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Generalized Low Rank Models

2016 Principal components analysis
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Release : 2016
Genre : Principal components analysis
Kind : eBook
Book Rating : 412/5 ( reviews)

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Book Synopsis Generalized Low Rank Models by : Madeleine Udell

Download or read book Generalized Low Rank Models written by Madeleine Udell. This book was released on 2016. 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. Here, we extend 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.

Generalized Low Rank Models

2015
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Release : 2015
Genre :
Kind : eBook
Book Rating : /5 ( reviews)

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Book Synopsis Generalized Low Rank Models by : Madeleine Udell

Download or read book Generalized Low Rank Models written by Madeleine Udell. This book was released on 2015. 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.

Multivariate Reduced-Rank Regression

2022-11-30 Mathematics
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Release : 2022-11-30
Genre : Mathematics
Kind : eBook
Book Rating : 937/5 ( reviews)

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Book Synopsis Multivariate Reduced-Rank Regression by : Gregory C. Reinsel

Download or read book Multivariate Reduced-Rank Regression written by Gregory C. Reinsel. This book was released on 2022-11-30. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an account of multivariate reduced-rank regression, a tool of multivariate analysis that enjoys a broad array of applications. In addition to a historical review of the topic, its connection to other widely used statistical methods, such as multivariate analysis of variance (MANOVA), discriminant analysis, principal components, canonical correlation analysis, and errors-in-variables models, is also discussed. This new edition incorporates Big Data methodology and its applications, as well as high-dimensional reduced-rank regression, generalized reduced-rank regression with complex data, and sparse and low-rank regression methods. Each chapter contains developments of basic theoretical results, as well as details on computational procedures, illustrated with numerical examples drawn from disciplines such as biochemistry, genetics, marketing, and finance. This book is designed for advanced students, practitioners, and researchers, who may deal with moderate and high-dimensional multivariate data. Because regression is one of the most popular statistical methods, the multivariate regression analysis tools described should provide a natural way of looking at large (both cross-sectional and chronological) data sets. This book can be assigned in seminar-type courses taken by advanced graduate students in statistics, machine learning, econometrics, business, and engineering.

Low-Rank Models in Visual Analysis

2017-06-06 Computers
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Release : 2017-06-06
Genre : Computers
Kind : eBook
Book Rating : 325/5 ( reviews)

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Book Synopsis Low-Rank Models in Visual Analysis by : Zhouchen Lin

Download or read book Low-Rank Models in Visual Analysis written by Zhouchen Lin. This book was released on 2017-06-06. 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

Ultra-dense Networks

2020-11-26 Technology & Engineering
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Release : 2020-11-26
Genre : Technology & Engineering
Kind : eBook
Book Rating : 131/5 ( reviews)

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Book Synopsis Ultra-dense Networks by : Haijun Zhang

Download or read book Ultra-dense Networks written by Haijun Zhang. This book was released on 2020-11-26. Available in PDF, EPUB and Kindle. Book excerpt: Understand the theoretical principles, key technologies and applications of UDNs with this authoritative survey. Theory is explained in a clear, step-by-step manner, and recent advances and open research challenges in UDN physical layer design, resource allocation and network management are described, with examples, in the context of B5G and 6G standardization. Topics covered include NOMA-based physical layer design, physical layer security. Interference management, 3D base station deployment, software defined UDNs, wireless edge caching in UDNs, UDN-based UAVs and field trials and tests. A perfect resource for graduate students, researchers and professionals who need to get up to speed on the state of the art and future opportunities in UDNs.

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