Outlier Detection via Kernel Preserving Embedding and Random Walk

Since outlier detection has a wide range of potential applications, it has become a fundamental and hot research topic in data mining. Recently, the technique of self-representation has attracted extensive attention and many low-rank representation based outlier detection algorithms have been witnessed. However, most of them pay more attention to minimize the reconstruction error of the data, without involving the manifold structure. Meanwhile, as a low-rank constraint, the single nuclear norm often leads to suboptimal solution. To alleviate these problems, in this paper, we propose a novel outlier detection method, which adopts kernel-based distance to retain the overall relations. Moreover, the double nuclear norm is exploited to address the suboptimal problem. Further, a tailored random walk is used to identify outliers, after the similarity relations of the data available. The extensive simulation experiments on five public datasets demonstrate the superiority of the proposed method in comparing to the state-of-the-art outlier detection algorithms.