arXiv 2102.037092021-02-07cs.LGcs.CG

Classification based on Topological Data Analysis

University of Chile（智利大学）；Universidad de Oriente（东方大学）；Center for Research in Mathematics（数学研究中心）；Institute of Biomedical Sciences（生物医学科学研究所）；Biomedical Neuroscience Institute（生物医学神经科学研究所）

Rolando Kindelan, José Frías, Mauricio Cerda, Nancy Hitschfeld

备注：: Preprint submitted to the Pattern Recognition Journal

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Topological Data Analysis (TDA) is an emergent field that aims to discover topological information hidden in a dataset. TDA tools have been commonly used to create filters and topological descriptors to improve Machine Learning (ML) methods. This paper proposes an algorithm that applies TDA directly to multi-class classification problems, even imbalanced datasets, without any further ML stage. The proposed algorithm built a filtered simplicial complex on the dataset. Persistent homology is then applied to guide choosing a sub-complex where unlabeled points obtain the label with most votes from labeled neighboring points. To assess the proposed method, 8 datasets were selected with several degrees of class entanglement, variability on the samples per class, and dimensionality. On average, the proposed TDABC method was capable of overcoming baseline classifiers (wk-NN and k-NN) in each of the computed metrics, especially on classifying entangled and minority classes.

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