Simplex Representation for Subspace Clustering

07/26/2018 ∙ by Jun Xu, et al. ∙ 8

Spectral clustering based methods have achieved leading performance on subspace clustering problem. State-of-the-art subspace clustering methods follow a three-stage framework: compute a coefficient matrix from the data by solving an optimization problem; construct an affinity matrix from the coefficient matrix; and obtain the final segmentation by applying spectral clustering to the affinity matrix. To construct a feasible affinity matrix, these methods mostly employ the operations of exponentiation, absolutely symmetrization, or squaring, etc. However, all these operations will force the negative entries (which cannot be explicitly avoided) in the coefficient matrix to be positive in computing the affinity matrix, and consequently damage the inherent correlations among the data. In this paper, we introduce the simplex representation (SR) to remedy this problem of representation based subspace clustering. We propose an SR based least square regression (SRLSR) model to construct a physically more meaningful affinity matrix by integrating the nonnegative property of graph into the representation coefficient computation while maintaining the discrimination of original data. The SRLSR model is reformulated as a linear equality-constrained problem, which is solved efficiently under the alternating direction method of multipliers framework. Experiments on benchmark datasets demonstrate that the proposed SRLSR algorithm is very efficient and outperforms state-of-the-art subspace clustering methods on accuracy.



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