Latent Low-Rank Representation

  • Guangcan Liu
  • Shuicheng Yan


As mentioned at the end of previous chapter, a key aspect of LRR is about the configuration of its dictionary matrix. Usually, the observed data matrix itself is chosen as the dictionary, resulting in a powerful method that is useful for both subspace clustering and error correction. However, such a strategy may depress the performance of LRR, especially when the observations are insufficient and/or grossly corrupted. In this chapter we therefore propose to construct the dictionary by using both observed and unobserved, hidden data. We show that the effects of the hidden data can be approximately recovered by solving a nuclear norm minimization problem, which is convex and can be solved efficiently. The formulation of the proposed method, called Latent Low-Rank Representation (LatLRR), seamlessly integrates subspace clustering and feature extraction into a unified framework, and thus provides us with a solution for both subspace clustering and feature extraction. As a subspace clustering algorithm, LatLRR is an enhanced version of LRR and outperforms the state-of-the-art algorithms. Being an unsupervised feature extraction algorithm, LatLRR is able to robustly extract salient features from corrupted data, and thus can work much better than the benchmark that utilizes the original data vectors as features for classification. Compared to dimension reduction based methods, LatLRR is more robust to noise.


Low-rank representation Latent variables Subspace clustering  Feature extraction Face recognition 


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Cornell UniversityIthacaUSA
  2. 2.National University of SingaporeSingaporeSingapore

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