Parallel Sparse Subspace Clustering via Joint Sample and Parameter Blockwise Partition

Abstract

Sparse subspace clustering (SSC) is a classical method to cluster data with specific subspace structure for each group. It has many desirable theoretical properties and has been shown to be effective in various applications. However, under the condition of a large-scale dataset, learning the sparse sample affinity graph is computationally expensive. To tackle the computation time cost challenge, we develop a memory-efficient parallel framework for computing SSC via an alternating direction method of multiplier (ADMM) algorithm. The proposed framework partitions the data matrix into column blocks and then decomposes the original problem into parallel multivariate Lasso regression subproblems and samplewise operations. The proposed method allows us to allocate multiple cores/machines for the processing of individual column blocks. We propose a stochastic optimization algorithm to minimize the objective function. Experimental results on real-world datasets demonstrate that the proposed blockwise ADMM framework is substantially more efficient than its matrix counterpart used by SSC, without sacrificing performance in applications. Moreover, our approach is directly applicable to parallel neighborhood selection for Gaussian graphical models structure estimation.