  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.
