An Efficient K-Hyperplane Clustering Algorithm and Its Application to Sparse Component Analysis

Based on eigenvalue decomposition, a novel efficient K-HPC algorithm is developed in this paper, which is easy to implement. And it enables us to detect the number of hyperplanes and helps to avoid local minima by overestimating the number of hyperplanes. A confidence index is proposed to evaluate which estimated hyperplanes are most significant and which are spurious. So we can choose those significant hyperplanes with high rank priority and remove the spurious hyperplanes according to their corresponding confidence indices. Furthermore, a multilayer clustering framework called “multilayer K-HPC” is proposed to further improve the clustering results. The K-HPC approach can be directly applied to sparse component analysis (SCA) to develop efficient SCA algorithm. Two examples including a sparse component analysis example demonstrate the proposed algorithm.