Data Clustering by Laplacian Regularized l1-Graph

l(1)-Graph has been proven to be effective in data clustering, which partitions the data space by using the sparse representation of the data as the similarity measure. However, the sparse representation is performed for each datum separately without taking into account the geometric structure of the data. Motivated by l(1)-Graph and manifold leaning, we propose Laplacian Regularized l(1)-Graph (LRl(1)-Graph) for data clustering. The sparse representations of LRl(1)-Graph are regularized by the geometric information of the data so that they vary smoothly along the geodesics of the data manifold by the graph Laplacian according to the manifold assumption. Moreover, we propose an iterative regularization scheme, where the sparse representation obtained from the previous iteration is used to build the graph Laplacian for the current iteration of regularization. The experimental results on real data sets demonstrate the superiority of our algorithm compared to l(1)-Graph and other competing clustering methods.