Regularized ℓ¹-Graph for data clustering

ℓ¹-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 independently without taking into account the geometric structure of the data. Motivated by ℓ¹-Graph and manifold leaning, we propose Regularized ℓ¹-Graph (Rℓ¹-Graph) for data clustering. Compared to ℓ¹-Graph, the sparse representations of Rℓ¹-Graph are regularized by the geometric information of the data. In accordance with the manifold assumption, the sparse representations vary smoothly along the geodesics of the data manifold through the graph Laplacian constructed by the sparse codes. Experimental results on various data sets demonstrate the superiority of our algorithm compared to ℓ¹-Graph and other competing clustering methods.