Multi-View Low-Rank Analysis with Applications to Outlier Detection

Detecting outliers or anomalies is a fundamental problem in various machine learning and data mining applications. Conventional outlier detection algorithms are mainly designed for single-view data. Nowadays, data can be easily collected from multiple views, and many learning tasks such as clustering and classification have benefited from multi-view data. However, outlier detection from multi-view data is still a very challenging problem, as the data in multiple views usually have more complicated distributions and exhibit inconsistent behaviors. To address this problem, we propose a multi-view low-rank analysis (MLRA) framework for outlier detection in this article. MLRA pursuits outliers from a new perspective, robust data representation. It contains two major components. First, the cross-view low-rank coding is performed to reveal the intrinsic structures of data. In particular, we formulate a regularized rank-minimization problem, which is solved by an efficient optimization algorithm. Second, the outliers are identified through an outlier score estimation procedure. Different from the existing multi-view outlier detection methods, MLRA is able to detect two different types of outliers from multiple views simultaneously. To this end, we design a criterion to estimate the outlier scores by analyzing the obtained representation coefficients. Moreover, we extend MLRA to tackle the multi-view group outlier detection problem. Extensive evaluations on seven UCI datasets, the MovieLens, the USPS-MNIST, and the WebKB datasets demon strate that our approach outperforms several state-of-the-art outlier detection methods.