http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
Tensors for Data Processing: Theory, Methods and Applications presents both classical and state-of-the-art methods on tensor computation for data processing, covering computation theories, processing methods, computing and engineering applications, with an emphasis on techniques for data processing. This reference is ideal for students, researchers and industry developers who want to understand and use tensor-based data processing theories and methods. As a higher-order generalization of a matrix, tensor-based processing can avoid multi-linear data structure loss that occurs in classical matrix-based data processing methods. This move from matrix to tensors is beneficial for many diverse application areas, including signal processing, computer science, acoustics, neuroscience, communication, medical engineering, seismology, psychometric, chemometrics, biometric, quantum physics and quantum chemistry.
Front Cover -- Tensors for Data Processing -- Copyright -- Contents -- List of contributors -- Preface -- 1 Tensor decompositions: computations, applications, and challenges -- 1.1 Introduction -- 1.1.1 What is a tensor? -- 1.1.2 Why do we need tensors? -- 1.2 Tensor operations -- 1.2.1 Tensor notations -- 1.2.2 Matrix operators -- 1.2.3 Tensor transformations -- 1.2.4 Tensor products -- 1.2.5 Structural tensors -- 1.2.6 Summary -- 1.3 Tensor decompositions -- 1.3.1 Tucker decomposition -- 1.3.2 Canonical polyadic decomposition -- 1.3.3 Block term decomposition
1.3.4 Tensor singular value decomposition -- 1.3.5 Tensor network -- 1.3.5.1 Hierarchical Tucker decomposition -- 1.3.5.2 Tensor train decomposition -- 1.3.5.3 Tensor ring decomposition -- 1.3.5.4 Other variants -- 1.4 Tensor processing techniques -- 1.5 Challenges -- References -- 2 Transform-based tensor singular value decomposition in multidimensional image recovery -- 2.1 Introduction -- 2.2 Recent advances of the tensor singular value decomposition -- 2.2.1 Preliminaries and basic tensor notations -- 2.2.2 The t-SVD framework -- 2.2.3 Tensor nuclear norm and tensor recovery
2.2.4 Extensions -- 2.2.4.1 Nonconvex surrogates -- 2.2.4.2 Additional prior knowledge -- 2.2.4.3 Multiple directions and higher-order tensors -- 2.2.5 Summary -- 2.3 Transform-based t-SVD -- 2.3.1 Linear invertible transform-based t-SVD -- 2.3.2 Beyond invertibility and data adaptivity -- 2.4 Numerical experiments -- 2.4.1 Examples within the t-SVD framework -- 2.4.2 Examples of the transform-based t-SVD -- 2.5 Conclusions and new guidelines -- References -- 3 Partensor -- 3.1 Introduction -- 3.1.1 Related work -- 3.1.2 Notation -- 3.2 Tensor decomposition -- 3.2.1 Matrix least-squares problems
3.2.1.1 The unconstrained case -- 3.2.1.2 The nonnegative case -- 3.2.1.3 The orthogonal case -- 3.2.2 Alternating optimization for tensor decomposition -- 3.3 Tensor decomposition with missing elements -- 3.3.1 Matrix least-squares with missing elements -- 3.3.1.1 The unconstrained case -- 3.3.1.2 The nonnegative case -- 3.3.2 Tensor decomposition with missing elements: the unconstrained case -- 3.3.3 Tensor decomposition with missing elements: the nonnegative case -- 3.3.4 Alternating optimization for tensor decomposition with missing elements -- 3.4 Distributed memory implementations
3.4.1 Some MPI preliminaries -- 3.4.1.1 Communication domains and topologies -- 3.4.1.2 Synchronization among processes -- 3.4.1.3 Point-to-point communication operations -- 3.4.1.4 Collective communication operations -- 3.4.1.5 Derived data types -- 3.4.2 Variable partitioning and data allocation -- 3.4.2.1 Communication domains -- 3.4.3 Tensor decomposition -- 3.4.3.1 The unconstrained and the nonnegative case -- 3.4.3.2 The orthogonal case -- 3.4.3.3 Factor normalization and acceleration -- 3.4.4 Tensor decomposition with missing elements -- 3.4.4.1 The unconstrained case
Includes bibliographical references and index.
San Diego : Elsevier Science & Technology, ©2021