Download or read book Spectral Learning on Matrices and Tensors written by Majid Janzamin and published by . This book was released on 2019-11-25 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Spectral Learning on Matrices and Tensors written by MAJID JANZAMIN;RONG GE;JEAN KOSSAIFI;ANIMA ANANDKU. and published by . This book was released on 2019 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book 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.
Download or read book Spectral Algorithms written by Ravindran Kannan and published by Now Publishers Inc. This book was released on 2009 with total page 153 pages. Available in PDF, EPUB and Kindle. Book excerpt: Spectral methods refer to the use of eigenvalues, eigenvectors, singular values and singular vectors. They are widely used in Engineering, Applied Mathematics and Statistics. More recently, spectral methods have found numerous applications in Computer Science to "discrete" as well as "continuous" problems. Spectral Algorithms describes modern applications of spectral methods, and novel algorithms for estimating spectral parameters. The first part of the book presents applications of spectral methods to problems from a variety of topics including combinatorial optimization, learning and clustering. The second part of the book is motivated by efficiency considerations. A feature of many modern applications is the massive amount of input data. While sophisticated algorithms for matrix computations have been developed over a century, a more recent development is algorithms based on "sampling on the fly" from massive matrices. Good estimates of singular values and low rank approximations of the whole matrix can be provably derived from a sample. The main emphasis in the second part of the book is to present these sampling methods with rigorous error bounds. It also presents recent extensions of spectral methods from matrices to tensors and their applications to some combinatorial optimization problems.
Download or read book Tensor Analysis written by Liqun Qi and published by SIAM. This book was released on 2017-04-19 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt: Tensors, or hypermatrices, are multi-arrays with more than two indices. In the last decade or so, many concepts and results in matrix theory?some of which are nontrivial?have been extended to tensors and have a wide range of applications (for example, spectral hypergraph theory, higher order Markov chains, polynomial optimization, magnetic resonance imaging, automatic control, and quantum entanglement problems). The authors provide a comprehensive discussion of this new theory of tensors. Tensor Analysis: Spectral Theory and Special Tensors is unique in that it is the first book on these three subject areas: spectral theory of tensors; the theory of special tensors, including nonnegative tensors, positive semidefinite tensors, completely positive tensors, and copositive tensors; and the spectral hypergraph theory via tensors. ?
Download or read book Algorithmic Aspects of Machine Learning written by Ankur Moitra and published by Cambridge University Press. This book was released on 2018-09-27 with total page 161 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduces cutting-edge research on machine learning theory and practice, providing an accessible, modern algorithmic toolkit.
Download or read book Discovery of Latent Factors in High dimensional Data Using Tensor Methods written by Furong Huang and published by . This book was released on 2016 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: Unsupervised learning aims at the discovery of hidden structure that drives the observations in the real world. It is essential for success in modern machine learning and artificial intelligence. Latent variable models are versatile in unsupervised learning and have applications in almost every domain, e.g., social network analysis, natural language processing, computer vision and computational biology. Training latent variable models is challenging due to the non-convexity of the likelihood objective function. An alternative method is based on the spectral decomposition of low order moment matrices and tensors. This versatile framework is guaranteed to estimate the correct model consistently. My thesis spans both theoretical analysis of tensor decomposition framework and practical implementation of various applications.This thesis presents theoretical results on convergence to globally optimal solution of tensor decomposition using the stochastic gradient descent, despite non-convexity of the objective. This is the first work that gives global convergence guarantees for the stochastic gradient descent on non-convex functions with exponentially many local minima and saddle points.This thesis also presents large-scale deployment of spectral methods (matrix and tensor decomposition) carried out on CPU, GPU and Spark platforms. Dimensionality reduction techniques such as random projection are incorporated for a highly parallel and scalable tensor decomposition algorithm. We obtain a gain in both accuracies and in running times by several orders of magnitude compared to the state-of-art variational methods.To solve real world problems, more advanced models and learning algorithms are proposed. After introducing tensor decomposition framework under latent Dirichlet allocation (LDA) model, this thesis discusses generalization of LDA model to mixed membership stochastic block model for learning hidden user commonalities or communities in social network, convolutional dictionary model for learning phrase templates and word-sequence embeddings, hierarchical tensor decomposition and latent tree structure model for learning disease hierarchy in healthcare analytics, and spatial point process mixture model for detecting cell types in neuroscience.
Download or read book Matrix and Tensor Decompositions in Signal Processing Volume 2 written by Gérard Favier and published by John Wiley & Sons. This book was released on 2021-08-31 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Spectral Methods for Data Science written by Yuxin Chen and published by . This book was released on 2021 with total page 249 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents a systematic, yet accessible introduction to spectral methods from a modern statistical perspective. It is essential reading for all students, researchers and practitioners working in Data Science.
Download or read book Tensor Computation for Data Analysis written by Yipeng Liu and published by Springer Nature. This book was released on 2021-08-31 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Tensors for Data Processing written by Yipeng Liu and published by Academic Press. This book was released on 2021-10-21 with total page 598 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book Matrix and Tensor Factorization Techniques for Recommender Systems written by Panagiotis Symeonidis and published by Springer. This book was released on 2017-01-29 with total page 101 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Nonnegative Matrix and Tensor Factorizations written by Andrzej Cichocki and published by John Wiley & Sons. This book was released on 2009-07-10 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Mathematics for Machine Learning written by Marc Peter Deisenroth and published by Cambridge University Press. This book was released on 2020-04-23 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: The fundamental mathematical tools needed to understand machine learning include linear algebra, analytic geometry, matrix decompositions, vector calculus, optimization, probability and statistics. These topics are traditionally taught in disparate courses, making it hard for data science or computer science students, or professionals, to efficiently learn the mathematics. This self-contained textbook bridges the gap between mathematical and machine learning texts, introducing the mathematical concepts with a minimum of prerequisites. It uses these concepts to derive four central machine learning methods: linear regression, principal component analysis, Gaussian mixture models and support vector machines. For students and others with a mathematical background, these derivations provide a starting point to machine learning texts. For those learning the mathematics for the first time, the methods help build intuition and practical experience with applying mathematical concepts. Every chapter includes worked examples and exercises to test understanding. Programming tutorials are offered on the book's web site.
Download or read book Spectra and Pseudospectra written by Lloyd N. Trefethen and published by Princeton University Press. This book was released on 2005-08-07 with total page 634 pages. Available in PDF, EPUB and Kindle. Book excerpt: Pure and applied mathematicians, physicists, scientists, and engineers use matrices and operators and their eigenvalues in quantum mechanics, fluid mechanics, structural analysis, acoustics, ecology, numerical analysis, and many other areas. However, in some applications the usual analysis based on eigenvalues fails. For example, eigenvalues are often ineffective for analyzing dynamical systems such as fluid flow, Markov chains, ecological models, and matrix iterations. That's where this book comes in. This is the authoritative work on nonnormal matrices and operators, written by the authorities who made them famous. Each of the sixty sections is written as a self-contained essay. Each document is a lavishly illustrated introductory survey of its topic, complete with beautiful numerical experiments and all the right references. The breadth of included topics and the numerous applications that provide links between fields will make this an essential reference in mathematics and related sciences.
Download or read book Spectra and Pseudospectra written by Lloyd N. Trefethen and published by Princeton University Press. This book was released on 2020-05-26 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Pure and applied mathematicians, physicists, scientists, and engineers use matrices and operators and their eigenvalues in quantum mechanics, fluid mechanics, structural analysis, acoustics, ecology, numerical analysis, and many other areas. However, in some applications the usual analysis based on eigenvalues fails. For example, eigenvalues are often ineffective for analyzing dynamical systems such as fluid flow, Markov chains, ecological models, and matrix iterations. That's where this book comes in. This is the authoritative work on nonnormal matrices and operators, written by the authorities who made them famous. Each of the sixty sections is written as a self-contained essay. Each document is a lavishly illustrated introductory survey of its topic, complete with beautiful numerical experiments and all the right references. The breadth of included topics and the numerous applications that provide links between fields will make this an essential reference in mathematics and related sciences.
Download or read book Nonnegative Matrix Factorization written by Nicolas Gillis and published by SIAM. This book was released on 2020-12-18 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonnegative matrix factorization (NMF) in its modern form has become a standard tool in the analysis of high-dimensional data sets. This book provides a comprehensive and up-to-date account of the most important aspects of the NMF problem and is the first to detail its theoretical aspects, including geometric interpretation, nonnegative rank, complexity, and uniqueness. It explains why understanding these theoretical insights is key to using this computational tool effectively and meaningfully. Nonnegative Matrix Factorization is accessible to a wide audience and is ideal for anyone interested in the workings of NMF. It discusses some new results on the nonnegative rank and the identifiability of NMF and makes available MATLAB codes for readers to run the numerical examples presented in the book. Graduate students starting to work on NMF and researchers interested in better understanding the NMF problem and how they can use it will find this book useful. It can be used in advanced undergraduate and graduate-level courses on numerical linear algebra and on advanced topics in numerical linear algebra and requires only a basic knowledge of linear algebra and optimization.
Download or read book Graph Representation Learning written by William L. William L. Hamilton and published by Springer Nature. This book was released on 2022-06-01 with total page 141 pages. Available in PDF, EPUB and Kindle. Book excerpt: Graph-structured data is ubiquitous throughout the natural and social sciences, from telecommunication networks to quantum chemistry. Building relational inductive biases into deep learning architectures is crucial for creating systems that can learn, reason, and generalize from this kind of data. Recent years have seen a surge in research on graph representation learning, including techniques for deep graph embeddings, generalizations of convolutional neural networks to graph-structured data, and neural message-passing approaches inspired by belief propagation. These advances in graph representation learning have led to new state-of-the-art results in numerous domains, including chemical synthesis, 3D vision, recommender systems, question answering, and social network analysis. This book provides a synthesis and overview of graph representation learning. It begins with a discussion of the goals of graph representation learning as well as key methodological foundations in graph theory and network analysis. Following this, the book introduces and reviews methods for learning node embeddings, including random-walk-based methods and applications to knowledge graphs. It then provides a technical synthesis and introduction to the highly successful graph neural network (GNN) formalism, which has become a dominant and fast-growing paradigm for deep learning with graph data. The book concludes with a synthesis of recent advancements in deep generative models for graphs—a nascent but quickly growing subset of graph representation learning.
