A Topological Data Analysis Based Classifier

• URL: http://arxiv.org/abs/2111.05214v2
• Date: Wed, 10 Nov 2021 14:33:02 GMT
• Title: A Topological Data Analysis Based Classifier
• Authors: Rolando Kindelan and Jos\'e Fr\'ias and Mauricio Cerda and Nancy Hitschfeld
• Abstract summary: This paper proposes an algorithm that applies Topological Data Analysis directly to multi-class classification problems. The proposed algorithm builds a filtered simplicial complex on the dataset. On average, the proposed TDABC method was better than KNN and weighted-KNN.
• Score: 1.6668132748773563
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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, without any further ML stage, showing advantages for imbalanced datasets. The proposed algorithm builds a filtered simplicial complex on the dataset. Persistent Homology (PH) is applied to guide the selection of a sub-complex where unlabeled points obtain the label with the majority of votes from labeled neighboring points. We select 8 datasets with different dimensions, degrees of class overlap and imbalanced samples per class. On average, the proposed TDABC method was better than KNN and weighted-KNN. It behaves competitively with Local SVM and Random Forest baseline classifiers in balanced datasets, and it outperforms all baseline methods classifying entangled and minority classes.

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