Scaled Simplex Representation for Subspace Clustering
This work provides an incremental improvement for researchers and practitioners in machine learning and computer vision by enhancing subspace clustering techniques for data analysis tasks.
The paper tackles the problem of subspace clustering by addressing the negative entries in coefficient matrices and inflexible affine constraints in existing methods, introducing a scaled simplex representation (SSR) that improves accuracy and efficiency, with experiments showing it outperforms state-of-the-art methods on benchmark datasets.
The self-expressive property of data points, i.e., each data point can be linearly represented by the other data points in the same subspace, has proven effective in leading subspace clustering methods. Most self-expressive methods usually construct a feasible affinity matrix from a coefficient matrix, obtained by solving an optimization problem. However, the negative entries in the coefficient matrix are forced to be positive when constructing the affinity matrix via exponentiation, absolute symmetrization, or squaring operations. This consequently damages the inherent correlations among the data. Besides, the affine constraint used in these methods is not flexible enough for practical applications. To overcome these problems, in this paper, we introduce a scaled simplex representation (SSR) for subspace clustering problem. Specifically, the non-negative constraint is used to make the coefficient matrix physically meaningful, and the coefficient vector is constrained to be summed up to a scalar s<1 to make it more discriminative. The proposed SSR based subspace clustering (SSRSC) 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 SSRSC algorithm is very efficient and outperforms state-of-the-art subspace clustering methods on accuracy. The code can be found at https://github.com/csjunxu/SSRSC.