Poster: Computing the Persistent Homology of Encrypted Data

Topological Data Analysis (TDA) offers a suite of computational tools that provide quantified shape features of high dimensional data that can be used by modern statistical and predictive machine learning (ML) models. Persistent homology (PH) transforms data (e.g., point clouds, images, time series) into persistence diagrams (PDs)--compact representations of its latent topological structures. Because PDs enjoy inherent noise tolerance, are interpretable, provide a solid basis for data analysis, and can be made compatible with the expansive set of well-established ML model architectures, PH has been widely adopted for model development including on sensitive data. Thus, TDA should be incorporated into secure end-to-end data analysis pipelines. This paper introduces a version of the fundamental algorithm to compute PH on encrypted data using homomorphic encryption (HE).