A Hyperplane Clustering Algorithm for Estimating the Mixing Matrix in Sparse Component Analysis

摘要

The method of sparse component analysis in general has two steps: the first step is to identify the mixing matrix \(\mathbf {A}\) in the linear model \(\mathbf {X}=\mathbf {AS}\), and the second step is to recover the sources \(\mathbf {S}\). To improve the first step, we propose a novel hyperplane clustering algorithm under some sparsity assumptions of the latent components \(\mathbf {S}\). We apply an existing clustering function with some modifications to detect the normal vectors of the hyperplanes concentrated by observed data \(\mathbf {X}\), then those normal vectors are clustered to identify the mixing matrix \(\mathbf {A}\). An adaptive gradient method is developed to optimize the clustering function. The experimental results indicate that our algorithm is faster and more effective than the existing algorithms. Moreover, our algorithm is robust to the insufficient sparse sources, and can be used in a sparser source assumption.