Similarity representation plays a central role in increasingly popular anomaly detection techniques, which have been successfully applied in various realistic scenes. Until now, many low-rank representation techniques have been introduced to measure the similarity relations of data; yet, they only concern to minimize reconstruction errors, without involving the structural information of data. Besides, the traditional low-rank representation methods often take nuclear norm as their low-rank constraints, easily yielding a suboptimal solution. To address the problems above, in this article, we propose a novel anomaly detection method, which exploits kernel preserving embedding, as well as the double nuclear norm, to explore the similarity relations of data. Based on the similarity relations, a kind of probability transition matrix is derived, and a tailored random walk is further adopted to reveal anomalies. The proposed method can not only preserve the manifold structural properties of the data, but also alleviate the suboptimal problem. To validate the superiority of our method, extensive experiments with eight popular anomaly detection algorithms were conducted on 12 widely used datasets. The experimental results show that our detection method outperformed the state-of-the-art anomaly detection algorithms in most cases.
LogDet Rank Minimization with Application to Subspace Clustering