2021/11/09 by Rolando Kindelan, Kindelan, Rolando, José María Martínez Frías +6 · 1 citation
Computer Science · #55N31 #62R07 #62R40 #68T09 #68T10 #Computational Geometry (cs.CG) #FOS: Computer and information sciences #Machine Learning (cs.LG) #Topological and Geometric Data Analysis #cs.CG #cs.LG #msc:55N31 #msc:62R07 #msc:62R40 #msc:68T09 #msc:68T10
paper · pdf · doi:10.48550/arxiv.2111.05214
The paper is under consideration at Advances in Data Analysis and Classification. arXiv admin note: text overlap with arXiv:2102.03709
openalex publication_date 2021/11/09 · arxiv created 2022/02/04 · arxiv updated 2022/02/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.