Sparse-TDA: Sparse Realization of Topological Data Analysis for Multi-Way Classification - 2018


Topological data analysis (TDA) has emerged as one of the foremost promising techniques to reconstruct the unknown shapes of high-dimensional spaces from observed knowledge samples. TDA, therefore, yields key shape descriptors in the shape of persistent topological options which will be used for any supervised or unsupervised learning task, including multi-way classification. Sparse sampling, on the other hand, provides a highly efficient technique to reconstruct signals in the spatial-temporal domain from simply a few rigorously-chosen samples. Here, we tend to gift a brand new technique, known as the Sparse-TDA algorithm, that combines favorable aspects of the two techniques. This combination is realized by selecting an optimal set of sparse pixel samples from the persistent options generated by a vector-based mostly TDA algorithm. These sparse samples are selected from a low-rank matrix illustration of persistent features using QR pivoting. We tend to show that the Sparse-TDA methodology demonstrates promising performance on three benchmark issues connected to human posture recognition and image texture classification.

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