Papers › Differentially Private Topological Data Analysis

Differentially Private Topological Data Analysis

5 May 2023arXiv:2305.03609archive 2025-07-28

Taegyu Kang, Sehwan Kim, Jinwon Sohn, Jordan Awan

This paper is the first to attempt differentially private (DP) topological data analysis (TDA), producing near-optimal private persistence diagrams. We analyze the sensitivity of persistence diagrams in terms of the bottleneck distance, and we show that the commonly used \v{C}ech complex has sensitivity that does not decrease as the sample size n increases. This makes it challenging for the persistence diagrams of \v{C}ech complexes to be privatized. As an alternative, we show that the persistence diagram obtained by the L¹-distance to measure (DTM) has sensitivity O(1/n). Based on the sensitivity analysis, we propose using the exponential mechanism whose utility function is defined in terms of the bottleneck distance of the L¹-DTM persistence diagrams. We also derive upper and lower bounds of the accuracy of our privacy mechanism; the obtained bounds indicate that the privacy error of our mechanism is near-optimal. We demonstrate the performance of our privatized persistence diagrams through simulations as well as on a real dataset tracking human movement.

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