Mapper Based Classifier
This work addresses robustness issues in machine learning classifiers, particularly against adversarial attacks, but appears incremental as it adapts an existing topological method to a new application.
The authors tackled the problem of improving classifier robustness by proposing a Mapper-based classifier that operates on data projected into a latent space via PCA or autoencoders, resulting in immunity to gradient-based attacks and enhanced robustness compared to traditional CNNs.
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.