Algorithms And Applications Of Multi-view Canonical Correlation Analysi

In resent years,the study about multi-view is wildly applied in the fields that include the biomedicine,the image processing,the satellite data analysis,the cross-lingual text analysis,the heterogeneous recognition or cross-view recognition and so on.In these real applications,data points usually have the multi-view structure.It will result in information missing and incapable of mining the underlying structure and characteristics of the data if these data points are viewed as the single view.Thus,it is very important to make use of multi-view information.The multiview canonical analysis(MCCA)is a multivariable statistical approach which aims at fusing each sub-variables(ie.each view)into a reduced one through a linear combination so that the fused m random variables achieve the maximum of a certain type of correlation.When the number of views m>2 and each reduced variable is one dimension,the model is commonly referred to as the maximal correlation problem(MCP).Existing methods for MCP may encounter slow convergence or inapplicable in the applications with high-dimensional features.Our goal is that provides a Krylov subspace type method by exploiting the special structure of the constraint.Both the global convergence and the local convergence rate are performed,and numerical verification of the efficiency is carried out on both synthetic examples and applications of the unsupervised feature fusion with real data.When the number of views m≥ 2 and each reduced variable is multiple dimensions,the model is commonly referred to as the MAXBET problem.For MAXBET,we are interested in establishing the connection of the MAXBET problem with a special nonlinear eigenvalue system.Based on the connection,we derive a novel and efficient algorithm that is self-consistentfield iteration(SCF)to tackle MAXBET and demonstrate the efficiency of the algorithm on both theoretical analysis and numerical testing.Furthermore,existing multi-view subspace learning methods mostly focus on shared features from all views via consistency,and so they do not specifically explore any view-specific information but suppress it.A few studies recently exploited both shared and view-specific features,but they are restricted to very limited and specific learning tasks such as clustering or to homogeneous features.We propose a new multi-view subspace learning framework to model shared and view-specific features through data reconstruction perspective.In the new framework,not only each view can be reconstructed from both shared and its view-specific features,but also the projections that produce the shared and view-specific features are mutually orthogonal.Two models are instantiated from the proposed framework with customized regularization for unsupervised and supervised learning.A novel optimization method is proposed to solve resulting challenging optimization problems with theoretically guaranteed convergence.Extensive experiments demonstrate that our proposed models produce superior learning results to existing methods.