Robust Graph Dimensionality Reduction

In this paper, we propose conducting Robust Graph Dimensionality Reduction (RGDR) by learning a transformation matrix to map original high-dimensional data into their low-dimensional intrinsic space without the influence of outliers. To do this, we propose simultaneously 1) adaptively learning three variables, \ie a reverse graph embedding of original data, a transformation matrix, and a graph matrix preserving the local similarity of original data in their low-dimensional intrinsic space; and 2) employing robust estimators to avoid outliers involving the processes of optimizing these three matrices. As a result, original data are cleaned by two strategies, \ie a prediction of original data based on three resulting variables and robust estimators, so that the transformation matrix can be learnt from accurately estimated intrinsic space with the helping of the reverse graph embedding and the graph matrix. Moreover, we propose a new optimization algorithm to the resulting objective function as well as theoretically prove the convergence of our optimization algorithm. Experimental results indicated that our proposed method outperformed all the comparison methods in terms of different classification tasks.

Authors

• Xiaofeng Zhu Guangxi Key Lab of Multisource Information Mining Security, Guangxi Normal University School of Computer Science and Engineering, University of Electronic Science and Technology of China
• Cong Lei
• Hao Yu University of Oulu
• Yonggang Li
• Jiangzhang Gan School of Computer Science and Technology, Hainan University, Haikou 570228, China
• Shichao Zhang Guangxi Normal University

Keywords

• Machine Learning: Dimensionality Reduction and Manifold Learning
• Machine Learning: Feature Selection; Learning Sparse Models
• Machine Learning: Unsupervised Learning