Shared Subspace Learning For Multi-view Data Analysis

With the rapid development of information technology, more and more digital data that people produced and collected in their daily lives has become increasingly accessible. Together with the high dimensionality of them, these digital data appears to be more complex due to their diversified characteristics of multi-modal, multi-source and multi-description. Therefore, these complex digital data are generally called multi-view data. The pervasive existence of multi-view data has made conventional single view data analysis methods confront with great challenge. The research on multi-view analysis methods has become one of active topics in the field of machine learning.From the point of shared subspace learning, this paper focuses on mining the potential shared information by constructing the correlation in a shared subspace. Towards the problems of local structure preservation, discrimination, and small sample in shared subspace learning, the main contributions of this dissertation are as follows:1. This paper proposes a model of local structure preserved discriminant multi-view analysis. In order to preserve the local geometrical structure of data in both shared subspace and original multi-view feature spaces, a graph constraint is introduced. Meanwhile, with the assist of prior class label, the boosted generalization ability of the proposed multi-view analysis model has been achieved. The experiments on the multi-view data retrieval and classification verify the effectiveness of the proposed model.2. For the small sample problem in the multi-view analysis, a new Tri-factorization based shared subspace analysis method for multi-view data is presented, which has been further shown to come down to a generalized singular value decomposition problem. In addition, an online extension for out-of-sample is also provided to avoid the high computational complexity of online learning.3. By developing the conventional canonical correlation analysis (CCA), this paper propose a more general correlation analysis model for multi-view data, which we name by generalized canonical correlation analysis (GCCA). On this basis, a cross graph constraint is proposed, with which both the local geometrical structure and the correlation characteristic of multi-view data can be guaranteed. To solve the non-convex optimization problem of the proposed GCCA, an efficient sequential optimization method is provided.