Semisupervised Support Vector Machines With Tangent Space Intrinsic Manifold Regularization

• Published in: IEEE transaction on neural networks and learning systems Vol. 27; no. 9; pp. 1827 - 1839
• Main Authors: Sun, Shiliang, Xie, Xijiong
• Format: Journal Article
• Language: English
• Published: United States IEEE 01.09.2016; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Data mining; Laplace equations; Learning; Manifold learning; Manifolds; Principal component analysis; Principal components analysis; Quadratic programming; Regularization; Regularization methods; semisupervised classification; Semisupervised learning; support vector machine (SVM); Support vector machines; tangent space intrinsic manifold regularization; Tangents; twin SVM (TSVM)
• ISSN: 2162-237X; 2162-2388
• DOI: 10.1109/TNNLS.2015.2461009

Semisupervised learning has been an active research topic in machine learning and data mining. One main reason is that labeling examples is expensive and time-consuming, while there are large numbers of unlabeled examples available in many practical problems. So far, Laplacian regularization has been widely used in semisupervised learning. In this paper, we propose a new regularization method called tangent space intrinsic manifold regularization. It is intrinsic to data manifold and favors linear functions on the manifold. Fundamental elements involved in the formulation of the regularization are local tangent space representations, which are estimated by local principal component analysis, and the connections that relate adjacent tangent spaces. Simultaneously, we explore its application to semisupervised classification and propose two new learning algorithms called tangent space intrinsic manifold regularized support vector machines (TiSVMs) and tangent space intrinsic manifold regularized twin SVMs (TiTSVMs). They effectively integrate the tangent space intrinsic manifold regularization consideration. The optimization of TiSVMs can be solved by a standard quadratic programming, while the optimization of TiTSVMs can be solved by a pair of standard quadratic programmings. The experimental results of semisupervised classification problems show the effectiveness of the proposed semisupervised learning algorithms.