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 involved 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, as well as building connections between computational topology and diffusion geometry.
- Recent Publications
- Bendich, P; Chin, SP; Clark, J; Desena, J; Harer, J; Munch, E; Newman, A; Porter, D; Rouse, D; Strawn, N; Watkins, A, Topological and statistical behavior classifiers for tracking applications,
IEEE Transactions on Aerospace and Electronic Systems, vol. 52 no. 6
(December, Accepted, 2016),
pp. 2644-2661 [doi] [abs]
- Bendich, P; Gasparovic, E; Harer, J; Tralie, C, Geometric models for musical audio data,
LIPIcs, vol. 51
pp. 65.1-65.5, ISBN 9783959770095 [doi] [abs]
- Bendich, P; Marron, JS; Miller, E; Pieloch, A; Skwerer, S, Persistent Homology Analysis of Brain Artery Trees.,
The annals of applied statistics, vol. 10 no. 1
(January, Accepted, 2016),
pp. 198-218, ISSN 1932-6157 (to appear.) [repository], [doi] [abs]
- Paul Bendich, Ellen Gasparovic, John Harer, and Christopher J. Tralie, Scaffoldings and Spines: Organizing High-Dimensional Data Using Cover Trees, Local Principal Component Analysis, and Persistent Homology
(Submitted, 2016) [1602.06245]
- Bendich, P; Gasparovic, E; Harer, J; Izmailov, R; Ness, L, Multi-scale local shape analysis and feature selection in machine learning applications,
Proceedings of the International Joint Conference on Neural Networks, vol. 2015-September
pp. 1-8 [arXiv:1410.3169], [repository], [doi] [abs]