Fusion Subspace Clustering for Incomplete Data

• URL: http://arxiv.org/abs/2205.10872v1
• Date: Sun, 22 May 2022 17:23:41 GMT
• Title: Fusion Subspace Clustering for Incomplete Data
• Authors: Usman Mahmood and Daniel Pimentel-Alarc\'on
• Abstract summary: This paper introduces em fusion subspace clustering, a novel method to learn low-dimensional structures that approximate large scale yet highly incomplete data. Our method allows low, high, and even full-rank data; it directly accounts for noise, and its sample complexity approaches the information-theoretic limit. We show through extensive experiments on real and synthetic data that our approach performs comparably to the state-of-the-art with complete data, and dramatically better if data is missing.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: This paper introduces {\em fusion subspace clustering}, a novel method to learn low-dimensional structures that approximate large scale yet highly incomplete data. The main idea is to assign each datum to a subspace of its own, and minimize the distance between the subspaces of all data, so that subspaces of the same cluster get {\em fused} together. Our method allows low, high, and even full-rank data; it directly accounts for noise, and its sample complexity approaches the information-theoretic limit. In addition, our approach provides a natural model selection {\em clusterpath}, and a direct completion method. We give convergence guarantees, analyze computational complexity, and show through extensive experiments on real and synthetic data that our approach performs comparably to the state-of-the-art with complete data, and dramatically better if data is missing.

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