Evolutionary Self-Expressive Models for Subspace Clustering

TL;DR

This paper introduces an evolutionary subspace clustering method that effectively clusters evolving data on low-dimensional subspaces by leveraging self-expressiveness and previous clustering information, outperforming existing algorithms.

Contribution

The paper presents a novel non-convex optimization framework for evolutionary subspace clustering that adaptively incorporates past clustering results and data evolution rates.

Findings

Outperforms state-of-the-art static and evolutionary clustering methods in accuracy.

Demonstrates effectiveness on both synthetic and real-world datasets.

Achieves better running time compared to existing approaches.

Abstract

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