  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.
