, multiscale analysis, signal processing, applications to machine learning, Markov decision processes, imaging.
Teaching (Spring 2014):
- MATH 431.01, ADVANCED CALCULUS I
- Social Sciences 124, MW 03:05 PM-04:20 PM
|PhD||Washington University, St. Louis||2002|
|MS||Washington University, St. Louis||2000|
|Laurea in Matematica||Universita' degli Studi di Milano, Italy||1999|
- Research Interests: Harmonic analysis, with applications to statistical analysis of high-dimensional data, machine learning, imaging.
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 high-dimensional 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 Euclidean-type 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
Markov decision processes
High-dimensional data analysis
Stochastic dynamical systems
Imaging (e.g. hyperspectral)
Geometric measure theory
- Harmonic • Multiscale • Spectral graph theory • Multiscale Dynamical systems • Laplacian • Hyperspectral • Imaging
- Current Ph.D. Students
- Postdocs Mentored
- David Lawlor (2012/10-present)
- Joshua Vogelstein (2012/10-present)
- Samuel Gerber (2012/10-present)
- Nate Strawn (2011 - present)
- Mark Iwen (2010 - 2013)
- Guangliang Chen (2009/12-present)
- Jake Bouvrie (2009 - 2012)
- Yoon-Mo Jung (2007 - 2009)
- Undergraduate Research Supervised
- Jason Lee (May, 2009 - May, 2010)
- Representative Publications
- Ronald R Coifman and Mauro Maggioni, Diffusion Wavelets,
Appl. Comp. Harm. Anal., vol. 21 no. 1
- 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
- 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
- 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
pp. 60910I, SPIE 
- Nets Hawk Katz and Elliot Krop and Mauro Maggioni, On the box problem,
Math. Research Letters, vol. 4
- Sridhar Mahadevan and Mauro Maggioni, Proto-value Functions: A Spectral Framework for Solving Markov Decision Processes,
- Mauro Maggioni and Sridhar Mahadevan, Multiscale Diffusion Bases for Policy Iteration in Markov Decision Processes,
- Recent Grant Support
- ATD: Online Multiscale Algorithms for Geometric Density Estimation in High-Dimensions and Persistent Homology of Data for Improved Threat, National Science Foundation, DMS-1222567, 2012/09-2016/08.
- EMSW21-RTG: Geometric, Topological and Statistical Methods for Analyzing Massive Datasets, National Science Foundation, DMS-1045153, 2011/08-2016/07.
- A Rigorous Statistical Framework for the Mathematics of Sensing, Exploitation and Execution, Defense Advanced Research Projects Agency, 2011/11-2014/11.
- X-Ray Scatter and Phase Imaging for Explosive Detection, US Department of Homeland Security, HSHQDC-11-C-00083, 2011/09-2014/09.
- CAREER: Multiscale methods for high-dimensional data, graphs and dynamical systems, National Science Foundation, DMS-0847388, 2009/07-2014/06.
- Knowledge Enhanced Exapixel Photography, Defense Advanced Research Projects Agency, N66001-11-1-4002, 2010/11-2013/11.
- Multiscale geometry for the analysis of high dimensional datasets, Washington State University, 113054 G002745, 2010/05-2013/05.
- NeTS: Small: Collaborative Research: Online Social Networks: Measurement and Characterization Methodologies, National Science Foundation, IIS-0916855, 2009/09-2012/08.
- Mathematical Foundations of Multiscale Graph Representations and Interactive Learning, National Science Foundation, CCF-0808847, 2008/05-2012/07.
- Collaborative Proposal: CDI-Type I: A multidisciplinary, multiscale approach to discover organizing principles in macromolecular dynamics and functions, National Science Foundation, NSF-CHE-0835712, 2008/10-2011/09.
- Collaborative Research: Learning Multiscale Representations Using Harmonic Analysis on Graphs, National Science Foundation, IIS-0803293, 2008/09-2011/08.
- Mathematical Foundations of Multiscale Graph Representations and Interactive Learning, National Science Foundation, NSF-0808847-001, 2009/05-2011/04.
- Mathematical Foundations of Multiscale Graph Representations and Interactive Learning, National Science Foundation, 2008/05-2011/04.
- Conferences Organized
- SAMSI-FODAVA Workshop on Interactive Visualization and Analysis of Massive Data, December 10, 2012
- Symposium of Knowledge Extraction at A.M.S. nat. meeing 2010, January 13, 2010
- Large Data Workshop, C.T.M.S., Duke, November 13, 2009
- A.A.A.I. workshop on manifold learning, November 5, 2009
- Internet Multi-Resolution Analysis: Foundations, Applications and Practice, Organizer, September, 2008 - December, 2008
- Workshop on Eigenfunctions of the Laplacian, ICIAM 2007, July 18, 2007
- Document Space, Organizer, January, 2006