Stochastic Multiresolution Persistent Homology Kernel / 2449
Xiaojin Zhu, Ara Vartanian, Manish Bansal, Duy Nguyen, Luke Brandl

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.

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