Research Interests for Paul L. Bendich

I work in computational topology, which for me means adapting and using tools from algebraic topology in order to study noisy and high-dimensional datasets arising from a variety of scientific applications. My thesis research involves the analysis of datasets for which the number of degrees of freedom varies across the parameter space. The main tools are local homology and intersection homology, suitably redefined in this fuzzy multi-scale context. I am also working on building connections between computational topology and various statistical data analysis algorithms, such as clustering or manifold learning.

Recent Publications

1. with David Cohen-Steiner, Herbert Edelsbrunner, John Harer, and Dmitriy Morozov, Inferring Local Homology from Sampled Stratified Spaces, In Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science, pages 536-546, 2007. (Accepted, 2007)
2. with Mikhail Belkin, Yuriy Mileyko, Dmitriy Morozov, and Sayan Mukherjee, A Probabilistic Perspective on Persistence Homologies, NIPS 2007 Workshop on Topology Learning. (Accepted, 2007)