Coupled low rank representation and subspace clustering

Subspace clustering is a technique utilized to find clusters within multiple subspaces. However, most existing methods cannot obtain an accurate block diagonal clustering structure to improve clustering performance. This drawback exists because these methods learn the similarity matrix in advance by utilizing a low dimensional matrix obtained directly from the data, where two unrelated data samples can stay related easily due to the influence of noise. This paper proposes a novel method based on coupled low-rank representation to tackle the above problem. First, our method constructs a manifold recovery structure to correct inadequacy in the low-rank representation of data. Then it obtains a clustering projection matrix that obeys the k-block diagonal property to learn an ideal similarity matrix. This similarity matrix denotes our clustering structure with a rank constraint on its normalized Laplacian matrix. Therefore, we avoid k-means spectral post-processing of the low dimensional embedding matrix, unlike most existing methods. Furthermore, we couple our method to allow the clustering structure to adaptively approximate the low-rank representation so as to find more optimal solutions. Several experiments on benchmark datasets demonstrate that our method outperforms similar state-of-the-art methods in Accuracy, Normalized Mutual Information, F-score, Recall, Precision, and Adjusted Rand Index evaluation metrics.