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Multidimensional Information Processing With Tensor Representation

Posted on:2015-08-25Degree:DoctorType:Dissertation
Country:ChinaCandidate:W W GuoFull Text:PDF
GTID:1228330479979621Subject:Information and Communication Engineering
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Tensors are arrays of data with more than two dimensions that generalize the concepts of vectors and matrices. They are natural representations of most of physical data in real world. This leads to a progressing need for analysis and knowledge extraction from such tensorial structured data. Tensor decompositions are a powerful technique which have been finding their emerging applications in pattern recognition, machine learning,computer vision, signal processing, web mining, bioinformatics and mentioned a few.In this thesis, we exploit the advantages of tensorial representations and develop taskdriven tensor decomposition techniques to obtain more efficient representations adapted to a wide variety of tasks.The contributions of this thesis are summarized as the following:1. Introduces a unifying task-driven tensor decomposition framework for systematic treatment of the tensor decomposition. It exploits intrinsic geometric manifold, low rank structure information of data and utilizes the label information to enhance the data representations adapted to a wide variety of tasks.2. Presents a novel unsupervised multilinear subspace learning approach integrating clustering and discriminative learning. This method first groups the data points into clusters in a embedding space by graph embedding method that captures the local geometric structure of the manifold which the data points may be on or around. Following it, the multiple projections matrices for higher-order tensor data are it- eratively learned by maximizing the clustering performance under the Fisher ra-tio criterion, i.e., maximizing the inter-cluster scatters while minimizing the intra-cluster scatters. Experimental results of face recognition tasks on two public dataset demonstrate the effectiveness of the proposed method.3. Presents a novel non-negative matrix and tensor factorization with two addition-al hard and soft constraints to obtain more physical interpretable representations.Specifically, the hard constraints conveyed by the labelled data points are imposed on the representation we explore to be consistent with labels. It is leading that the data points that belong to the same class have the same low dimensional represen-tation. Furthermore, the soft constraint is imposed by regularizing the factorization by a graph Laplacian regularization term. This soft constraint is motivated to pre-serves the local geometry structure of manifold that the data may reside and requires that the learned representations of the nearby points be as close as possible. The re-sulted constrained optimization problem is solved with multiplicative update rules.Experimental results of semi-supervised face recognition task on several publicly available datasets demonstrate that proposed method performs in par or consider-ably better than state of the art methods.4. Introduces supervised PARAFAC decomposition of tensors of multiple modes and allows the simultaneous projections of an input tensor to more than one direction-s along each mode. Two empirical risk functions are studied, namely the square loss and the ?-insensitive loss functions. The former leads to higher rank Tensor Ridge Regression(hr TRR) and the latter to higher rank Support Tensor Regres-sion(hr STR), both formulated using the Frobenius norm for regularization. We also use the group sparsity norm for regularization, favouring in that way the low rank decomposition of the tensorial weight. In that way we achieve the automatic selection of the rank during the learning process and obtain the optimal rank TR-R(or TRR) and optimal rank STR(or STR). Experiments conducted for the prob-lems of head pose, human age and 3D body pose estimation using real data from publicly available databases, verified not only the superiority of tensors over their vector-counterparts but also the efficiency of the proposed algorithms.5. Introduced sparse Bayesian PARAFAC decomposition for high resolution parame-ters estimation for multidimensional harmonic Retrieval problem and real-time 3Dacoustic imaging. Since exact Bayesian estimation of the unknown parameters is intractable, an approximation scheme based on Variational Bayesian principle is de-veloped. The significant features of this approach are that the unknown number of targets are efficiently estimated as a part of Bayesian inference process and more-over, it provides high estimation performance. Experimental results on MIMO radar multidimensional Do A estimation and real-time 3D acoustic imaging demonstrate the effectiveness of the proposed method.
Keywords/Search Tags:Tensor, PARAFAC, TUCKER, Spectral Clustering, Manifold Learn-ing, Graph Regularized, Nonnegative Matrix Factorization, Nonnegative Tensor Factorization, Sparse Bayesian Learning, Tensor Regression, Face Recognition, Head Pose Estimation, Age Estimation
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