  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, even imbalanced datasets, without any
further ML stage. The proposed algorithm built a filtered simplicial complex on
the dataset. Persistent homology is then applied to guide choosing a
sub-complex where unlabeled points obtain the label with most votes from
labeled neighboring points. To assess the proposed method, 8 datasets were
selected with several degrees of class entanglement, variability on the samples
per class, and dimensionality. On average, the proposed TDABC method was
capable of overcoming baseline classifiers (wk-NN and k-NN) in each of the
computed metrics, especially on classifying entangled and minority classes.
