A Group Norm Regularized LRR Factorization Model for Spectral Clustering

Spectral clustering is a very important and classic graph clustering method. Its clustering results are heavily dependent on affine matrix produced by data. Solving Low-Rank Representation~(LRR) problems is a very effective method to obtain affine matrix. This paper proposes LRR factorization model based on group norm regularization and uses Augmented Lagrangian Method~(ALM) algorithm to solve this model. We adopt group norm regularization to make the columns of the factor matrix sparse, thereby achieving the purpose of low rank. And no Singular Value Decomposition~(SVD) is required, computational complexity of each step is great reduced. We get the affine matrix by different LRR model and then perform cluster testing on synthetic noise data and real data~(Hopkin155 and EYaleB) respectively. Compared to traditional models and algorithms, ours are faster to solve affine matrix and more robust to noise. The final clustering results are better. And surprisingly, the numerical results show that our algorithm converges very fast, and the convergence condition is satisfied in only about ten steps. Group norm regularized LRR factorization model with the algorithm designed for it is effective and fast to obtain a better affine matrix.