Download or read book Sparse and Low Rank Modeling on High Dimensional Data written by Xiao Bian and published by . This book was released on 2014 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book High Dimensional Data Analysis with Low Dimensional Models written by John Wright and published by Cambridge University Press. This book was released on 2022-01-13 with total page 718 pages. Available in PDF, EPUB and Kindle. Book excerpt: Connecting theory with practice, this systematic and rigorous introduction covers the fundamental principles, algorithms and applications of key mathematical models for high-dimensional data analysis. Comprehensive in its approach, it provides unified coverage of many different low-dimensional models and analytical techniques, including sparse and low-rank models, and both convex and non-convex formulations. Readers will learn how to develop efficient and scalable algorithms for solving real-world problems, supported by numerous examples and exercises throughout, and how to use the computational tools learnt in several application contexts. Applications presented include scientific imaging, communication, face recognition, 3D vision, and deep networks for classification. With code available online, this is an ideal textbook for senior and graduate students in computer science, data science, and electrical engineering, as well as for those taking courses on sparsity, low-dimensional structures, and high-dimensional data. Foreword by Emmanuel Candès.
Download or read book High Dimensional Data Analysis with Low Dimensional Models written by John Wright and published by Cambridge University Press. This book was released on 2022-01-13 with total page 717 pages. Available in PDF, EPUB and Kindle. Book excerpt: Connects fundamental mathematical theory with real-world problems, through efficient and scalable optimization algorithms.
Download or read book Sparse Graphical Modeling for High Dimensional Data written by Faming Liang and published by CRC Press. This book was released on 2023-08-02 with total page 151 pages. Available in PDF, EPUB and Kindle. Book excerpt: A general framework for learning sparse graphical models with conditional independence tests Complete treatments for different types of data, Gaussian, Poisson, multinomial, and mixed data Unified treatments for data integration, network comparison, and covariate adjustment Unified treatments for missing data and heterogeneous data Efficient methods for joint estimation of multiple graphical models Effective methods of high-dimensional variable selection Effective methods of high-dimensional inference
Download or read book Generalized Low Rank Models written by Madeleine Udell and published by . This book was released on 2015 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Principal components analysis (PCA) is a well-known technique for approximating a tabular data set by a low rank matrix. This dissertation extends the idea of PCA to handle arbitrary data sets consisting of numerical, Boolean, categorical, ordinal, and other data types. This framework encompasses many well known techniques in data analysis, such as nonnegative matrix factorization, matrix completion, sparse and robust PCA, k-means, k-SVD, and maximum margin matrix factorization. The method handles heterogeneous data sets, and leads to coherent schemes for compressing, denoising, and imputing missing entries across all data types simultaneously. It also admits a number of interesting interpretations of the low rank factors, which allow clustering of examples or of features. We propose several parallel algorithms for fitting generalized low rank models, and describe implementations and numerical results.
Download or read book Prediction and Model Selection for High dimensional Data with Sparse Or Low rank Structure written by Rina Foygel Barber and published by . This book was released on 2012 with total page 201 pages. Available in PDF, EPUB and Kindle. Book excerpt: For sparse regression and sparse graphical models, we consider the model selection problem, where the goal is to identify the structure of an underlying sparse model that exactly describes the distribution of the data. We analyze the extended Bayesian information criterion and its connection to the Bayesian posterior distribution over models in a high-dimensional scenario. The model selection properties of these methods are explored further with experiments on spam email filtering data and precipitation pattern data.
Download or read book Deep Learning through Sparse and Low Rank Modeling written by Zhangyang Wang and published by Academic Press. This book was released on 2019-04-26 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: Deep Learning through Sparse Representation and Low-Rank Modeling bridges classical sparse and low rank models-those that emphasize problem-specific Interpretability-with recent deep network models that have enabled a larger learning capacity and better utilization of Big Data. It shows how the toolkit of deep learning is closely tied with the sparse/low rank methods and algorithms, providing a rich variety of theoretical and analytic tools to guide the design and interpretation of deep learning models. The development of the theory and models is supported by a wide variety of applications in computer vision, machine learning, signal processing, and data mining. This book will be highly useful for researchers, graduate students and practitioners working in the fields of computer vision, machine learning, signal processing, optimization and statistics. Combines classical sparse and low-rank models and algorithms with the latest advances in deep learning networks Shows how the structure and algorithms of sparse and low-rank methods improves the performance and interpretability of Deep Learning models Provides tactics on how to build and apply customized deep learning models for various applications
Download or read book Low Rank and Sparse Modeling for Data Analysis written by Zhao Kang and published by . This book was released on 2017 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nowadays, many real-world problems must deal with collections of high-dimensional data. High dimensional data usually have intrinsic low-dimensional representations, which are suited for subsequent analysis or processing. Therefore, finding low-dimensional representations is an essential step in many machine learning and data mining tasks. Low-rank and sparse modeling are emerging mathematical tools dealing with uncertainties of real-world data. Leveraging on the underlying structure of data, low-rank and sparse modeling approaches have achieved impressive performance in many data analysis tasks. Since the general rank minimization problem is computationally NP-hard, the convex relaxation of original problem is often solved. One popular heuristic method is to use the nuclear norm to approximate the rank of a matrix. Despite the success of nuclear norm minimization in capturing the low intrinsic-dimensionality of data, the nuclear norm minimizes not only the rank, but also the variance of matrix and may not be a good approximation to the rank function in practical problems. To mitigate above issue, this thesis proposes several nonconvex functions to approximate the rank function. However, It is often difficult to solve nonconvex problem. In this thesis, an optimization framework for nonconvex problem is further developed. The effectiveness of this approach is examined on several important applications, including matrix completion, robust principle component analysis, clustering, and recommender systems. Another issue associated with current clustering methods is that they work in two separate steps including similarity matrix computation and subsequent spectral clustering. The learned similarity matrix may not be optimal for subsequent clustering. Therefore, a unified algorithm framework is developed in this thesis. To capture the nonlinear relations among data points, we formulate this method in kernel space. Furthermore, the obtained continuous spectral solutions could severely deviate from the true discrete cluster labels, a discrete transformation is further incorporated in our model. Finally, our framework can simultaneously learn similarity matrix, kernel, and discrete cluster labels. The performance of the proposed algorithms is established through extensive experiments. This framework can be easily extended to semi-supervised classification.
Download or read book Metric Learning written by Aurélien Muise and published by Springer Nature. This book was released on 2022-05-31 with total page 139 pages. Available in PDF, EPUB and Kindle. Book excerpt: Similarity between objects plays an important role in both human cognitive processes and artificial systems for recognition and categorization. How to appropriately measure such similarities for a given task is crucial to the performance of many machine learning, pattern recognition and data mining methods. This book is devoted to metric learning, a set of techniques to automatically learn similarity and distance functions from data that has attracted a lot of interest in machine learning and related fields in the past ten years. In this book, we provide a thorough review of the metric learning literature that covers algorithms, theory and applications for both numerical and structured data. We first introduce relevant definitions and classic metric functions, as well as examples of their use in machine learning and data mining. We then review a wide range of metric learning algorithms, starting with the simple setting of linear distance and similarity learning. We show how one may scale-up these methods to very large amounts of training data. To go beyond the linear case, we discuss methods that learn nonlinear metrics or multiple linear metrics throughout the feature space, and review methods for more complex settings such as multi-task and semi-supervised learning. Although most of the existing work has focused on numerical data, we cover the literature on metric learning for structured data like strings, trees, graphs and time series. In the more technical part of the book, we present some recent statistical frameworks for analyzing the generalization performance in metric learning and derive results for some of the algorithms presented earlier. Finally, we illustrate the relevance of metric learning in real-world problems through a series of successful applications to computer vision, bioinformatics and information retrieval. Table of Contents: Introduction / Metrics / Properties of Metric Learning Algorithms / Linear Metric Learning / Nonlinear and Local Metric Learning / Metric Learning for Special Settings / Metric Learning for Structured Data / Generalization Guarantees for Metric Learning / Applications / Conclusion / Bibliography / Authors' Biographies
Download or read book Low Rank Models in Visual Analysis written by Zhouchen Lin and published by Academic Press. This book was released on 2017-06-06 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: Low-Rank Models in Visual Analysis: Theories, Algorithms, and Applications presents the state-of-the-art on low-rank models and their application to visual analysis. It provides insight into the ideas behind the models and their algorithms, giving details of their formulation and deduction. The main applications included are video denoising, background modeling, image alignment and rectification, motion segmentation, image segmentation and image saliency detection. Readers will learn which Low-rank models are highly useful in practice (both linear and nonlinear models), how to solve low-rank models efficiently, and how to apply low-rank models to real problems. Presents a self-contained, up-to-date introduction that covers underlying theory, algorithms and the state-of-the-art in current applications Provides a full and clear explanation of the theory behind the models Includes detailed proofs in the appendices
Download or read book High Dimensional Covariance Estimation written by Mohsen Pourahmadi and published by John Wiley & Sons. This book was released on 2013-06-24 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: Methods for estimating sparse and large covariance matrices Covariance and correlation matrices play fundamental roles in every aspect of the analysis of multivariate data collected from a variety of fields including business and economics, health care, engineering, and environmental and physical sciences. High-Dimensional Covariance Estimation provides accessible and comprehensive coverage of the classical and modern approaches for estimating covariance matrices as well as their applications to the rapidly developing areas lying at the intersection of statistics and machine learning. Recently, the classical sample covariance methodologies have been modified and improved upon to meet the needs of statisticians and researchers dealing with large correlated datasets. High-Dimensional Covariance Estimation focuses on the methodologies based on shrinkage, thresholding, and penalized likelihood with applications to Gaussian graphical models, prediction, and mean-variance portfolio management. The book relies heavily on regression-based ideas and interpretations to connect and unify many existing methods and algorithms for the task. High-Dimensional Covariance Estimation features chapters on: Data, Sparsity, and Regularization Regularizing the Eigenstructure Banding, Tapering, and Thresholding Covariance Matrices Sparse Gaussian Graphical Models Multivariate Regression The book is an ideal resource for researchers in statistics, mathematics, business and economics, computer sciences, and engineering, as well as a useful text or supplement for graduate-level courses in multivariate analysis, covariance estimation, statistical learning, and high-dimensional data analysis.
Download or read book Pattern Recognition and Computer Vision written by Yuxin Peng and published by Springer Nature. This book was released on 2020-10-11 with total page 789 pages. Available in PDF, EPUB and Kindle. Book excerpt: The three-volume set LNCS 12305, 12306, and 12307 constitutes the refereed proceedings of the Third Chinese Conference on Pattern Recognition and Computer Vision, PRCV 2020, held virtually in Nanjing, China, in October 2020. The 158 full papers presented were carefully reviewed and selected from 402 submissions. The papers have been organized in the following topical sections: Part I: Computer Vision and Application, Part II: Pattern Recognition and Application, Part III: Machine Learning.
Download or read book Brain and Nature Inspired Learning Computation and Recognition written by Licheng Jiao and published by Elsevier. This book was released on 2020-01-18 with total page 788 pages. Available in PDF, EPUB and Kindle. Book excerpt: Brain and Nature-Inspired Learning, Computation and Recognition presents a systematic analysis of neural networks, natural computing, machine learning and compression, algorithms and applications inspired by the brain and biological mechanisms found in nature. Sections cover new developments and main applications, algorithms and simulations. Developments in brain and nature-inspired learning have promoted interest in image processing, clustering problems, change detection, control theory and other disciplines. The book discusses the main problems and applications pertaining to bio-inspired computation and recognition, introducing algorithm implementation, model simulation, and practical application of parameter setting. Readers will find solutions to problems in computation and recognition, particularly neural networks, natural computing, machine learning and compressed sensing. This volume offers a comprehensive and well-structured introduction to brain and nature-inspired learning, computation, and recognition. Presents an invaluable systematic introduction to brain and nature-inspired learning, computation and recognition Describes the biological mechanisms, mathematical analyses and scientific principles behind brain and nature-inspired learning, calculation and recognition Systematically analyzes neural networks, natural computing, machine learning and compression, algorithms and applications inspired by the brain and biological mechanisms found in nature Discusses the theory and application of algorithms and neural networks, natural computing, machine learning and compression perception
Download or read book Big Data written by Hai Jin and published by Springer Nature. This book was released on 2019-11-27 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the proceedings of the 7th CCF Conference on Big Data, BigData 2019, held in Wuhan, China, in October 2019. The 30 full papers presented in this volume were carefully reviewed and selected from 324 submissions. They were organized in topical sections as follows: big data modelling and methodology; big data support and architecture; big data processing; big data analysis; and big data application.
Download or read book Introduction to High Dimensional Statistics written by Christophe Giraud and published by CRC Press. This book was released on 2021-08-25 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: Praise for the first edition: "[This book] succeeds singularly at providing a structured introduction to this active field of research. ... it is arguably the most accessible overview yet published of the mathematical ideas and principles that one needs to master to enter the field of high-dimensional statistics. ... recommended to anyone interested in the main results of current research in high-dimensional statistics as well as anyone interested in acquiring the core mathematical skills to enter this area of research." —Journal of the American Statistical Association Introduction to High-Dimensional Statistics, Second Edition preserves the philosophy of the first edition: to be a concise guide for students and researchers discovering the area and interested in the mathematics involved. The main concepts and ideas are presented in simple settings, avoiding thereby unessential technicalities. High-dimensional statistics is a fast-evolving field, and much progress has been made on a large variety of topics, providing new insights and methods. Offering a succinct presentation of the mathematical foundations of high-dimensional statistics, this new edition: Offers revised chapters from the previous edition, with the inclusion of many additional materials on some important topics, including compress sensing, estimation with convex constraints, the slope estimator, simultaneously low-rank and row-sparse linear regression, or aggregation of a continuous set of estimators. Introduces three new chapters on iterative algorithms, clustering, and minimax lower bounds. Provides enhanced appendices, minimax lower-bounds mainly with the addition of the Davis-Kahan perturbation bound and of two simple versions of the Hanson-Wright concentration inequality. Covers cutting-edge statistical methods including model selection, sparsity and the Lasso, iterative hard thresholding, aggregation, support vector machines, and learning theory. Provides detailed exercises at the end of every chapter with collaborative solutions on a wiki site. Illustrates concepts with simple but clear practical examples.
Download or read book Exploring Low rank Prior in High dimensional Data written by He Lyu and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: High-dimensional data plays a ubiquitous role in real applications, ranging from biology, computer vision, to social media. The large dimensionality poses new challenges on statistical methods due to the "curse of dimensionality". To overcome these challenges, many statistical and machine learning approaches have been developed based on imposing additional assumptions on the data. One popular assumption is the low-rank prior, which assumes the high-dimensional data lies in a low-dimensional subspace, and approximately exhibits low-rank structure.In this dissertation, we explore various applications of low-rank prior. Chapter 2 studies the stability of leading singular subspaces. Various widely used algorithms have been proposed in numerical analysis, matrix completion, and matrix denoising based on the low-rank assumption, such as Principal Component Analysis and Singular Value Hard Thresholding. Many of these methods involve the computation of Singular Value Decomposition (SVD). To study the stability of these algorithms, in Chapter 2 we establish a useful set of formulae for the sinÎ8 distance between the original and the perturbed singular subspaces. Following this, we further derive a collection of new results on SVD perturbation related problems.In Chapter 3, we employ the low-rank prior for manifold denoising problems. Specifically, we generalize the Robust PCA (RPCA) method to manifold setting and propose an optimization framework that separates the sparse component from the noisy data. It is worth noting that in this chapter, we generalize the low-rank prior to a more general form to accommodate data with a more complex structure, instead of assuming the data itself lies in a low-dimensional subspace as in RPCA, we assume the clean data is distributed around a low-dimensional manifold. Therefore, if we consider a local neighborhood, the sub-matrix will be approximately low rank.Subsequently, in Chapter 4 we study the stability of invariant subspaces for eigensystems. Specifically, we focus on the case where the eigensystem is ill-conditioned and explore how the condition numbers affect the stability of invariant subspaces.The material presented in this dissertation encompasses several publications and preprints in the fields of Statistical, Numerical Linear Algebra, and Machine Learning, including Lyu and Wang (2020a); Lyu et al. (2019); Lyu and Wang (2022).
Download or read book Computer Vision ACCV 2014 written by Daniel Cremers and published by Springer. This book was released on 2015-04-15 with total page 743 pages. Available in PDF, EPUB and Kindle. Book excerpt: The five-volume set LNCS 9003--9007 constitutes the thoroughly refereed post-conference proceedings of the 12th Asian Conference on Computer Vision, ACCV 2014, held in Singapore, Singapore, in November 2014. The total of 227 contributions presented in these volumes was carefully reviewed and selected from 814 submissions. The papers are organized in topical sections on recognition; 3D vision; low-level vision and features; segmentation; face and gesture, tracking; stereo, physics, video and events; and poster sessions 1-3.
