Provable Self-Representation Based Outlier Detection in a Union of Subspaces
This addresses the problem of detecting outliers in computer vision data, but it is incremental as it builds on existing sparse and low-rank representation methods.
The paper tackles outlier detection in data with inliers lying in low-dimensional subspaces by proposing a method that combines sparse representation with random walks on a graph, achieving superior performance compared to state-of-the-art methods in experiments on image databases.
Many computer vision tasks involve processing large amounts of data contaminated by outliers, which need to be detected and rejected. While outlier detection methods based on robust statistics have existed for decades, only recently have methods based on sparse and low-rank representation been developed along with guarantees of correct outlier detection when the inliers lie in one or more low-dimensional subspaces. This paper proposes a new outlier detection method that combines tools from sparse representation with random walks on a graph. By exploiting the property that data points can be expressed as sparse linear combinations of each other, we obtain an asymmetric affinity matrix among data points, which we use to construct a weighted directed graph. By defining a suitable Markov Chain from this graph, we establish a connection between inliers/outliers and essential/inessential states of the Markov chain, which allows us to detect outliers by using random walks. We provide a theoretical analysis that justifies the correctness of our method under geometric and connectivity assumptions. Experimental results on image databases demonstrate its superiority with respect to state-of-the-art sparse and low-rank outlier detection methods.