关键词: p-Laplacian算子, 局部相似性, 自适应和最优近邻, 秩约束

Abstract: Spectral clustering algorithm can obtain a better graph cut criterion by introducing p-Laplacian operator. But the similarity matrix doesn't fully exploit the local information of the dataset in the algorithm. Simultaneously, the similarity measurement and data clustering are often conducted in two seperated steps, the learned data similarity may not be optimal one for data clustering and lead to the suboptimal results. Therefore, this paper proposes p-spectral clustering algorithm with the optimization of local similarity. The algorithm learns the data similarity matrix by assigning the adaptive and optimal neighbors for each data point based on the local distances. Meanwhile, the new rank constraint is imposed to the Laplacian matrix of the data similarity matrix, such that the connected components in the resulted similarity matrix are exactly equal to the cluster number. The experiments show that p-spectral clustering algorithm based on local similarity optimization can produce better clustering results.

Key words: p-Laplacian operator, local similarity, adaptive and optimal neighbors, rank constraint