Large-Scale Subspace Clustering via k-Factorization
This work addresses the computational bottleneck of subspace clustering for large datasets, which is a significant problem for researchers and practitioners working with big data in machine learning.
This paper introduces k-Factorization Subspace Clustering (k-FSC), a method that directly factorizes data into k groups by leveraging structured sparsity in a matrix factorization model. This approach bypasses the need for affinity matrix learning and eigenvalue decomposition, achieving linear time and space complexity on large datasets. Experiments show k-FSC outperforms state-of-the-art methods on large-scale real datasets.
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.