A unified dimensionality reduction framework for semi-paired and semi-supervised multi-view data

semi-supervised multi-view data Xiaohong Chen, Songcan Chen, Hui Xue , Xudong Zhou 1 Department of Mathematics, Nanjing University of Aeronautics & Astronautics, Nanjing, 210016, China 2 Department of Computer Science and Engineering, Nanjing University of Aeronautics & Astronautics, Nanjing, 210016, China 3 State Key Laboratory for Novel Software Technology, Nanjing University, Nanjing, 210093, China 4 School of Computer Science and Engineering, Southeast University, Nanjing, 210096, China Abstract—Canonical correlation analysis (CCA) is a popular and powerful dimensionality reduction method to analyze paired multi-view data. However, when facing semi-paired and semi-supervised multi-view data which widely exist in real-world problems, CCA usually performs poorly due to its requirement of data pairing between different views and un-supervision in nature. Recently, several extensions of CCA have been proposed, however, they just handle the semi-paired scenario by utilizing structure information in each view or just deal with semi-supervised scenario by incorporating the discriminant information. In this paper, we present a general dimensionality reduction framework for semi-paired and semi-supervised multi-view data which naturally generalizes existing related works by using different kinds of prior information. Based on the framework, we develop a novel dimensionality reduction method, termed as semi-paired and semi-supervised generalized correlation analysis (SGCA). SGCA exploits a small amount of paired data to perform CCA and at the same time, utilizes both the global structural information captured from the unlabeled data and the local discriminative information captured from the limited labeled data to compensate the limited pairedness. Consequently, SGCA can find the directions which make not only maximal correlation between the paired data but also maximal separability of the labeled data. Experimental results on artificial and four real-world datasets show its effectiveness compared to the existing related dimensionality reduction methods.