Irina Rish's Sparse modeling : theory, algorithms, and applications PDF

By Irina Rish

ISBN-10: 1439828709

ISBN-13: 9781439828700

Sparse versions are relatively important in clinical purposes, resembling biomarker discovery in genetic or neuroimaging information, the place the interpretability of a predictive version is vital. Sparsity may also dramatically increase the associated fee potency of sign processing.

Sparse Modeling: conception, Algorithms, and Applications presents an advent to the starting to be box of sparse modeling, together with program examples, challenge formulations that yield sparse options, algorithms for locating such recommendations, and up to date theoretical effects on sparse restoration. The e-book will get you up to the mark at the most recent sparsity-related advancements and may encourage you to keep learning concerning the field.

The authors first current motivating examples and a high-level survey of key contemporary advancements in sparse modeling. The e-book then describes optimization difficulties concerning widely used sparsity-enforcing instruments, offers crucial theoretical effects, and discusses numerous cutting-edge algorithms for locating sparse options.

The authors pass directly to tackle numerous sparse restoration difficulties that reach the elemental formula to extra subtle types of based sparsity and to assorted loss capabilities. additionally they research a specific category of sparse graphical versions and canopy dictionary studying and sparse matrix factorizations.

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Extra info for Sparse modeling : theory, algorithms, and applications

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Summary and Bibliographical Notes . . . . . . . . . . . . . . . . 16 18 19 20 21 22 23 27 30 33 The focus of this chapter is on optimization problems that arise in sparse signal recovery. We start with a simple case of noiseless linear measurements, which is later extended to more realistic noisy recovery formulation(s). Since the ultimate problem of finding the sparsest solution – the solution with the smallest number of nonzeros, also called the l0 -norm – is computationally hard (specifically, NP-hard) due to its nonconvex combinatorial nature, one must resort to approximations.

Beyond LASSO: Other Loss Functions and Regularizers . . . . . . Summary and Bibliographical Notes . . . . . . . . . . . . . . . . 16 18 19 20 21 22 23 27 30 33 The focus of this chapter is on optimization problems that arise in sparse signal recovery. We start with a simple case of noiseless linear measurements, which is later extended to more realistic noisy recovery formulation(s). Since the ultimate problem of finding the sparsest solution – the solution with the smallest number of nonzeros, also called the l0 -norm – is computationally hard (specifically, NP-hard) due to its nonconvex combinatorial nature, one must resort to approximations.

Surprising Empirical Results . . . . . . . . . . . . . . . . . . . . Signal Recovery from Incomplete Frequency Information . . . . . . Mutual Coherence . . . . . . . . . . . . . . . . . . . . . . . . . Spark and Uniqueness of (P0 ) Solution . . . . . . . . . . . . . . . Null Space Property and Uniqueness of (P1 ) Solution . . . . . . . . Restricted Isometry Property (RIP) . . . . . . . . .

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Sparse modeling : theory, algorithms, and applications by Irina Rish


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