Fast Online $L_0$ Elastic Net Subspace Clustering via A Novel Dictionary Update Strategy

TL;DR

This paper introduces a fast online $L_0$ elastic net subspace clustering method that adaptively updates dictionaries using support points, improving real-time clustering of evolving data streams.

Contribution

It proposes a novel $L_0$ elastic net model with a support point-based dictionary update strategy for online subspace clustering.

Findings

Enhanced clustering accuracy on dynamic data streams

Improved computational efficiency for real-time processing

Proven convergence of the proposed algorithm

Abstract

With the rapid growth of data volume and the increasing demand for real-time analysis, online subspace clustering has emerged as an effective tool for processing dynamic data streams. However, existing online subspace clustering methods often struggle to capture the complex and evolving distribution of such data due to their reliance on rigid dictionary learning mechanisms. In this paper, we propose a novel $\ell_0$ elastic net subspace clustering model by integrating the $\ell_0$ norm and the Frobenius norm, which owns the desirable block diagonal property. To address the challenges posed by the evolving data distributions in online data, we design a fast online alternating direction method of multipliers with an innovative dictionary update strategy based on support points, which are a set of data points to capture the underlying distribution of the data. By selectively updating dictionary atoms according to the support points, the proposed method can dynamically adapt to the evolving data characteristics, thereby enhancing both adaptability and computational efficiency. Moreover, we rigorously prove the convergence of the algorithm. Finally, extensive numerical experiments demonstrate that the proposed method improves clustering performance and computational efficiency, making it well-suited for real-time and large-scale data processing tasks.