research

Research Interests:

Computational and applied mathematics, machine learning, analysis of large data sets, pattern recognition, nonlinear function approximation, time series analysis, optimal low-dimensional systems, optimization and mathematical modeling, signal and image processing

An Overview of Current and Past Research:

My current focus is on developing resource allocation techniques for uncertain renewable resources such as wind. I have developed a recursive statistical estimation tool that has exceptionally fast updating rules. I designed this method for stochastic search that arises throughout applications in renewable energy systems. I am working on nonlinear function approximation problems in the context of approximate dynamic programming, with applications to energy systems. This work is highlighted in the recent issue of Princeton University Innovation Magazine.

In the past, I developed Time Variant Radial Basis Functions and novel techniques for parsimonious modeling of spatio-temporal dynamics over high dimensional domains. I developed a biologically inspired image reconstruction scheme to model sparse and low rate sampled images.

I was involved in conducting fundamental research in mathematics of large data sets and nonlinear signal processing. This involved design of new Radial Basis Functions, and efficient multivariate algorithms for constructing nonlinear models from high-dimensional scattered data. The developed methods do not require adjustment of any ad hoc parameters. The developed algorithms have a wide range of applications such as modeling data on manifolds and prediction of financial time-series.

I worked on biologically inspired adaptive methods for object classification in changing environments from multi-aspect views. I also worked on various feature extraction schemes, neural network paradigms, wavelets and different variations of the Kalman filter.

Presentations:

“Nonparameteric Methods for Value Function Approximation Using Dirichlet Clouds”, INFORMS Annual meeting, (Phoenix, AZ), October 2012.

“Recent Developments on High Dimensinal Function Approximation and Various Important Applications”, Institute of Mathematics and its Applications, (Minneapolis, MN), March 2012 (poster). (Invited Talk)

“Novel Kernels and Algorithms for Modeling Sparse Data”, NEC Labs America, (Princeton, NJ), May 2011. (Invited Talk)

“Multiscale Data Analysis over High Dimensional Domains”, Princeton University, (Princeton, NJ), May 2011.

“Sparse representation of spatial-temporal systems and Images”, Katholieke University Leuven, (Leuven, Belgium), August 2009. (Invited Talk)

“How to Learn Efficiently from High Dimensional Data”, Imperial College London, (London, UK), February 2009.

“Skew-Radial Basis Functions for Modeling Edges and Jumps”, 8^th IMA International Conference on Mathematics in Signal Processing, (Cirencester, U.K.), December 2008.

“Advances in Radial Basis Functions and Connections to Manifold Learning”, Princeton University, (Princeton, NJ), July 2008. (Invited Talk)

“A Glimse to Nonlinear Signal Porcessing”, American Institute of Mathematics, (Palo Alto, CA), July 2008. (Contributtion Talk)

“Geometric Representation of High Dimensional Scattered Data as Graph of Functions”, Workshop on Applications of Topology in Science and Engineering, Mathematical Science Research Institute, University of California-Berkeley, (Berkeley, CA), September 2006.

“Parsimonious Geometric Modeling of Financial Instruments”, SIAM Conference on Financial Mathematics and Engineering, (Boston, MA), July 2006.

“Examples of Compactly Supported functions for Radial Basis Function Approximations”, International Conference on Machine Learning; Models, Technologies and Applications, and International Conference on Scientific Computing, (Las Vegas, NV), June 2006.

“A New Spatio-Temporal Resource Allocation Network (ST-RAN)”, Seminar in Geometric Methods for the Analysis of High-Dimensional Data, CSU, (Fort Collins, CO), Spring 2005.

“Low Order Nonlinear Models”, Information Science and Technology Colloquium, CSU, (Fort Collins, CO), April 2005. (Poster)

“Radial Basis Function Model Order Determination Using Statistical Hypothesis Testing”, Third Annual Intermountain/Southwest Conference on Industrial and Interdisciplinary Mathematics, Arizona State University, (Tempe, AZ), February 2004. (Poster)

“Target Identification using Zernike Moments and Neural Networks”, SPIE conference on Automatic Target Recognition XI, (Orlando, FL), April 2001.

“Comparison of Confidence Level of Different Classification Paradigms for Underwater Target Discrimination”, SPIE conference on Detection and Remediation Technologies for Mines and Mine like Targets VI, (Orlando, FL), April 2001.

Technical Workshops:

Machine Learning: Theory and Computation Workshop, Institute for Mathematics and its Applications, (Minneapolis, MN), March 26-30, 2012. Supported by IMA and Princeton ORFE.

New Directions Course: Applied Algebraic Topology, Institute for Mathematics and its Applications, (Minneapolis, MN), June 15-26, 2009. Supported by IMA.

Workshop on Geometry and Representation Theory of Tensors for Computer Science, Statistics and other Areas, American Institue of Mathematics, (Palo Alto, CA), July 20-25, 2008. Supported by AIM.

Workshop on Topological Methods in Combinatorics, Computational Geometry, and the Study of Algorithms, Mathematical Science Research Institute, University of California-Berkeley, (Berkeley, CA), October 2-6, 2006. Supported by an MSRI award.

Workshop on Data Driven Modeling, Department of Mathematics, CSU, (Fort Collins, CO), September 28, 2006.

Workshop on Applications of Topology in Science and Engineering, Mathematical Science Research Institute, University of California-Berkeley, (Berkeley, CA), September 18-22, 2006. Supported by an MSRI award.

Graduate Summer School: Data Assimilation for the Carbon Cycle, Mathematical Science Research Institute, University of California-Berkeley, (Berkeley, CA), July 16-29, 2006. Supported by an MSRI award.

Multi-scale Methods and Statistics, Graybill Workshop, CSU, (Fort Collins, CO), June 11-13, 2006.

Graduate Summer School: Intelligent Extraction of Information from Graphs and High Dimensional Data, Institute of Pure and Applied Mathematics, UCLA, (Los Angeles, CA), July 11-29, 2005. Supported by IPAM.

Statistics in Information Theory, Graybill Workshop, CSU, (Fort Collins, CO), June 2-3, 2005.

Workshop on Geometry and Symmetry in Numerical Computation, CSU, (Fort Collins, CO), August 8-10, 2005.