Multi-View Manifold Representation For Multimedia Data Analysis

Most problems of machine learning engage in handling large amount of high-dimensional multimedia data.Also,how to extract discriminative features from nonlinear multiple modalities of multimedia data is a challenge to most algorithms.This dissertation presents solutions to these challenges by exploiting the property that,data in high-dimensions often lies in lower-dimensions in real-world applications and its geometry can be represented as a manifold or graph.Particularly,a significant progress is made with a presentation of three novel methods for multimedia data analysis.These include dictionary-induced least squares framework with multi-manifold embeddings,a generalized multi-dictionary least squares framework regularized with multi-graph embeddings,and manifold alignment via global and local structures preserving PCA framework.The first approach extends the principal component analysis(PCA)idea of minimizing least squares reconstruction errors to include data distribution and a dictionary to rediscover outliers-free global structure from missing and noisy data points.It further includes multiple manifold embeddings to preserve non-redundant local structure.Thus,this approach can obtain discriminative information in lower-dimensional projections while maintaining a balance in preserving both global and local structures.Extensive experiments in multimedia data analysis show that the proposed approach has superior performance compare to state-of-the-art methods.Furthermore,a second approach is proposed to include multiple dictionaries;an extension to the first approach.The multiple dictionaries further enhance discrimination against noise and redundant data points that characterize multi-view datasets.Then by evaluating these multiple dictionaries base on two different constraints,two novel methods with close-form solutions are further developed under this approach.Experimental results show improvements of the proposed approach over the comparative methods which are statistically significant below the 0.05 significance level.Finally,we proposed a manifold alignment framework that can align manifolds across instances and also across features,while preserving both global and local domain structures in multiple datasets.We preserve local structure through multiple manifold embedding methods.Moreover,we view manifold embedding methods as special forms of PCA and thus,present a dictionary PCA approach to preserve noise-free global structure.Finally,a close-form solution is presented in manifold alignment.This approach can concurrently match pair-wise correspondence and preserve both global and local structures of each dataset to obtain a latent low-dimensional space.Extensive experiments prove that the proposed approach achieves significantly better results than the comparative methods.