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Subspace clustering is a useful technique for many computer visionapplications in which the intrinsic dimension of high-dimensional data is oftensmaller than the ambient dimension. Spectral clustering, as one of the mainapproaches to subspace clustering, often takes on a sparse representation or alow-rank representation to learn a block diagonal self-representation matrixfor subspace generation. However, existing methods require solving a largescale convex optimization problem with a large set of data, with computationalcomplexity reaches O(N^3) for N data points. Therefore, the efficiency andscalability of traditional spectral clustering methods can not be guaranteedfor large scale datasets. In this paper, we propose a subspace clustering modelbased on the Kronecker product. Due to the property that the Kronecker productof a block diagonal matrix with any other matrix is still a block diagonalmatrix, we can efficiently learn the representation matrix which is formed bythe Kronecker product of k smaller matrices. By doing so, our modelsignificantly reduces the computational complexity to O(kN^{3/k}). Furthermore,our model is general in nature, and can be adapted to different regularizationbased subspace clustering methods. Experimental results on two public datasetsshow that our model significantly improves the efficiency compared with severalstate-of-the-art methods. Moreover, we have conducted experiments on syntheticdata to verify the scalability of our model for large scale datasets.

Fast Subspace Clustering Based on the Kronecker Product