A topological data analysis based classifier

We will discuss about “A topological data analysis based classifier”, Kindelan et al., arXiv, 2022

Abstract: Topological Data Analysis is an emergent field that aims to discover the underlying dataset’s topological information. Topological Data Analysis tools have been commonly used to create filters and topological descriptors to improve Machine Learning (ML) methods. This paper proposes a different Topological Data Analysis pipeline to classify balanced and imbalanced multi-class datasets without additional ML methods. Our proposed method was designed to solve multi-class problems. It resolves multi-class imbalanced classification problems with no data resampling preprocessing stage. The proposed Topological Data Analysis-based classifier builds a filtered simplicial complex on the dataset representing high-order data relationships. Following the assumption that a meaningful sub-complex exists in the filtration that approximates the data topology, we apply Persistent Homology to guide the selection of that sub-complex by considering detected topological features. We use each unlabeled point’s link and star operators to provide different sized and multi-dimensional neighborhoods to propagate labels from labeled to unlabeled points. The labeling function depends on the filtration entire history of the filtered simplicial complex and is encoded within the persistent diagrams at various dimensions. We select eight datasets with different dimensions, degrees of class overlap, and imbalanced samples per class. The TDABC outperforms all baseline methods classifying multi-class imbalanced data with high imbalanced ratios and data with overlapped classes. Also, on average, the proposed method was better than KNN and weighted-KNN and behaved competitively with SVM and Random Forest baseline classifiers in balanced datasets.