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
- Solomon, E; Bendich, P, Geometric fusion via joint delay embeddings,
Proceedings of 2020 23rd International Conference on Information Fusion, Fusion 2020
(July, 2020) [doi] [abs]
- Yao, L; Bendich, P, Graph Spectral Embedding for Parsimonious Transmission of Multivariate Time Series,
Ieee Aerospace Conference Proceedings
(March, 2020), ISBN 9781728127347 [doi] [abs]
- Blasch, E; Grewe, LL; Waltz, EL; Bendich, P; Pavlovic, V; Kadar, I; Chong, CY, Machine learning in/with information fusion for infrastructure understanding, panel summary,
Smart Structures and Materials 2005: Active Materials: Behavior and Mechanics, vol. 11423
(January, 2020), ISBN 9781510636231 [doi] [abs]
- Bendich, P; Bubenik, P; Wagner, A, Stabilizing the unstable output of persistent homology computations,
Journal of Applied and Computational Topology
pp. 1-30, SPRINGER [abs]
- Tralie, CJ; Bendich, P; Harer, J, Multi-Scale Geometric Summaries for Similarity-Based Sensor Fusion,
Ieee Aerospace Conference Proceedings, vol. 2019-March
(March, 2019), ISBN 9781538668542 [doi] [abs]