Evolutionary Self-Expressive Models for Subspace Clustering

Abstract

The problem of organizing data that evolves over time into clusters is\nencountered in a number of practical settings. We introduce evolutionary\nsubspace clustering, a method whose objective is to cluster a collection of\nevolving data points that lie on a union of low-dimensional evolving subspaces.\nTo learn the parsimonious representation of the data points at each time step,\nwe propose a non-convex optimization framework that exploits the\nself-expressiveness property of the evolving data while taking into account\nrepresentation from the preceding time step. To find an approximate solution to\nthe aforementioned non-convex optimization problem, we develop a scheme based\non alternating minimization that both learns the parsimonious representation as\nwell as adaptively tunes and infers a smoothing parameter reflective of the\nrate of data evolution. The latter addresses a fundamental challenge in\nevolutionary clustering -- determining if and to what extent one should\nconsider previous clustering solutions when analyzing an evolving data\ncollection. Our experiments on both synthetic and real-world datasets\ndemonstrate that the proposed framework outperforms state-of-the-art static\nsubspace clustering algorithms and existing evolutionary clustering schemes in\nterms of both accuracy and running time, in a range of scenarios.\n