Sparse-TDA: Sparse Realization of Topological Data Analysis for Multi-Way Classification
This work addresses the challenge of computational efficiency in shape reconstruction for machine learning tasks, but it appears incremental as it combines existing techniques without a major breakthrough.
The authors tackled the problem of efficiently reconstructing high-dimensional shapes for multi-way classification by combining topological data analysis with sparse sampling, resulting in the Sparse-TDA algorithm that showed promising performance on human posture recognition and image texture classification benchmarks.
Topological data analysis (TDA) has emerged as one of the most promising techniques to reconstruct the unknown shapes of high-dimensional spaces from observed data samples. TDA, thus, yields key shape descriptors in the form of persistent topological features that can 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 just a few carefully-chosen samples. Here, we present a new method, referred to 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 features generated by a vector-based TDA algorithm. These sparse samples are selected from a low-rank matrix representation of persistent features using QR pivoting. We show that the Sparse-TDA method demonstrates promising performance on three benchmark problems related to human posture recognition and image texture classification.