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In general, low-rank representation (LRR) aims to find the lowest rank representation with respect to a dictionary. In fact, the dictionary is a key aspect of low-rank representation. However, a lot of low-rank representation methods usually use the data itself as a dictionary (i.e., a fixed dictionary), which may degrade their performances due to the lack of clustering ability of a fixed dictionary. To this end, we propose learning a locality-preserving dictionary instead of the fixed dictionary for low-rank representation, where the locality-preserving dictionary is constructed by using a graph regularization technique to capture the intrinsic geometric structure of the dictionary and, hence, the locality-preserving dictionary has an underlying clustering ability. In this way, the obtained low-rank representation via the locality-preserving dictionary has a better grouping-effect representation. Inversely, a better grouping-effect representation can help to learn a good dictionary. The locality-preserving dictionary and the grouping-effect representation interact with each other, where dual pursuit is called. The proposed method, namely, Dual Pursuit for Subspace Learning, provides us with a robust method for clustering and classification simultaneously, and compares favorably with the other state-of-the-art methods.
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