Most existing approaches address multi-view subspace clustering problem byconstructing the affinity matrix on each view separately and afterwards proposehow to extend spectral clustering algorithm to handle multi-view data. Thispaper presents an approach to multi-view subspace clustering that learns ajoint subspace representation by constructing affinity matrix shared among allviews. Relying on the importance of both low-rank and sparsity constraints inthe construction of the affinity matrix, we introduce the objective thatbalances between the agreement across different views, while at the same timeencourages sparsity and low-rankness of the solution. Related low-rank andsparsity constrained optimization problem is for each view solved using thealternating direction method of multipliers. Furthermore, we extend ourapproach to cluster data drawn from nonlinear subspaces by solving thecorresponding problem in a reproducing kernel Hilbert space. The proposedalgorithm outperforms state-of-the-art multi-view subspace clusteringalgorithms on one synthetic and four real-world datasets.
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