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Topological data analysis (TDA) has emerged as one of the most promisingtechniques to reconstruct the unknown shapes of high-dimensional spaces fromobserved data samples. TDA, thus, yields key shape descriptors in the form ofpersistent topological features that can be used for any supervised orunsupervised learning task, including multi-way classification. Sparsesampling, on the other hand, provides a highly efficient technique toreconstruct signals in the spatial-temporal domain from just a fewcarefully-chosen samples. Here, we present a new method, referred to as theSparse-TDA algorithm, that combines favorable aspects of the two techniques.This combination is realized by selecting an optimal set of sparse pixelsamples from the persistent features generated by a vector-based TDA algorithm.These sparse samples are selected from a low-rank matrix representation ofpersistent features using QR pivoting. We show that the Sparse-TDA methoddemonstrates promising performance on three benchmark problems related to humanposture recognition and image texture classification.

Sparse-TDA: Sparse Realization of Topological Data Analysis for Multi-Way Classification