This paper proposes a one-step spectral clustering method by learning an intrinsic affinity matrix (i.e., the clustering result) from the low-dimensional space (i.e., intrinsic subspace) of original data. Specifically, the intrinsic affinity matrix is learnt by: 1) the alignment of the initial affinity matrix learnt from original data; 2) the adjustment of the transformation matrix, which transfers the original feature space into its intrinsic subspace by simultaneously conducting feature selection and subspace learning; and 3) the clustering result constraint, i.e., the graph constructed by the intrinsic affinity matrix has exact c connected components where c is the number of clusters. In this way, two affinity matrices and a transformation matrix are iteratively updated until achieving their individual optimum, so that these two affinity matrices are consistent and the intrinsic subspace is learnt via the transformation matrix. Experimental results on both synthetic and benchmark datasets verified that our proposed method outputted more effective clustering result than the previous clustering methods.
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