Tensor Decompositions and Algorithms for Efficient Multidimensional Signal Processing PDF Download

Author: Liana Khamidullina
Publisher:
ISBN:
Category :
Languages : en
Pages : 0

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Author: Gérard Favier
Publisher: John Wiley & Sons
ISBN: 1786301555
Category : Technology & Engineering
Languages : en
Pages : 386

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Book Description
The second volume will deal with a presentation of the main matrix and tensor decompositions and their properties of uniqueness, as well as very useful tensor networks for the analysis of massive data. Parametric estimation algorithms will be presented for the identification of the main tensor decompositions. After a brief historical review of the compressed sampling methods, an overview of the main methods of retrieving matrices and tensors with missing data will be performed under the low rank hypothesis. Illustrative examples will be provided.

Author: Yipeng Liu
Publisher: Academic Press
ISBN: 0323859658
Category : Technology & Engineering
Languages : en
Pages : 598

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Book Description
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. Provides a complete reference on classical and state-of-the-art tensor-based methods for data processing Includes a wide range of applications from different disciplines Gives guidance for their application

Author: Oguz Kaya
Publisher:
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Category :
Languages : en
Pages : 0

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Tensor factorization has been increasingly used to analyze high-dimensional low-rank data ofmassive scale in numerous application domains, including recommender systems, graphanalytics, health-care data analysis, signal processing, chemometrics, and many others.In these applications, efficient computation of tensor decompositions is crucial to be able tohandle such datasets of high volume. The main focus of this thesis is on efficient decompositionof high dimensional sparse tensors, with hundreds of millions to billions of nonzero entries,which arise in many emerging big data applications. We achieve this through three majorapproaches.In the first approach, we provide distributed memory parallel algorithms with efficientpoint-to-point communication scheme for reducing the communication cost. These algorithmsare agnostic to the partitioning of tensor elements and low rank decomposition matrices, whichallow us to investigate effective partitioning strategies for minimizing communication cost whileestablishing computational load balance. We use hypergraph-based techniques to analyze computational and communication requirements in these algorithms, and employ hypergraphpartitioning tools to find suitable partitions that provide much better scalability.Second, we investigate effective shared memory parallelizations of these algorithms. Here, we carefully determine unit computational tasks and their dependencies, and express them using aproper data structure that exposes the parallelism underneath.Third, we introduce a tree-based computational scheme that carries out expensive operations(involving the multiplication of the tensor with a set of vectors or matrices, found at the core ofthese algorithms) faster by factoring out and storing common partial results and effectivelyre-using them. With this computational scheme, we asymptotically reduce the number oftensor-vector and -matrix multiplications for high dimensional tensors, and thereby rendercomputing tensor decompositions significantly cheaper both for sequential and parallelalgorithms.Finally, we diversify this main course of research with two extensions on similar themes.The first extension involves applying the tree-based computational framework to computingdense tensor decompositions, with an in-depth analysis of computational complexity andmethods to find optimal tree structures minimizing the computational cost. The second workfocuses on adapting effective communication and partitioning schemes of our parallel sparsetensor decomposition algorithms to the widely used non-negative matrix factorization problem,through which we obtain significantly better parallel scalability over the state of the artimplementations.We point out that all theoretical results in the thesis are nicely corroborated by parallelexperiments on both shared-memory and distributed-memory platforms. With these fastalgorithms as well as their tuned implementations for modern HPC architectures, we rendertensor and matrix decomposition algorithms amenable to use for analyzing massive scaledatasets.

Author: Roumen Kountchev
Publisher: Springer Nature
ISBN: 9811978425
Category : Technology & Engineering
Languages : en
Pages : 287

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Book Description
This book is a collection of papers presented at the International Workshop on New Approaches for Multidimensional Signal Processing (NAMSP 2022), held at Technical University of Sofia, Sofia, Bulgaria, during 23–25 June 2022. The book covers research papers in the field of N-dimensional multicomponent image processing, multidimensional image representation and super-resolution, 3D image processing and reconstruction, MD computer vision systems, multidimensional multimedia systems, neural networks for MD image processing, data-based MD image retrieval and knowledge data mining, watermarking, hiding and encryption of MD images, MD image processing in robot systems, tensor-based data processing, 3D and multi-view visualization, forensic analysis systems for MD images and many more.

Author: Yipeng Liu
Publisher: Springer Nature
ISBN: 3030743861
Category : Technology & Engineering
Languages : en
Pages : 347

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Book Description
Tensor is a natural representation for multi-dimensional data, and tensor computation can avoid possible multi-linear data structure loss in classical matrix computation-based data analysis. This book is intended to provide non-specialists an overall understanding of tensor computation and its applications in data analysis, and benefits researchers, engineers, and students with theoretical, computational, technical and experimental details. It presents a systematic and up-to-date overview of tensor decompositions from the engineer's point of view, and comprehensive coverage of tensor computation based data analysis techniques. In addition, some practical examples in machine learning, signal processing, data mining, computer vision, remote sensing, and biomedical engineering are also presented for easy understanding and implementation. These data analysis techniques may be further applied in other applications on neuroscience, communication, psychometrics, chemometrics, biometrics, quantum physics, quantum chemistry, etc. The discussion begins with basic coverage of notations, preliminary operations in tensor computations, main tensor decompositions and their properties. Based on them, a series of tensor-based data analysis techniques are presented as the tensor extensions of their classical matrix counterparts, including tensor dictionary learning, low rank tensor recovery, tensor completion, coupled tensor analysis, robust principal tensor component analysis, tensor regression, logistical tensor regression, support tensor machine, multilinear discriminate analysis, tensor subspace clustering, tensor-based deep learning, tensor graphical model and tensor sketch. The discussion also includes a number of typical applications with experimental results, such as image reconstruction, image enhancement, data fusion, signal recovery, recommendation system, knowledge graph acquisition, traffic flow prediction, link prediction, environmental prediction, weather forecasting, background extraction, human pose estimation, cognitive state classification from fMRI, infrared small target detection, heterogeneous information networks clustering, multi-view image clustering, and deep neural network compression.

Author: Roumen Kountchev
Publisher: Springer Nature
ISBN: 9813346760
Category : Technology & Engineering
Languages : en
Pages : 268

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Book Description
This book is a collection of papers presented at the International Workshop on New Approaches for Multidimensional Signal Processing (NAMSP 2020), held at Technical University of Sofia, Sofia, Bulgaria, during 09–11 July 2020. The book covers research papers in the field of N-dimensional multicomponent image processing, multidimensional image representation and super-resolution, 3D image processing and reconstruction, MD computer vision systems, multidimensional multimedia systems, neural networks for MD image processing, data-based MD image retrieval and knowledge data mining, watermarking, hiding and encryption of MD images, MD image processing in robot systems, tensor-based data processing, 3D and multi-view visualization, forensic analysis systems for MD images and many more.

Author: Zequn Zheng
Publisher:
ISBN:
Category :
Languages : en
Pages : 0

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Book Description
Tensors or multidimensional arrays are higher order generalizations of matrices. They are natural structures for expressing data that have inherent higher order structures. Tensor decompositions and Tensor approximations play an important role in learning those hidden structures. They have many applications in machine learning, statistical learning, data science, signal processing, neuroscience, and more. Canonical Polyadic Decomposition (CPD) is a tensor decomposition that decomposes a tensor to minimal number of summation of rank 1 tensors. While for a given tensor, Low-Rank Tensor Approximation (LRTA) aims at finding a new one whose rank is small and that is close to the given one. We study the generating polynomials for computing tensor decompositions and low-rank approximations for given tensors and propose methods that can compute tensor decompositions for generic tensors under certain rank conditions. For low-rank tensor approximation, the proposed method guarantees that the constructed tensor is a good enough low-rank approximation if the tensor is to be approximated is close enough to a low-rank one. The proof built on perturbation analysis is presented. When the rank is higher than the second dimension, we are not able to find the common zeros of generating polynomials directly. In this case, we need to use the quadratic equations that we get from those generating polynomials. We show that under certain conditions, we are able to find the tensor decompositions using standard linear algebra operations (i.e., solving linear systems, singular value decompositions, QR decompositions). Numerical examples and some comparisons are presented to show the performance of our algorithm. Multi-view learning is frequently used in data science. The pairwise correlation maximization is a classical approach for exploring the consensus of multiple views. Since the pairwise correlation is inherent for two views, the extensions to more views can be diversified and the intrinsic interconnections among views are generally lost. To address this issue, we propose to maximize the high-order tensor correlation. This can be formulated as a low-rank approximation problem with the high-order correlation tensor of multi-view data. We propose to use the generating polynomial method to efficiently solve the high-order correlation maximization problem of tensor canonical correlation analysis for multi-view learning. Numerical results on simulated data and two real multi-view data sets demonstrate that our proposed method not only consistently outperforms existing methods but also is efficient for large scale tensors.

Author: Andrzej Cichocki
Publisher: John Wiley & Sons
ISBN: 9780470747285
Category : Science
Languages : en
Pages : 500

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This book provides a broad survey of models and efficient algorithms for Nonnegative Matrix Factorization (NMF). This includes NMF’s various extensions and modifications, especially Nonnegative Tensor Factorizations (NTF) and Nonnegative Tucker Decompositions (NTD). NMF/NTF and their extensions are increasingly used as tools in signal and image processing, and data analysis, having garnered interest due to their capability to provide new insights and relevant information about the complex latent relationships in experimental data sets. It is suggested that NMF can provide meaningful components with physical interpretations; for example, in bioinformatics, NMF and its extensions have been successfully applied to gene expression, sequence analysis, the functional characterization of genes, clustering and text mining. As such, the authors focus on the algorithms that are most useful in practice, looking at the fastest, most robust, and suitable for large-scale models. Key features: Acts as a single source reference guide to NMF, collating information that is widely dispersed in current literature, including the authors’ own recently developed techniques in the subject area. Uses generalized cost functions such as Bregman, Alpha and Beta divergences, to present practical implementations of several types of robust algorithms, in particular Multiplicative, Alternating Least Squares, Projected Gradient and Quasi Newton algorithms. Provides a comparative analysis of the different methods in order to identify approximation error and complexity. Includes pseudo codes and optimized MATLAB source codes for almost all algorithms presented in the book. The increasing interest in nonnegative matrix and tensor factorizations, as well as decompositions and sparse representation of data, will ensure that this book is essential reading for engineers, scientists, researchers, industry practitioners and graduate students across signal and image processing; neuroscience; data mining and data analysis; computer science; bioinformatics; speech processing; biomedical engineering; and multimedia.

Author: Artyom M. Grigoryan
Publisher: CRC Press
ISBN: 9780824745967
Category : Technology & Engineering
Languages : en
Pages : 550

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Book Description
This reference presents a more efficient, flexible, and manageable approach to unitary transform calculation and examines novel concepts in the design, classification, and management of fast algorithms for different transforms in one-, two-, and multidimensional cases. Illustrating methods to construct new unitary transforms for best algorithm selection and development in real-world applications, the book contains a wide range of examples to compare the efficacy of different algorithms in a variety of one-, two-, and three-dimensional cases. Multidimensional Discrete Unitary Transforms builds progressively from simple representative cases to higher levels of generalization.