Mapper Based Classifier

Abstract

Topological data analysis aims to extract topological quantities from data, which tend to focus on the broader global structure of the data rather than local information. The Mapper method, specifically, generalizes clustering methods to identify significant global mathematical structures, which are out of reach of many other approaches. We propose a classifier based on applying the Mapper algorithm to data projected onto a latent space. We obtain the latent space by using PCA or autoencoders. Notably, a classifier based on the Mapper method is immune to any gradient based attack, and improves robustness over traditional CNNs (convolutional neural networks). We report theoretical justification and some numerical experiments that confirm our claims.