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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

Low-Rank and Sparse Modeling for Visual Analysis

2014-10-30 Computers
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Release : 2014-10-30
Genre : Computers
Kind : eBook
Book Rating : 00X/5 ( reviews)

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Book Synopsis Low-Rank and Sparse Modeling for Visual Analysis by : Yun Fu

Download or read book Low-Rank and Sparse Modeling for Visual Analysis written by Yun Fu. This book was released on 2014-10-30. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a view of low-rank and sparse computing, especially approximation, recovery, representation, scaling, coding, embedding and learning among unconstrained visual data. The book includes chapters covering multiple emerging topics in this new field. It links multiple popular research fields in Human-Centered Computing, Social Media, Image Classification, Pattern Recognition, Computer Vision, Big Data, and Human-Computer Interaction. Contains an overview of the low-rank and sparse modeling techniques for visual analysis by examining both theoretical analysis and real-world applications.

Low-rank Models for Tensorial Data in Visual Analysis

2023 Calculus of tensors
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Release : 2023
Genre : Calculus of tensors
Kind : eBook
Book Rating : /5 ( reviews)

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Book Synopsis Low-rank Models for Tensorial Data in Visual Analysis by : Ming Yang

Download or read book Low-rank Models for Tensorial Data in Visual Analysis written by Ming Yang. This book was released on 2023. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we study the 3D array image data completion, robust principal component analysis (PCA) and multi-view subspace clustering problems via a non-convex low-rank representation under the framework of tensors. Most recent studies of tensor-based linear models use the Tensor Nuclear Norm (TNN) as a convex surrogate of the tensor rank. However, since the tensor nuclear norm is linearly proportional to the sum of singular values, the tensor rank approximation using the tensor nuclear norm may become problematic if the ratios of the nonzero singular values are far away from 1. This paper proposes some non-convex tensor-based functions as the objective function regularizer, aiming to achieve a better tensor low-rank approximation. A corresponding algorithm associated with the augmented Lagrangian multipliers is established. The constructed convergent sequence to the desirable Karush-Kuhn-Tucker (KKT) critical point solution is mathematically validated in detail. Extensive simulations are provided on eight benchmark image datasets and full comparisons with the latest existing approaches. The results demonstrate that our proposed method significantly outperforms those convex approaches currently available in the literature.

Deep Learning through Sparse and Low-Rank Modeling

2019-04-11 Computers
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Release : 2019-04-11
Genre : Computers
Kind : eBook
Book Rating : 60X/5 ( reviews)

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Book Synopsis Deep Learning through Sparse and Low-Rank Modeling by : Zhangyang Wang

Download or read book Deep Learning through Sparse and Low-Rank Modeling written by Zhangyang Wang. This book was released on 2019-04-11. 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

Low-Rank Approximation

2018-08-03 Technology & Engineering
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Release : 2018-08-03
Genre : Technology & Engineering
Kind : eBook
Book Rating : 202/5 ( reviews)

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Book Synopsis Low-Rank Approximation by : Ivan Markovsky

Download or read book Low-Rank Approximation written by Ivan Markovsky. This book was released on 2018-08-03. Available in PDF, EPUB and Kindle. Book excerpt: This book is a comprehensive exposition of the theory, algorithms, and applications of structured low-rank approximation. Local optimization methods and effective suboptimal convex relaxations for Toeplitz, Hankel, and Sylvester structured problems are presented. A major part of the text is devoted to application of the theory with a range of applications from systems and control theory to psychometrics being described. Special knowledge of the application fields is not required. The second edition of /Low-Rank Approximation/ is a thoroughly edited and extensively rewritten revision. It contains new chapters and sections that introduce the topics of: • variable projection for structured low-rank approximation;• missing data estimation;• data-driven filtering and control;• stochastic model representation and identification;• identification of polynomial time-invariant systems; and• blind identification with deterministic input model. The book is complemented by a software implementation of the methods presented, which makes the theory directly applicable in practice. In particular, all numerical examples in the book are included in demonstration files and can be reproduced by the reader. This gives hands-on experience with the theory and methods detailed. In addition, exercises and MATLAB^® /Octave examples will assist the reader quickly to assimilate the theory on a chapter-by-chapter basis. “Each chapter is completed with a new section of exercises to which complete solutions are provided.” Low-Rank Approximation (second edition) is a broad survey of the Low-Rank Approximation theory and applications of its field which will be of direct interest to researchers in system identification, control and systems theory, numerical linear algebra and optimization. The supplementary problems and solutions render it suitable for use in teaching graduate courses in those subjects as well.

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