k-Factorization Subspace Clustering
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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.
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