Laplacian Regularized Low Rank Representation and Its Applications
Low rank representation (LRR) has recently attracted a great deal of attention due to its pleasing efficacy in exploring low dimensional subspace structures embedded in data. For a given set of observed data corrupted with sparse errors, LRR aims at learning a lowest rank representation of all data jointly. LRR has broad applications in pattern recognition, computer vision and signal processing. In the real world, data often reside on low dimensional manifolds embedded in a high dimensional ambient space. However, the LRR method does not take into account the non linear geometric structures within data, thus the locality and similarity information among data may be missing in the learning process. To improve LRR in this regard, we propose a general Laplacian regularized low rank representation framework for data representation where a hypergraph Laplacian regularizer can be readily introduced into, i.e. a Non negative Sparse Hyper Laplacian regularized LRR model (NSHLRR) By taking advantage of the graph regularizer, our proposed method not only can represent the global low dimensional structures, but also capture the intrinsic non linear geometric information in data. The extensive experimental results on image clustering, semi supervised image classification and dimensionality reduction tasks demonstrate the effectiveness of the proposed method.
IEEE Transactions on Pattern Analysis and Machine Intelligence