Enforced block diagonal subspace clustering with closed form solution

Highlights：

• The relation between the spectral clustering and the subspace clustering based on block diagonal representation is shown in this work. Specifically, we can conclude that the spectral clustering with radial basis function kernel can be regarded as the proposed EBDSC.

• We propose a novel subspace clustering which satisfies the EBD conditions for effectiveness since the solution is block diagonal if the clustering satisfies EBD conditions and subspaces are independent. Moreover, the proposed enforced block diagonal subspace clustering is general since it can be extended to many cases.

• We show the solution to the proposed enforced block diagonal subspace clustering is analytical, nonnegative and symmetrical. Compared with most existing methods for subspace clustering, the proposed framework simultaneously learns coefficient matrix and conducts the nonnegative and symmetrical constraints, whereas the existing ones use two separate steps to treat them.

• This paper shows a unified clustering framework which jointly considers the EBD conditions and the solution which is analytical, nonnegative and symmetrical. Extensive experiments on benchmark datasets demonstrate the effectiveness and efficiency of our model. Our source codes will be released upon acceptance.