An Algorithm Based on Topological Data Analysis for Solving Unsupervised Machine Learning Problems

Topological Data Analysis (TDA) refers to approaches that utilize applied topology and computational geometry to extract information about data. While TDA has been used extensively to infer qualitative information from different data structures, there has been a lack of approaches to utilize TDA in an algorithmic fashion for data analysis. In this work, we developed an open-source TDA-based algorithm that can be directly applied to point cloud data to perform unsupervised learning. This technique does not need to know the number of clusters a priori. We applied the developed algorithm to different data sets and illustrated that this algorithm outperforms existing unsupervised approaches. The developed algorithm is flexible in design to allow handling noisy data and address ambiguous scenarios in which the number of clusters is not obvious to novice (non-domain-expert) users.