A Topological Data Analysis Based Classifier
This addresses classification challenges, particularly for imbalanced datasets, by introducing a novel TDA-based approach, though it is incremental as it builds on existing TDA tools.
The paper tackles multi-class classification by directly applying Topological Data Analysis without additional machine learning stages, showing that the proposed TDABC method outperforms baseline classifiers like KNN and weighted-KNN on average, and excels in classifying entangled and minority classes in imbalanced datasets.
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.