Stochastic Multiresolution Persistent Homology Kernel
Proceedings of the Twenty-Fifth International Joint Conference on Artificial Intelligence. Pages 2449-2456.
Abstract
We introduce a new topological feature representation for point cloud objects. Specifically, we construct a Stochastic Multiresolution Persistent Homology (SMURPH) kernel which represents an object's persistent homology at different resolutions. Under the SMURPH kernel two objects are similar if they have similar number and sizes of holes at these resolutions. Our multiresolution kernel can capture both global topology and fine-grained topological texture in the data. Importantly, on large point clouds the SMURPH kernel is more computationally tractable compared to existing topological data analysis methods. We demonstrate SMURPH's potential for clustering and classification on several applications, including eye disease classification and human activity recognition.
@inproceedings{ijcai2016p349,
title = {Stochastic Multiresolution Persistent Homology Kernel},
author = {Zhu, Xiaojin and Vartanian, Ara and Bansal, Manish and Nguyen, Duy and Brandl, Luke},
booktitle = {Proceedings of the Twenty-Fifth International Joint Conference on
Artificial Intelligence, {IJCAI-16}},
publisher = {AAAI Press / International Joint Conferences on Artificial Intelligence},
editor = {Subbarao Kambhampati},
pages = {2449--2456},
year = {2016},
month = {7},
url = {https://ijcai.org/proceedings/2016/349},
}
TY - CPAPER TI - Stochastic Multiresolution Persistent Homology Kernel AU - Zhu, Xiaojin AU - Vartanian, Ara AU - Bansal, Manish AU - Nguyen, Duy AU - Brandl, Luke T2 - Proceedings of the Twenty-Fifth International Joint Conference on Artificial Intelligence, IJCAI-16 PB - AAAI Press / International Joint Conferences on Artificial Intelligence PY - 2016 SP - 2449 EP - 2456 UR - https://ijcai.org/proceedings/2016/349 ER -Copied
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