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Mathematical Problems in Engineering
Volume 2015 (2015), Article ID 706180, 10 pages
Research Article

Semisupervised Tangent Space Discriminant Analysis

Shanghai Key Laboratory of Multidimensional Information Processing, Department of Computer Science and Technology, East China Normal University, 500 Dongchuan Road, Shanghai 200241, China

Received 8 July 2014; Revised 5 November 2014; Accepted 14 November 2014

Academic Editor: Xin Xu

Copyright © 2015 Yang Zhou and Shiliang Sun. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A novel semisupervised dimensionality reduction method named Semisupervised Tangent Space Discriminant Analysis (STSD) is presented, where we assume that data can be well characterized by a linear function on the underlying manifold. For this purpose, a new regularizer using tangent spaces is developed, which not only can capture the local manifold structure from both labeled and unlabeled data, but also has the complementarity with the Laplacian regularizer. Furthermore, STSD has an analytic form of the global optimal solution which can be computed by solving a generalized eigenvalue problem. To perform nonlinear dimensionality reduction and process structured data, a kernel extension of our method is also presented. Experimental results on multiple real-world data sets demonstrate the effectiveness of the proposed method.