## Topological Data Analysis

#### Machine Learning Research

Researching ways to incorporate multiresolution persistent homology representations into probability models. For background on persistent homology, refer to the following papers:

- Gunnar Carlsson "Topology and Data" Bulletin of the American Mathematical Society 46(2): 255-308, 2009.
- H. Edelsbrunner and J. Harer "Computational Topology: An Introduction" Applied Mathematics, American Mathematical Society, 2010.
- Xiaojin Zhu "Persistent homology: An introduction and a new text representation for natural language processing" In The 23rd International Joint Conference on Artificial Intelligence (IJCAI), 2013.

My interest in this particular problem was piqued upon reading the following papers dealing with multiresolution persistent homology:

- X. Zhu, A. Vartanian, M. Bansal, D. Nguyen, and L. Brandl "Stochastic Multiresolution Persistent Homology Kernel" In The 25th International Joint Conference on Artificial Intelligence (IJCAI) 2016.
- K. Xia, Z. Zhao, and GW. Wei "Multiresolution topological simplification" In Journal of Computational Biology 22(9): 887-91, 2015.
- M. Ahmed, B. T. Fasy, and C. Wenk "Local persistent homology based distance between maps" In SIGSPATIAL. ACM, Nov. 2014.

If interested in hearing more about this project, feel free to contact me.