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# Matrix And Tensor Decomposition

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**📒Matrix And Tensor Factorization Techniques For Recommender Systems ✍ Panagiotis Symeonidis**

**Matrix and Tensor Factorization Techniques for Recommender Systems**

✏Author :

**Panagiotis Symeonidis**

✏Publisher :

**Springer**

✏Release Date :

**2017-01-29**

✏Pages :

**102**

✏ISBN :

**9783319413570**

✏Available Language :

**English, Spanish, And French**

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**✏Matrix and Tensor Factorization Techniques for Recommender Systems Book Summary :** This book presents the algorithms used to provide recommendations by exploiting matrix factorization and tensor decomposition techniques. It highlights well-known decomposition methods for recommender systems, such as Singular Value Decomposition (SVD), UV-decomposition, Non-negative Matrix Factorization (NMF), etc. and describes in detail the pros and cons of each method for matrices and tensors. This book provides a detailed theoretical mathematical background of matrix/tensor factorization techniques and a step-by-step analysis of each method on the basis of an integrated toy example that runs throughout all its chapters and helps the reader to understand the key differences among methods. It also contains two chapters, where different matrix and tensor methods are compared experimentally on real data sets, such as Epinions, GeoSocialRec, Last.fm, BibSonomy, etc. and provides further insights into the advantages and disadvantages of each method. The book offers a rich blend of theory and practice, making it suitable for students, researchers and practitioners interested in both recommenders and factorization methods. Lecturers can also use it for classes on data mining, recommender systems and dimensionality reduction methods.

**📒Matrix And Tensor Decomposition ✍ Christian Jutten**

**Matrix and Tensor Decomposition**

✏Author :

**Christian Jutten**

✏Publisher :

✏Release Date :

✏Pages :

✏ISBN :

**0128157607**

✏Available Language :

**English, Spanish, And French**

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**✏Matrix and Tensor Decomposition Book Summary :**

**Matrix and Tensor Decompositions in Signal Processing**

✏Author :

**Favier**

✏Publisher :

**Wiley-Blackwell**

✏Release Date :

**2018-11-20**

✏Pages :

**200**

✏ISBN :

**1786301555**

✏Available Language :

**English, Spanish, And French**

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**✏Matrix and Tensor Decompositions in Signal Processing Book Summary :**

**📒Tensor Decomposition Meets Approximation Theory ✍ Ferre Knaepkens**

**Tensor Decomposition Meets Approximation Theory**

✏Author :

**Ferre Knaepkens**

✏Publisher :

✏Release Date :

**2017**

✏Pages :

✏ISBN :

**OCLC:1050023083**

✏Available Language :

**English, Spanish, And French**

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**✏Tensor Decomposition Meets Approximation Theory Book Summary :** This thesis studies three different subjects, namely tensors and tensor decomposition, sparse interpolation and Pad\'e or rational approximation theory. These problems find their origin in various fields within mathematics: on the one hand tensors originate from algebra and are of importance in computer science and knowledge technology, while on the other hand sparse interpolation and Pad\'e approximations stem from approximation theory. Although all three problems seem totally unrelated, they are deeply intertwined. The connection between them is exactly he goal of this thesis. These connections are of importance since they allow us to solve the symmetric tensor decomposition problem by means of a corresponding sparse interpolation problem or an appropriate Pad\'e approximant. The first section gives a short introduction on tensors. Here, starting from the points of view of matrices and vectors, a generalization is made to tensors. Also a link is made to other known concepts within matrix-algebra. Subsequently, three definitions of tensor rank are discussed. The first definition is the most general and is based on the decomposition by means of the outer product of vectors. The second definition is only applicable for symmetric tensors and is based on a decomposition by means of symmetric outer products of vectors. Finally, the last definition is also only applicable for symmetric tensors and is based o the decomposition of a related homogeneous polynomial. It can be shown that these last two definitions are equal and they are also the only definitions used in the continuation of the thesis. In particular, this last definition since it supplies the connection with approximation theory. Finally, a well-known method (ALS) to find these tensor decompositions is shortly discussed. However, ALS has some shortcomings en that is exactly the reason that the connections to approximation theory are of such importance. Sections two and three discuss the first problem of both within approximation theory, namely sparse interpolation. In the second section, The univariate problem is considered. This problem can be solved with Prony's method, which consists of finding the zeroes of a related polynomial or solving a generalized eigenvalue problem. The third section continues on the second since it discusses multivariate sparse interpolation. Prony's method for the univariate case is changed to also provide a solution for the multivariate problem. The fourth and fifth section have as subject Pad\'e or rational approximation theory. Like the name suggests, it consists of approximating a power series by a rational function. Section four first introduces univariate Pad\'e approximants and states some important properties of them. Here, shortly the connection is made with continued fraction to use this theory later on. Finally, some methods to find Pad\'e approximants are discussed, namely the Levinson algorithm, the determinant formulas and the qd-algorithm. Section five continues on section four and discusses multivariate Pad\'e approximation theory. It is shown that a shift of the univariate conditions occurs, however, despite this shift still a lot of the important properties of the univariate case remain true. Also an extension of the qd-algorithm for multivariate Pad\'e approximants is discussed. Section six bundles all previous sections to expose the connections between the three seemingly different problems. The discussion of these connections is done in two steps in the univariate case, first the tensor decomposition problem is rewritten as a sparse interpolation problem and subsequently, it is shown that the sparse interpolation problem can be solved by means of Pad\'e approximants. In the multivariate case, also the connection between tensor decomposition and sparse interpolation is discussed first. Subsequently, a parameterized approach is introduces, which converts the multivariate problem to a parameterized univariate problem such that the connections of the first part apply. This parameterized approach also lead to the connection between tensor decomposition, multivariate sparse interpolation and multivariate Pad\'e approximation theory. The last or seventh section consists of two examples, a univariate problem and a multivariate one. The techniques of previous sections are used to demonstrate the connections of section six. This section also serves as illustration of the methods of sections two until five to solve sparse interpolation and Pad\'e approximation problems.

**Low Rank Tensor Decomposition for Feature Extraction and Tensor Recovery**

✏Author :

**Qiquan Shi**

✏Publisher :

✏Release Date :

**2018**

✏Pages :

**218**

✏ISBN :

**OCLC:1066258974**

✏Available Language :

**English, Spanish, And French**

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**✏Low Rank Tensor Decomposition for Feature Extraction and Tensor Recovery Book Summary :** Feature extraction and tensor recovery problems are important yet challenging, particularly for multi-dimensional data with missing values and/or noise. Low-rank tensor decomposition approaches are widely used for solving these problems. This thesis focuses on three common tensor decompositions (CP, Tucker and t-SVD) and develops a set of decomposition-based approaches. The proposed methods aim to extract low-dimensional features from complete/incomplete data and recover tensors given partial and/or grossly corrupted observations.

**📒Spectral Learning On Matrices And Tensors ✍ Majid Janzamin**

**Spectral Learning on Matrices and Tensors**

✏Author :

**Majid Janzamin**

✏Publisher :

✏Release Date :

**2019-11-25**

✏Pages :

**156**

✏ISBN :

**1680836404**

✏Available Language :

**English, Spanish, And French**

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**✏Spectral Learning on Matrices and Tensors Book Summary :** The authors of this monograph survey recent progress in using spectral methods including matrix and tensor decomposition techniques to learn many popular latent variable models. With careful implementation, tensor-based methods can run efficiently in practice, and in many cases they are the only algorithms with provable guarantees on running time and sample complexity. The focus is on a special type of tensor decomposition called CP decomposition, and the authors cover a wide range of algorithms to find the components of such tensor decomposition. They also discuss the usefulness of this decomposition by reviewing several probabilistic models that can be learned using such tensor methods. The second half of the monograph looks at practical applications. This includes using Tensorly, an efficient tensor algebra software package, which has a simple python interface for expressing tensor operations. It also has a flexible back-end system supporting NumPy, PyTorch, TensorFlow, and MXNet. Spectral Learning on Matrices and Tensors provides a theoretical and practical introduction to designing and deploying spectral learning on both matrices and tensors. It is of interest for all students, researchers and practitioners working on modern day machine learning problems.

**📒Higher Order Kronecker Products And Tensor Decompositions ✍ Carla Dee Martin**

**Higher order Kronecker Products and Tensor Decompositions**

✏Author :

**Carla Dee Martin**

✏Publisher :

✏Release Date :

**2005**

✏Pages :

**482**

✏ISBN :

**CORNELL:31924104143064**

✏Available Language :

**English, Spanish, And French**

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**✏Higher order Kronecker Products and Tensor Decompositions Book Summary :** The second problem in this dissertation involves solving shifted linear systems of the form (A - lambdaI) x = b when A is a Kronecker product of matrices. The Schur decomposition is used to reduce the shifted Kronecker product system to a Kronecker product of quasi-triangular matrices. The system is solved using a recursive block procedure which circumvents formation of the explicit product.

**📒A Multilingual Exploration Of Semantics In The Brain Using Tensor Decomposition ✍ Sharmistha Bardhan**

**A Multilingual Exploration of Semantics in the Brain Using Tensor Decomposition**

✏Author :

**Sharmistha Bardhan**

✏Publisher :

✏Release Date :

**2018**

✏Pages :

**85**

✏ISBN :

**0438430441**

✏Available Language :

**English, Spanish, And French**

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**✏A Multilingual Exploration of Semantics in the Brain Using Tensor Decomposition Book Summary :** The semantic concept processing mechanism of the brain shows that different neural activity patterns occur for different semantic categories. Multivariate Pattern Analysis of the brain fMRI data shows promising results in identifying active brain regions for a specific semantic category. Unsupervised learning technique such as tensor decomposition discovers the hidden structure from the brain data and proved to be useful as well. However, the existing methods are used for analyzing data from subjects who speak in one language and do not consider the cultural effect on it. This thesis presents an exploratory analysis of the neuro-semantic problem in a new dimension. The brain fMRI tensors of subjects who speak in Chinese or Italian language are analyzed both individually and together to discover the hidden structure. The Chinese and Italian tensors are jointly analyzed by coupling them along the stimuli object mode to discover the cultural effect. Moreover, the joint analysis of semantic features and brain fMRI tensor using the Advanced Coupled Matrix Tensor Factorization (ACMTF) method finds latent variables that explain the correlation between them. The results of the joint analysis of the tensors support the preliminary predictive analysis and find meaningful clusters for the different categories of stimuli object. Moreover, for a rank 2 decomposition, the prediction of brain activation pattern given semantic features gives an accuracy of 71.43%. It is expected that, the proposed exploratory and predictive analysis will improve existing approaches of analyzing conceptual knowledge representation of brain and guide future research in this domain.

**📒Nonnegative Matrix And Tensor Factorizations ✍ Andrzej Cichocki**

**Nonnegative Matrix and Tensor Factorizations**

✏Author :

**Andrzej Cichocki**

✏Publisher :

**John Wiley & Sons**

✏Release Date :

**2009-07-10**

✏Pages :

**500**

✏ISBN :

**0470747285**

✏Available Language :

**English, Spanish, And French**

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**✏Nonnegative Matrix and Tensor Factorizations Book Summary :** 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.

**📒Advances In Knowledge Discovery And Data Mining ✍ Qiang Yang**

**Advances in Knowledge Discovery and Data Mining**

✏Author :

**Qiang Yang**

✏Publisher :

**Springer**

✏Release Date :

**2019-05-20**

✏Pages :

**627**

✏ISBN :

**9783030161484**

✏Available Language :

**English, Spanish, And French**

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**✏Advances in Knowledge Discovery and Data Mining Book Summary :** The three-volume set LNAI 11439, 11440, and 11441 constitutes the thoroughly refereed proceedings of the 23rd Pacific-Asia Conference on Knowledge Discovery and Data Mining, PAKDD 2019, held in Macau, China, in April 2019. The 137 full papers presented were carefully reviewed and selected from 542 submissions. The papers present new ideas, original research results, and practical development experiences from all KDD related areas, including data mining, data warehousing, machine learning, artificial intelligence, databases, statistics, knowledge engineering, visualization, decision-making systems, and the emerging applications. They are organized in the following topical sections: classification and supervised learning; text and opinion mining; spatio-temporal and stream data mining; factor and tensor analysis; healthcare, bioinformatics and related topics; clustering and anomaly detection; deep learning models and applications; sequential pattern mining; weakly supervised learning; recommender system; social network and graph mining; data pre-processing and feature selection; representation learning and embedding; mining unstructured and semi-structured data; behavioral data mining; visual data mining; and knowledge graph and interpretable data mining.

**📒Decomposability Of Tensors ✍ Luca Chiantini**

**Decomposability of Tensors**

✏Author :

**Luca Chiantini**

✏Publisher :

**MDPI**

✏Release Date :

**2019-02-15**

✏Pages :

**160**

✏ISBN :

**9783038975908**

✏Available Language :

**English, Spanish, And French**

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**✏Decomposability of Tensors Book Summary :** This book is a printed edition of the Special Issue "Decomposability of Tensors" that was published in Mathematics

**📒Tensors ✍ J. M. Landsberg**

**Tensors**

✏Author :

**J. M. Landsberg**

✏Publisher :

**American Mathematical Soc.**

✏Release Date :

**2011-12-14**

✏Pages :

**439**

✏ISBN :

**9780821869079**

✏Available Language :

**English, Spanish, And French**

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**✏Tensors Book Summary :** Tensors are ubiquitous in the sciences. The geometry of tensors is both a powerful tool for extracting information from data sets, and a beautiful subject in its own right. This book has three intended uses: a classroom textbook, a reference work for researchers in the sciences, and an account of classical and modern results in (aspects of) the theory that will be of interest to researchers in geometry. For classroom use, there is a modern introduction to multilinear algebra and to the geometry and representation theory needed to study tensors, including a large number of exercises. For researchers in the sciences, there is information on tensors in table format for easy reference and a summary of the state of the art in elementary language. This is the first book containing many classical results regarding tensors. Particular applications treated in the book include the complexity of matrix multiplication, P versus NP, signal processing, phylogenetics, and algebraic statistics. For geometers, there is material on secant varieties, G-varieties, spaces with finitely many orbits and how these objects arise in applications, discussions of numerous open questions in geometry arising in applications, and expositions of advanced topics such as the proof of the Alexander-Hirschowitz theorem and of the Weyman-Kempf method for computing syzygies.

**📒Tensor Multidimensional Array Decomposition Regression And Software For Statistics And Machine Learning ✍ James Yi-Wei Li**

**Tensor multidimensional Array Decomposition Regression and Software for Statistics and Machine Learning**

✏Author :

**James Yi-Wei Li**

✏Publisher :

✏Release Date :

**2014**

✏Pages :

**130**

✏ISBN :

**OCLC:892507540**

✏Available Language :

**English, Spanish, And French**

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**✏Tensor multidimensional Array Decomposition Regression and Software for Statistics and Machine Learning Book Summary :** This thesis illustrates connections between statistical models for tensors, introduces a novel linear model for tensors with 3 modes, and implements tensor software in the form of an R package. Tensors, or multidimensional arrays, are a natural generalization of the vectors and matrices that are ubiquitous in statistical modeling. However, while matrix algebra has been well-studied and plays a crucial role in the interaction between data and the parameters of any given model, algebra of higher-order arrays has been relatively overlooked in data analysis and statistical theory. The emergence of multilinear datasets - where observations are vector-variate, matrix-variate, or even tensor-variate - only serve to emphasize the relative lack of statistical understanding around tensor data structures. In the first half of the thesis, we highlight classic tensor algebraic results and models used in image analysis, chemometrics, and psychometrics, as well as connect them to recent statistical models. The second half of the thesis features a linear model that is based off a recently introduced tensor multiplication. For this model, we prove some of the classic properties that we would expect from a 3-tensor generalization of the matrix ordinary least squares. We also apply our model to a functional dataset to demonstrate one possible usage. We conclude this thesis with an exposition of the software developed to facilitate tensor modeling and manipulation in R. This software implements many of the classic tensor decomposition models as well as our own linear model.

**Multimodal Analytics for Next Generation Big Data Technologies and Applications**

✏Author :

**Kah Phooi Seng**

✏Publisher :

**Springer**

✏Release Date :

**2019-07-18**

✏Pages :

**391**

✏ISBN :

**9783319975986**

✏Available Language :

**English, Spanish, And French**

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**✏Multimodal Analytics for Next Generation Big Data Technologies and Applications Book Summary :** This edited book will serve as a source of reference for technologies and applications for multimodality data analytics in big data environments. After an introduction, the editors organize the book into four main parts on sentiment, affect and emotion analytics for big multimodal data; unsupervised learning strategies for big multimodal data; supervised learning strategies for big multimodal data; and multimodal big data processing and applications. The book will be of value to researchers, professionals and students in engineering and computer science, particularly those engaged with image and speech processing, multimodal information processing, data science, and artificial intelligence.

**📒From Algebraic Structures To Tensors ✍ Gérard Favier**

**From Algebraic Structures to Tensors**

✏Author :

**Gérard Favier**

✏Publisher :

**John Wiley & Sons**

✏Release Date :

**2020-01-02**

✏Pages :

**318**

✏ISBN :

**9781786301543**

✏Available Language :

**English, Spanish, And French**

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**✏From Algebraic Structures to Tensors Book Summary :** Nowadays, tensors play a central role for the representation, mining, analysis, and fusion of multidimensional, multimodal, and heterogeneous big data in numerous fields. This set on Matrices and Tensors in Signal Processing aims at giving a self-contained and comprehensive presentation of various concepts and methods, starting from fundamental algebraic structures to advanced tensor-based applications, including recently developed tensor models and efficient algorithms for dimensionality reduction and parameter estimation. Although its title suggests an orientation towards signal processing, the results presented in this set will also be of use to readers interested in other disciplines. This first book provides an introduction to matrices and tensors of higher-order based on the structures of vector space and tensor space. Some standard algebraic structures are first described, with a focus on the hilbertian approach for signal representation, and function approximation based on Fourier series and orthogonal polynomial series. Matrices and hypermatrices associated with linear, bilinear and multilinear maps are more particularly studied. Some basic results are presented for block matrices. The notions of decomposition, rank, eigenvalue, singular value, and unfolding of a tensor are introduced, by emphasizing similarities and differences between matrices and tensors of higher-order.

**📒Tensor Spaces And Numerical Tensor Calculus ✍ Wolfgang Hackbusch**

**Tensor Spaces and Numerical Tensor Calculus**

✏Author :

**Wolfgang Hackbusch**

✏Publisher :

**Springer Science & Business Media**

✏Release Date :

**2012-02-23**

✏Pages :

**500**

✏ISBN :

**9783642280276**

✏Available Language :

**English, Spanish, And French**

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**✏Tensor Spaces and Numerical Tensor Calculus Book Summary :** Special numerical techniques are already needed to deal with nxn matrices for large n.Tensor data are of size nxnx...xn=n^d, where n^d exceeds the computer memory by far. They appear for problems of high spatial dimensions. Since standard methods fail, a particular tensor calculus is needed to treat such problems. The monograph describes the methods how tensors can be practically treated and how numerical operations can be performed. Applications are problems from quantum chemistry, approximation of multivariate functions, solution of pde, e.g., with stochastic coefficients, etc.

**📒Matrix Computations ✍ Gene H. Golub**

**Matrix Computations**

✏Author :

**Gene H. Golub**

✏Publisher :

**JHU Press**

✏Release Date :

**2013-02-15**

✏Pages :

**784**

✏ISBN :

**9781421408590**

✏Available Language :

**English, Spanish, And French**

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**✏Matrix Computations Book Summary :** The fourth edition of Gene H. Golub and Charles F. Van Loan's classic is an essential reference for computational scientists and engineers in addition to researchers in the numerical linear algebra community. Anyone whose work requires the solution to a matrix problem and an appreciation of its mathematical properties will find this book to be an indispensible tool. This revision is a cover-to-cover expansion and renovation of the third edition. It now includes an introduction to tensor computations and brand new sections on • fast transforms • parallel LU • discrete Poisson solvers • pseudospectra • structured linear equation problems • structured eigenvalue problems • large-scale SVD methods • polynomial eigenvalue problems Matrix Computations is packed with challenging problems, insightful derivations, and pointers to the literatureâ€”everything needed to become a matrix-savvy developer of numerical methods and software. The second most cited math book of 2012 according to MathSciNet, the book has placed in the top 10 for since 2005.

**Architecture aware Algorithm Design of Sparse Tensor matrix Primitives for GPUs**

✏Author :

**Israt J. Nisa**

✏Publisher :

✏Release Date :

**2019**

✏Pages :

**174**

✏ISBN :

**OCLC:1178630011**

✏Available Language :

**English, Spanish, And French**

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**✏Architecture aware Algorithm Design of Sparse Tensor matrix Primitives for GPUs Book Summary :** parse matrix/tensor operations have been a common computational motif in a wide spectrum of domains - numerical linear algebra, graph analytics, machine larning, health-care, etc. Sparse kernels play a key role in numerous machine learning algorithms and the rising popularity of this domain increases the significance of the primitives like SpMV (Sparse Matrix-Vector Multiplication), SDDMM (Sampled Dense-Dense Matrix Multiplication), MF/TF(Sparse Matrix/Tensor Factorization), etc. These primitives are data-parallel and highly suitable for GPU-like architectures that provide massive parallelism. Real-world matrices and tensors are large-scale and have millions of data points, which is sufficient to utilize all the cores of a GPU. Yet, a data-parallel algorithm can become the bottleneck of an application and perform way below than the upper bound of the roofline model. Some common reasons are frequent irregular global memory access, low data reuse, and imbalanced work distribution. However, efficient utilization of GPU memory hierarchy, reduced thread communication, increased data locality, and an even workload distribution can provide ample opportunities for significant performance improvement. The challenge lies in utilizing the techniques across applications and achieve an even performance in spite of the irregularity of the input matrices or tensors. In this work, we systematically identify the performance bottlenecks of the important sparse algorithms and provide optimized and high performing solutions.

**📒Multilinear Operators For Higher Order Decompositions ✍ Tamara Gibson Kolda**

**Multilinear Operators for Higher order Decompositions**

✏Author :

**Tamara Gibson Kolda**

✏Publisher :

✏Release Date :

**2006**

✏Pages :

**28**

✏ISBN :

**OCLC:316326195**

✏Available Language :

**English, Spanish, And French**

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**✏Multilinear Operators for Higher order Decompositions Book Summary :** We propose two new multilinear operators for expressing the matrix compositions that are needed in the Tucker and PARAFAC (CANDECOMP) decompositions. The first operator, which we call the Tucker operator, is shorthand for performing an n-mode matrix multiplication for every mode of a given tensor and can be employed to concisely express the Tucker decomposition. The second operator, which we call the Kruskal operator, is shorthand for the sum of the outer-products of the columns of N matrices and allows a divorce from a matricized representation and a very concise expression of the PARAFAC decomposition. We explore the properties of the Tucker and Kruskal operators independently of the related decompositions. Additionally, we provide a review of the matrix and tensor operations that are frequently used in the context of tensor decompositions.

**Theory and Computation of Complex Tensors and its Applications**

✏Author :

**Maolin Che**

✏Publisher :

**Springer Nature**

✏Release Date :

✏Pages :

✏ISBN :

**9789811520594**

✏Available Language :

**English, Spanish, And French**

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**✏Theory and Computation of Complex Tensors and its Applications Book Summary :**

**📒Algorithms In Data Mining Using Matrix And Tensor Methods ✍ Berkant Savas**

**Algorithms in Data Mining Using Matrix and Tensor Methods**

✏Author :

**Berkant Savas**

✏Publisher :

✏Release Date :

**2008**

✏Pages :

**138**

✏ISBN :

**STANFORD:36105123682820**

✏Available Language :

**English, Spanish, And French**

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**✏Algorithms in Data Mining Using Matrix and Tensor Methods Book Summary :**

**📒Recommender Systems For Location Based Social Networks ✍ Panagiotis Symeonidis**

**Recommender Systems for Location based Social Networks**

✏Author :

**Panagiotis Symeonidis**

✏Publisher :

**Springer Science & Business Media**

✏Release Date :

**2014-02-08**

✏Pages :

**108**

✏ISBN :

**9781493902866**

✏Available Language :

**English, Spanish, And French**

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**✏Recommender Systems for Location based Social Networks Book Summary :** Online social networks collect information from users' social contacts and their daily interactions (co-tagging of photos, co-rating of products etc.) to provide them with recommendations of new products or friends. Lately, technological progressions in mobile devices (i.e. smart phones) enabled the incorporation of geo-location data in the traditional web-based online social networks, bringing the new era of Social and Mobile Web. The goal of this book is to bring together important research in a new family of recommender systems aimed at serving Location-based Social Networks (LBSNs). The chapters introduce a wide variety of recent approaches, from the most basic to the state-of-the-art, for providing recommendations in LBSNs. The book is organized into three parts. Part 1 provides introductory material on recommender systems, online social networks and LBSNs. Part 2 presents a wide variety of recommendation algorithms, ranging from basic to cutting edge, as well as a comparison of the characteristics of these recommender systems. Part 3 provides a step-by-step case study on the technical aspects of deploying and evaluating a real-world LBSN, which provides location, activity and friend recommendations. The material covered in the book is intended for graduate students, teachers, researchers, and practitioners in the areas of web data mining, information retrieval, and machine learning.

**📒Tensor Numerical Methods In Quantum Chemistry ✍ Venera Khoromskaia**

**Tensor Numerical Methods in Quantum Chemistry**

✏Author :

**Venera Khoromskaia**

✏Publisher :

**Walter de Gruyter GmbH & Co KG**

✏Release Date :

**2018-06-11**

✏Pages :

**297**

✏ISBN :

**9783110365832**

✏Available Language :

**English, Spanish, And French**

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**✏Tensor Numerical Methods in Quantum Chemistry Book Summary :** The conventional numerical methods when applied to multidimensional problems suffer from the so-called "curse of dimensionality", that cannot be eliminated by using parallel architectures and high performance computing. The novel tensor numerical methods are based on a "smart" rank-structured tensor representation of the multivariate functions and operators discretized on Cartesian grids thus reducing solution of the multidimensional integral-differential equations to 1D calculations. We explain basic tensor formats and algorithms and show how the orthogonal Tucker tensor decomposition originating from chemometrics made a revolution in numerical analysis, relying on rigorous results from approximation theory. Benefits of tensor approach are demonstrated in ab-initio electronic structure calculations. Computation of the 3D convolution integrals for functions with multiple singularities is replaced by a sequence of 1D operations, thus enabling accurate MATLAB calculations on a laptop using 3D uniform tensor grids of the size up to 1015. Fast tensor-based Hartree-Fock solver, incorporating the grid-based low-rank factorization of the two-electron integrals, serves as a prerequisite for economical calculation of the excitation energies of molecules. Tensor approach suggests efficient grid-based numerical treatment of the long-range electrostatic potentials on large 3D finite lattices with defects.The novel range-separated tensor format applies to interaction potentials of multi-particle systems of general type opening the new prospects for tensor methods in scientific computing. This research monograph presenting the modern tensor techniques applied to problems in quantum chemistry may be interesting for a wide audience of students and scientists working in computational chemistry, material science and scientific computing.

**📒Tensors In Image Processing And Computer Vision ✍ Santiago Aja-Fernández**

**Tensors in Image Processing and Computer Vision**

✏Author :

**Santiago Aja-Fernández**

✏Publisher :

**Springer Science & Business Media**

✏Release Date :

**2009-05-21**

✏Pages :

**470**

✏ISBN :

**9781848822993**

✏Available Language :

**English, Spanish, And French**

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**✏Tensors in Image Processing and Computer Vision Book Summary :** Tensor signal processing is an emerging field with important applications to computer vision and image processing. This book presents the state of the art in this new branch of signal processing, offering a great deal of research and discussions by leading experts in the area. The wide-ranging volume offers an overview into cutting-edge research into the newest tensor processing techniques and their application to different domains related to computer vision and image processing. This comprehensive text will prove to be an invaluable reference and resource for researchers, practitioners and advanced students working in the area of computer vision and image processing.

**📒Text Mining ✍ Ashok N. Srivastava**

**Text Mining**

✏Author :

**Ashok N. Srivastava**

✏Publisher :

**CRC Press**

✏Release Date :

**2009-06-15**

✏Pages :

**328**

✏ISBN :

**1420059459**

✏Available Language :

**English, Spanish, And French**

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**✏Text Mining Book Summary :** The Definitive Resource on Text Mining Theory and Applications from Foremost Researchers in the Field Giving a broad perspective of the field from numerous vantage points, Text Mining: Classification, Clustering, and Applications focuses on statistical methods for text mining and analysis. It examines methods to automatically cluster and classify text documents and applies these methods in a variety of areas, including adaptive information filtering, information distillation, and text search. The book begins with chapters on the classification of documents into predefined categories. It presents state-of-the-art algorithms and their use in practice. The next chapters describe novel methods for clustering documents into groups that are not predefined. These methods seek to automatically determine topical structures that may exist in a document corpus. The book concludes by discussing various text mining applications that have significant implications for future research and industrial use. There is no doubt that text mining will continue to play a critical role in the development of future information systems and advances in research will be instrumental to their success. This book captures the technical depth and immense practical potential of text mining, guiding readers to a sound appreciation of this burgeoning field.

**📒Algorithmic Aspects Of Machine Learning ✍ Ankur Moitra**

**Algorithmic Aspects of Machine Learning**

✏Author :

**Ankur Moitra**

✏Publisher :

**Cambridge University Press**

✏Release Date :

**2018-09-27**

✏Pages :

**176**

✏ISBN :

**9781107184589**

✏Available Language :

**English, Spanish, And French**

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**✏Algorithmic Aspects of Machine Learning Book Summary :** Introduces cutting-edge research on machine learning theory and practice, providing an accessible, modern algorithmic toolkit.

**Matrix Methods in Data Mining and Pattern Recognition Second Edition**

✏Author :

**Lars Elden**

✏Publisher :

**SIAM**

✏Release Date :

**2019-08-30**

✏Pages :

**229**

✏ISBN :

**9781611975864**

✏Available Language :

**English, Spanish, And French**

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**✏Matrix Methods in Data Mining and Pattern Recognition Second Edition Book Summary :** This thoroughly revised second edition provides an updated treatment of numerical linear algebra techniques for solving problems in data mining and pattern recognition. Adopting an application-oriented approach, the author introduces matrix theory and decompositions, describes how modern matrix methods can be applied in real life scenarios, and provides a set of tools that students can modify for a particular application. Building on material from the first edition, the author discusses basic graph concepts and their matrix counterparts. He introduces the graph Laplacian and properties of its eigenvectors needed in spectral partitioning and describes spectral graph partitioning applied to social networks and text classification. Examples are included to help readers visualize the results. This new edition also presents matrix-based methods that underlie many of the algorithms used for big data. The book provides a solid foundation to further explore related topics and presents applications such as classification of handwritten digits, text mining, text summarization, PageRank computations related to the Google search engine, and facial recognition. Exercises and computer assignments are available on a Web page that supplements the book. This book is primarily for undergraduate students who have previously taken an introductory scientific computing/numerical analysis course and graduate students in data mining and pattern recognition areas who need an introduction to linear algebra techniques.

**Multimedia Content Representation Classification and Security**

✏Author :

**Bilge Gunsel**

✏Publisher :

**Springer Science & Business Media**

✏Release Date :

**2006-09-04**

✏Pages :

**804**

✏ISBN :

**9783540393924**

✏Available Language :

**English, Spanish, And French**

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**✏Multimedia Content Representation Classification and Security Book Summary :** This book constitutes the refereed proceedings of the International Workshop on Multimedia Content Representation, Classification and Security, MRCS 2006. The book presents 100 revised papers together with 4 invited lectures. Coverage includes biometric recognition, multimedia content security, steganography, watermarking, authentication, classification for biometric recognition, digital watermarking, content analysis and representation, 3D object retrieval and classification, representation, analysis and retrieval in cultural heritage, content representation, indexing and retrieval, and more.

**📒Unsupervised Feature Extraction Applied To Bioinformatics ✍ Y-h. Taguchi**

**Unsupervised Feature Extraction Applied to Bioinformatics**

✏Author :

**Y-h. Taguchi**

✏Publisher :

**Springer Nature**

✏Release Date :

**2019-08-23**

✏Pages :

**321**

✏ISBN :

**9783030224561**

✏Available Language :

**English, Spanish, And French**

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**✏Unsupervised Feature Extraction Applied to Bioinformatics Book Summary :** This book proposes applications of tensor decomposition to unsupervised feature extraction and feature selection. The author posits that although supervised methods including deep learning have become popular, unsupervised methods have their own advantages. He argues that this is the case because unsupervised methods are easy to learn since tensor decomposition is a conventional linear methodology. This book starts from very basic linear algebra and reaches the cutting edge methodologies applied to difficult situations when there are many features (variables) while only small number of samples are available. The author includes advanced descriptions about tensor decomposition including Tucker decomposition using high order singular value decomposition as well as higher order orthogonal iteration, and train tenor decomposition. The author concludes by showing unsupervised methods and their application to a wide range of topics. Allows readers to analyze data sets with small samples and many features; Provides a fast algorithm, based upon linear algebra, to analyze big data; Includes several applications to multi-view data analyses, with a focus on bioinformatics.

**The Matrix and Tensor Quarterly**

✏Author :

✏Publisher :

✏Release Date :

**1983**

✏Pages :

✏ISBN :

**UCSC:32106020192925**

✏Available Language :

**English, Spanish, And French**

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**✏The Matrix and Tensor Quarterly Book Summary :**