Large-Scale Subspace Clustering via k-Factorization

TL;DR

This paper introduces k-Factorization Subspace Clustering (k-FSC), a scalable method that directly factorizes data into subspaces, reducing computational complexity and effectively handling noise, outliers, and missing data in large datasets.

Contribution

The paper proposes k-FSC, a novel large-scale subspace clustering method that avoids affinity matrix learning, offers theoretical guarantees, and extends to streaming data.

Findings

k-FSC achieves linear time and space complexity.

It outperforms state-of-the-art methods on large datasets.

Handles noise, outliers, and missing data effectively.

Abstract

Subspace clustering (SC) aims to cluster data lying in a union of low-dimensional subspaces. Usually, SC learns an affinity matrix and then performs spectral clustering. Both steps suffer from high time and space complexity, which leads to difficulty in clustering large datasets. This paper presents a method called k-Factorization Subspace Clustering (k-FSC) for large-scale subspace clustering. K-FSC directly factorizes the data into k groups via pursuing structured sparsity in the matrix factorization model. Thus, k-FSC avoids learning affinity matrix and performing eigenvalue decomposition, and has low (linear) time and space complexity on large datasets. This paper proves the effectiveness of the k-FSC model theoretically. An efficient algorithm with convergence guarantee is proposed to solve the optimization of k-FSC. In addition, k-FSC is able to handle sparse noise, outliers, and missing data, which are pervasive in real applications. This paper also provides online extension and out-of-sample extension for k-FSC to handle streaming data and cluster arbitrarily large datasets. Extensive experiments on large-scale real datasets show that k-FSC and its extensions outperform state-of-the-art methods of subspace clustering.