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 hence has low time and space complexity on large datasets. An efficient algorithm is proposed to solve the optimization of k-FSC. In addition, k-FSC is able to handle noise, outliers, and missing data and applicable to arbitrarily large datasets and streaming data. Extensive experiments show that k-FSC outperforms state-of-the-art subspace clustering methods.

本文介绍了一种名为k-Factorization Subspace Clustering (k-FSC)的方法，用于大规模子空间聚类。该方法通过追求矩阵分解模型中的结构稀疏性，直接将数据因式分解成k组，从而避免了学习亲和矩阵和进行特征值分解，能够在大数据集上实现低时间和空间复杂度，并能够处理噪声、离群值和缺失数据。实验证明，k-FSC和其扩展版本优于现有的子空间聚类方法。

基于k-分解的大规模子空间聚类