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.
- Analysis of Molecular Dynamics Data: in collaboration with Cecilia Clementi, Mary Rohrdanz and Wenwei Zheng, we use the geometric structure of data generated from molecular dynamics data to construct observables that provide reaction coordinates and reduced, low-dimensional dynamics that well-approximates the long-time dynamics of the original system.
- Multiscale Analysis of Markov Decision Processes
- Visualization of large data sets.
- 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
Postdocs and students
OPEN POSITIONS! My lab has open positions for graduate students and postdocs. See the ads on mathjobs.
Current & past: Jake Bouvrie, Guangliang Chen, Miles Crosskey (now at CoVar Applied Technologies), Mark Iwen, David Lawlor, Stas Minsker, Jason Lee, Nate Strawn (currently at Georgetown University), Josh Vogelstein
Past: Yoon-Mo Jung, Prakash Balachandran, Anna V Little.
Pointers to some future, present and recent past happenings
NEW!! Duke Workshop on Sensing and Analysis of High-Dimensional Data, July 23-25, 2013
Structure in Complex Data Set Duke Mathematics N.S.F.-funded Research Training Grant.
Mathematical Biology Duke Mathematics N.S.F.-funded Research Training Grant.
Computational Geometry Week, including ACM SoCG 2012, June 17-20, in Chapel Hill, NC, USA. Special workshop Connections between analysis and computational geometry, organized by Chris Bishop. See also the special workshop Computational Geometric Learning Ð Exploring geometric structure in high dimensions organized by J. Giesen, C.K. Müller, G. Rote.
Challenges in Geometry, Analysis and Computation: High_Dimensional Synthesis June 4-6 2012. A conference in honor of R.R. Coifman, P.W. Jones and V. Rokhlin.
ICIAM Minisymposium on Harmonic Analysis on Graphs and Networks on July 22, 2011
Duke workshop on Sensing and Analysis of High-Dimensional Data on July 26-28th
AMS Special Session on The Mathematics of Information and Knowledge: a page with links and some of the slides of the talks here.
CTMS Workshop on Large Data Sets: Computation and Structure, Nov. 13th, Duke University, NC. The schedule will be available here.
Forum on Geometric Aspects of Machine Learning and Visual Analytics, Oct 11-12, IEEE VisWeek, Atlantic City, NJ.
SAMSI opening workshop on stochastic dynamics, part of the long program on stochastic dynamics.
Our Probability Wiki and working group 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.
Compressive Sensing Workshop at Duke (slides and video lectures available).
Cecilia Clementi, Ronald R. Coifman, David Brady, Jason Lee, 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
- Special issue of Science on Dealing with Data
- 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.
- 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...)