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.

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.

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: 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

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.

This book provides a comprehensive introduction to the latest advances in the mathematical theory and computational tools for modeling high-dimensional data drawn from one or multiple low-dimensional subspaces (or manifolds) and potentially corrupted by noise, gross errors, or outliers. This challenging task requires the development of new algebraic, geometric, statistical, and computational methods for efficient and robust estimation and segmentation of one or multiple subspaces. The book also presents interesting real-world applications of these new methods in image processing, image and video segmentation, face recognition and clustering, and hybrid system identification etc. This book is intended to serve as a textbook for graduate students and beginning researchers in data science, machine learning, computer vision, image and signal processing, and systems theory. It contains ample illustrations, examples, and exercises and is made largely self-contained with three Appendices which survey basic concepts and principles from statistics, optimization, and algebraic-geometry used in this book. René Vidal is a Professor of Biomedical Engineering and Director of the Vision Dynamics and Learning Lab at The Johns Hopkins University. Yi Ma is Executive Dean and Professor at the School of Information Science and Technology at ShanghaiTech University. S. Shankar Sastry is Dean of the College of Engineering, Professor of Electrical Engineering and Computer Science and Professor of Bioengineering at the University of California, Berkeley.

Build predictive models using large data volumes and deploy them to production using cutting-edge techniques Key Features • Build highly accurate state-of-the-art machine learning models against large-scale data • Deploy models for batch, real-time, and streaming data in a wide variety of target production systems • Explore all the new features of the H2O AI Cloud end-to-end machine learning platform Book Description H2O is an open source, fast, and scalable machine learning framework that allows you to build models using big data and then easily productionalize them in diverse enterprise environments. Machine Learning at Scale with H2O begins with an overview of the challenges faced in building machine learning models on large enterprise systems, and then addresses how H2O helps you to overcome them. You'll start by exploring H2O's in-memory distributed architecture and find out how it enables you to build highly accurate and explainable models on massive datasets using your favorite ML algorithms, language, and IDE. You'll also get to grips with the seamless integration of H2O model building and deployment with Spark using H2O Sparkling Water. You'll then learn how to easily deploy models with H2O MOJO. Next, the book shows you how H2O Enterprise Steam handles admin configurations and user management, and then helps you to identify different stakeholder perspectives that a data scientist must understand in order to succeed in an enterprise setting. Finally, you'll be introduced to the H2O AI Cloud platform and explore the entire machine learning life cycle using multiple advanced AI capabilities. By the end of this book, you'll be able to build and deploy advanced, state-of-the-art machine learning models for your business needs. What you will learn • Build and deploy machine learning models using H2O • Explore advanced model-building techniques • Integrate Spark and H2O code using H2O Sparkling Water • Launch self-service model building environments • Deploy H2O models in a variety of target systems and scoring contexts • Expand your machine learning capabilities on the H2O AI Cloud Who this book is for This book is for data scientists and machine learning engineers who want to gain hands-on machine learning experience by building and deploying state-of-the-art models with advanced techniques using H2O technology. An understanding of the data science process and experience in Python programming is recommended. This book will also benefit students by helping them understand how machine learning works in real-world enterprise scenarios.