Robust Joint Graph Sparse Coding for Unsupervised Spectral Feature Selection

• Published in: IEEE transaction on neural networks and learning systems Vol. 28; no. 6; pp. 1263 - 1275
• Main Authors: Zhu, Xiaofeng, Li, Xuelong, Zhang, Shichao, Ju, Chunhua, Wu, Xindong
• Format: Journal Article
• Language: English
• Published: United States IEEE 01.06.2017; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Coding; Computational modeling; Data models; Design optimization; Dimensionality reduction; Embedding; Encoding; Graphical representations; Learning systems; Linear programming; manifold learning; Manifolds; Objective function; Outliers (statistics); regression; Robustness; Robustness (mathematics); sparse coding; State of the art
• ISSN: 2162-237X; 2162-2388
• DOI: 10.1109/TNNLS.2016.2521602

In this paper, we propose a new unsupervised spectral feature selection model by embedding a graph regularizer into the framework of joint sparse regression for preserving the local structures of data. To do this, we first extract the bases of training data by previous dictionary learning methods and, then, map original data into the basis space to generate their new representations, by proposing a novel joint graph sparse coding (JGSC) model. In JGSC, we first formulate its objective function by simultaneously taking subspace learning and joint sparse regression into account, then, design a new optimization solution to solve the resulting objective function, and further prove the convergence of the proposed solution. Furthermore, we extend JGSC to a robust JGSC (RJGSC) via replacing the least square loss function with a robust loss function, for achieving the same goals and also avoiding the impact of outliers. Finally, experimental results on real data sets showed that both JGSC and RJGSC outperformed the state-of-the-art algorithms in terms of k -nearest neighbor classification performance.