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Dictionary learning algorithms and applications

Author: Bogdan Dumitrescu; Paul Irofti
Publisher: Cham, Switzerland : Springer, [2018] ©2018
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
This book covers all the relevant dictionary learning algorithms, presenting them in full detail and showing their distinct characteristics while also revealing the similarities. It gives implementation tricks that are often ignored but that are crucial for a successful program. Besides MOD, K-SVD, and other standard algorithms, it provides the significant dictionary learning problem variations, such as  Read more...
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Genre/Form: Electronic books
Additional Physical Format: (OCoLC)1027130144
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Bogdan Dumitrescu; Paul Irofti
ISBN: 9783319786742 3319786741
OCLC Number: 1031706383
Description: 1 online resource (xiv, 284 pages) : illustrations
Contents: Intro; Preface; Contents; 1 Sparse Representations; 1.1 The Sparse Model; 1.2 Algorithms; 1.3 Orthogonal Matching Pursuit; 1.4 Algorithms for Basis Pursuit: FISTA; 1.5 Guarantees; 1.6 The Choice of a Dictionary: Fixed vs Learned; Problems; 2 Dictionary Learning Problem; 2.1 The Optimization Problem; 2.2 An Analysis of the DL Problem; 2.3 Test Problems; 2.3.1 Representation Error; 2.3.2 Dictionary Recovery; 2.4 Applications: A Quick Overview; 2.4.1 Denoising; 2.4.2 Inpainting; 2.4.3 Compression; 2.4.4 Compressed Sensing; 2.4.5 Classification; Problems; 3 Standard Algorithms 3.1 Basic Strategy: Alternating Optimization3.2 Sparse Coding; 3.3 Simple Descent Methods; 3.3.1 Gradient Descent; 3.3.2 Coordinate Descent; 3.4 Method of Optimal Directions (MOD); 3.5 K-SVD; 3.6 Parallel Algorithms; 3.7 SimCO; 3.8 Refinements; 3.9 Practical Issues; 3.9.1 Initialization; 3.9.2 Dictionary Size and Other Size Parameters; 3.9.3 Unused or Redundant Atoms; 3.9.4 Randomization; 3.10 Comparisons: Theory; 3.11 Comparisons: Some Experimental Results; 3.11.1 Representation Error Results; 3.11.2 Dictionary Recovery Result; 3.11.3 Denoising Results 3.12 Impact of Sparse Representation AlgorithmProblems; 4 Regularization and Incoherence; 4.1 Learning with a Penalty; 4.2 Regularization; 4.2.1 Sparse Coding; 4.2.2 Regularized K-SVD; 4.2.3 Comparison Between Regularized K-SVD and SimCO; 4.3 Frames; 4.4 Joint Optimization of Error and Coherence; 4.5 Optimizing an Orthogonal Dictionary; 4.6 Imposing Explicit Coherence Bounds; 4.7 Atom-by-Atom Decorrelation; Problems; 5 Other Views on the DL Problem; 5.1 Representations with Variable Sparsity Levels; 5.2 A Simple Algorithm for DL with l1 Penalty; 5.3 A Majorization Algorithm 5.4 Proximal Methods5.5 A Gallery of Objectives; 5.6 Task-Driven DL; 5.7 Dictionary Selection; 5.8 Online DL; 5.8.1 Online Coordinate Descent; 5.8.2 RLS DL; 5.9 DL with Incomplete Data; Problems; 6 Optimizing Dictionary Size; 6.1 Introduction: DL with Imposed Error; 6.2 A General Size-Optimizing DL Structure; 6.3 Stagewise K-SVD; 6.4 An Initialization Method; 6.5 An Atom Splitting Procedure; 6.6 Clustering as a DL Tool; 6.7 Other Methods; 6.8 Size-Reducing OMP; Problems; 7 Structured Dictionaries; 7.1 Short Introduction; 7.2 Sparse Dictionaries; 7.2.1 Double Sparsity; 7.2.2 Greedy Selection 7.2.3 Multi-Layer Sparse DL7.2.4 Multiscale Dictionaries; 7.3 Orthogonal Blocks; 7.3.1 Orthogonal Basis Training; 7.3.2 Union of Orthonormal Bases; 7.3.3 Single Block Orthogonal DL; 7.4 Shift Invariant Dictionaries; 7.4.1 Circulant Dictionaries; 7.4.2 Convolutional Sparse Coding; 7.5 Separable Dictionaries; 7.5.1 2D-OMP; 7.5.2 SeDiL; 7.6 Tensor Strategies; 7.6.1 CP Decomposition; 7.6.2 CP Dictionary Update; 7.6.3 Tensor Singular Valued Decomposition; 7.6.4 t-SVD Dictionary Update; 7.7 Composite Dictionaries; 7.7.1 Convex Approach; 7.7.2 Composite Dictionaries with Orthogonal Blocks; Problems
Responsibility: Bogdan Dumitrescu, Paul Irofti.

Abstract:

This book covers all the relevant dictionary learning algorithms, presenting them in full detail and showing their distinct characteristics while also revealing the similarities. It gives implementation tricks that are often ignored but that are crucial for a successful program. Besides MOD, K-SVD, and other standard algorithms, it provides the significant dictionary learning problem variations, such as regularization, incoherence enforcing, finding an economical size, or learning adapted to specific problems like classification. Several types of dictionary structures are treated, including shift invariant; orthogonal blocks or factored dictionaries; and separable dictionaries for multidimensional signals. Nonlinear extensions such as kernel dictionary learning can also be found in the book. The discussion of all these dictionary types and algorithms is enriched with a thorough numerical comparison on several classic problems, thus showing the strengths and weaknesses of each algorithm. A few selected applications, related to classification, denoising and compression, complete the view on the capabilities of the presented dictionary learning algorithms. The book is accompanied by code for all algorithms and for reproducing most tables and figures. Presents all relevant dictionary learning algorithms - for the standard problem and its main variations - in detail and ready for implementation; Covers all dictionary structures that are meaningful in applications; Examines the numerical properties of the algorithms and shows how to choose the appropriate dictionary learning algorithm.

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