Subspace Clustering via Block-Diagonal Decomposition

The subspace clustering has been addressed by learning the block-diagonal self-expressive matrix. This block-diagonal structure heavily affects the accuracy of clustering but is rather challenging to obtain. A novel and effective subspace clustering model, i.e., subspace clustering via block-diagonal decomposition (SCBD), is proposed, which can simultaneously capture the block-diagonal structure and gain the clustering result. In our model, a strict block-diagonal decomposition is introduced to directly pursue the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$k$</tex> block-diagonal structure corresponding to <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$k$</tex> clusters. In this novel decomposition, the self-expressive matrix is decomposed into the block indicator matrix to demonstrate the cluster each sample belongs to. Based on the strict block-diagonal decomposition, the block-diagonal shift is proposed to capture the local intra-cluster structure, which shifts the samples in the same cluster to get smaller distances and results in more discriminative features for clustering. Extensive experimental results on synthetic and real databases demonstrate the superiority of SCBD over other state-of-the-art methods.