Mapper Based Classifier

TL;DR

This paper introduces a Mapper-based classifier that leverages topological data analysis to enhance robustness against gradient-based attacks, using latent space projections via PCA or autoencoders.

Contribution

It presents a novel classifier combining Mapper with latent space projections, offering improved robustness over traditional CNNs and providing theoretical and experimental validation.

Findings

Mapper classifier is immune to gradient-based attacks

It outperforms CNNs in robustness

Theoretical and numerical validation supports claims

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.