Semin Oh (오세민), May 12, Tuesday, 6-7 PM, Denoising data reduction algorithm for Topological Data Analysis
Keimyung Discrete Math Seminar (계명 이산수학 세미나)
Date and Time: May 12, Tuesday, 6-7 PM
Title : Denoising data reduction algorithm for Topological Data Analysis
Speaker: Semin Oh (오세민), KNU G-LAMP Project Group, Kyungpook National University (경북대학교)
Location: Room 324
Abstract : Persistent homology is a central tool in topological data analysis, but its application to large and noisy datasets is often limited by computational cost and the presence of spurious topological features. Noise not only increases data size but also obscures the underlying structure of the data.
In this talk, we propose the Refined Characteristic Lattice Algorithm (RCLA), a grid-based method that integrates data reduction with threshold-based denoising in a single procedure. By incorporating a threshold parameter k, RCLA removes noise while preserving the essential structure of the data. We further provide a theoretical guarantee by proving a stability theorem under a homogeneous Poisson noise model. This theorem bounds the bottleneck distance between the persistence diagrams of the output and the underlying shape with high probability. In addition, we introduce an automatic parameter selection method based on nearest-neighbor statistics. Experimental results show that RCLA offers advantages over existing denoising methods in both the accuracy and stability of topological feature extraction, measured by the bottleneck distance between persistence diagrams. Its effectiveness is further validated on a 3D shape classification task. For further details, we refer the reader to the preprint (arXiv:2603.29248).
Keimyung Discrete Math Seminar (계명 이산수학 세미나)
This is a kind reminder for today's presentation by Semin Oh.