RESEARCH INTERESTS
My interests are in harmonic analysis, wavelets, multiscale analysis in general, and in particular with applications to the analysis of graphs and data sets viewed as discrete or sampled continuous geometric structures embedded in high-dimensional spaces. I am interested in machine learning problems, mostly from the point of view of approximation and fitting of functions under random noise and random sampling.
- Diffusion Wavelets: a recent construction of new families of wavelets and Multi-resolution Analyses on graphs, manifolds and point clouds. Pictures, papers and presentations available.
- Diffusion Geometries: here are some links to the use of diffusion geometries in data analysis.
- Multiscale Analysis of Markov Decision Processes
- Harmonic Analysis and Wavelets: here I talk a bit about Harmonic Analysis and provide links to related web pages.
- HyperSpectral Imaging and Pathology : hyper-spectral imaging applied to pathology
Current students and postdocs
Prakash Balachandran, Yoon-Mo Jung, Anna V Little.New!
Our Probability Wiki at Duke. As of Spring 09, we are meeting every Tuesday at 1pm in Room 259 in the Physics building, to discuss topics of interest to the audience. It is informal, highly interdisciplinary, and fun. Papers/talks are collected on the wiki. Feel free to join us (or the mailing list).
Symposium on Manifold Learning to be held on Nov. 5-7 in Arlington, VA.
The Compressive Sensing Workshop at Duke (slides and video lectures available).
Collaborators
Ronald R. Coifman, David Brady, Sridhar Mahadevan, Raanan Schul, Sayan Mukherjee, Andreas Coppi, Frank B. Geshwind, Richard DeVerse, Gustave L. Davis, Francis Woolfe, Peter W. Jones, Stephane Lafon, Sridhar Mahadevan, M. Mahoney, Francois Meyer, Hrushikesh Mhaskar, Arthur D. Szlam, Johan Walden, Frederick J. Warner, Steven W. Zucker, Petros Drineas, James C. Bremer Jr., Anna Lin, Eric Monson, Xilin Shen, William Goetzmann
Links of Interest
- Statistical Theory and Methods for Complex, High-Dimensional Data, Isaac Newton Institute for Mathematical Sciences, Cambridge, U.K.
- Slides of talks given at the workshop on eigenfunctions of the Laplacian, organized by N. Saito and myslef, held at ICIAM 2007.
- Tutorial on Manifold and Spectral Methods for MDPs, by S. Mahadevan and myself, held at ICML 2006.
- Mathematics Calendar from AMS.
- Institute for Pure and Applied Mathematics (IPAM) at UCLA. Conference on Document Space at IPAM on January 2006. Summer School on Intelligent Extraction of Information from Graphs and High Dimensional Data (July 2005), talks available in pdf and video formats.
- Institute for Mathematics and Applications (IMA) at the University of Minnesota, MSRI at Berkeley, SAMSI at Research Triangle Park, Sissa,Trieste,
- TTI Chicago. Conference on Machine Learning (summer 2005). Talks available in pdf and video formats.
- Manifold Learning Page , Fast Manifold Learning ,
- Mathematics Department,Applied Mathematics at Yale University.
- MathsciNet
- American Mathematical Society
- The Society of Mathematical Biology - meetings, conferences and workshops
- Applications of Analysis to Mathematical Biology conference at Duke.
- Visualization Tools by Mario Valle. In particular see ParaView and Ggobi
- Home pages of mathematicians (under construction): Michael Christ, David Donoho , Timothy Gowers, Fan Chung Graham, Terry Tao,Isabella Laba ,...
- The journal Applied Computational Harmonic Analysis
- The summer school on Wavelet and Multifractals (Corsica, 2004)
- Math/Harmonic Analysis Blog
- Tutorial on spectral clustering , by C. Ding
Programming, Code, etc...
- Lightspeed Matlab package, and useful Matlab speeding up packages and suggestions.
- Matlab tricks and tips
- Sparse Reconstruction packages:
- Software by Kevin Murphy, mostly Matlab packages (e.g. HMM, MDP, graphs...)
Data Sets
- UCI benchmark repository and UCI KDD archive.
- Benchmark data sets for semisupervised classification, from the book Chapelle et al.
- Benchmark repository at the Intelligent Data Analysis Group Fraunhofer.
- Regression data sets available at LIACC.
- JSE data archive .
- Statlib data set archive .
Miscellanea
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Newspapers (giornali): Il giornale , Il resto del carlino