Epsilon-Net Induced Lazy Witness Complex for Topological Data Analysis

Explore an innovative approach to topological data analysis in this one-hour conference talk. Delve into the concept of epsilon-net induced lazy witness complex, a method designed to improve the efficiency and scalability of persistent homology computation. Learn how this technique economically defines an approximate representation using selected points called landmarks, and discover the theoretical guarantees provided by the epsilon-net landmark selection method. Examine the proof that epsilon-net landmarks create an epsilon-approximate representation and how the induced lazy witness complex approximates the Rips complex. Investigate the proposed iterative algorithms for constructing epsilon-net landmarks in point clouds and graphs, understanding their log-linear time and linear space complexities. Compare this approach to state-of-the-art approximations, noting improvements in complexity and approximation ratio. Follow the talk's structure from introduction through literature review, algorithm explanation, complexity analysis, and concluding summary to gain a comprehensive understanding of this advanced topic in topological data analysis.