A Deterministic Analysis for LRR.

The recently proposed low-rank representation (LRR) method has been empirically shown to be useful in various tasks such as motion segmentation, image segmentation, saliency detection and face recognition. While potentially powerful, LRR depends heavily on the configuration of its key parameter, $\lambda$<alternatives><inline-graphic xlink:type="simple" xlink:href="liu-ieq1-2453969.gif"/></alternatives> . In realistic environments where the prior knowledge about data is lacking, however, it is still unknown how to choose $\lambda$<alternatives> <inline-graphic xlink:type="simple" xlink:href="liu-ieq2-2453969.gif"/></alternatives> in a suitable way. Even more, there is a lack of rigorous analysis about the success conditions of the method, and thus the significance of LRR is a little bit vague. In this paper we therefore establish a theoretical analysis for LRR, striving for figuring out under which conditions LRR can be successful, and deriving a moderately good estimate to the key parameter $\lambda$<alternatives><inline-graphic xlink:type="simple" xlink:href="liu-ieq3-2453969.gif"/> </alternatives> as well. Simulations on synthetic data points and experiments on real motion sequences verify our claims. [ABSTRACT FROM PUBLISHER]