关键词: 分式函数, 稀疏表示, 块对角结构, 子空间聚类, 谱聚类

Abstract:

This paper proposes a novel sparse subspace clustering model which is based on the constraints of fractional function in order to overcome the shortcoming of sparse subspace clustering algorithm that the coefficient matrix obtained by this algorithm cannot reflect the sparsity of data distribution in high-dimensional space accurately and solves this model by applying the alternating direction iteration method. It is proved that the coefficient matrix obtained by this method has block diagonal structure without any noise, which provides a theoretical guarantee to acquire its data structure accurately. Under the condition of noise, the fractional function constraint is also used as the regular term for outlier noise to improve the robustness of the model. Experimental results on artificial data sets, Extended Yale B database and Hopkins155 data set show that the sparse subspace clustering method based on fractional function constraint not only improves the accuracy of clustering results and also improves the robustness to outlier noise.

Key words: fractional function, sparse representation, block diagonal structure, subspace clustering, spectral clustering