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Everything about Sparse approximation
Concept in mathematics
Sparse approximation theory deals with sparse solutions for systems of linear equations. Techniques for finding these solutions and exploiting them in applications have found wide use in image processing, signal processing, machine learning, medical imaging, and more. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Sparse approximationA 5-minute orientation
- Skim a recent paper: Variational Bayesian approximation of inverse problems using sparse precision matricesInfluential work since 2022
- Pick up a classic book: Analyses of the Lanczos algorithm and of the approximation problem in Richardson's methodThe most-reprinted book on the subject
- Read the landmark paper: Greed is Good: Algorithmic Results for Sparse ApproximationCited 2,676 times
- Go sideways: K-SVDA closely related topic
- Go sideways: Basis pursuit denoisingA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
Greed is Good: Algorithmic Results for Sparse Approximation
Sparse Reconstruction by Separable Approximation
Double Sparsity: Learning Sparse Dictionaries for Sparse Signal Approximation
DC approximation approaches for sparse optimization
Sparse pseudospectral approximation method
Sparse Approximation via Penalty Decomposition Methods
Sparse Signal Approximation via Nonseparable Regularization
Sparse deterministic approximation of Bayesian inverse problems
🆕 Influential since 2022
Variational Bayesian approximation of inverse problems using sparse precision matrices
Efficient Incremental Offline Reinforcement Learning With Sparse Broad Critic Approximation
Sparse Approximation of Triangular Transports, Part II: The Infinite-Dimensional Case
Sparse Grid Approximation in Weighted Wiener Spaces
Sparse Approximation of Triangular Transports, Part I: The Finite-Dimensional Case
📚 Books worth reading
- 📕Analyses of the Lanczos algorithm and of the approximation problem in Richardson's methodJoseph F. Grcar · 1981
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- K-SVD In applied mathematics, k-SVD is a dictionary learning algorithm for creating a dictionary for sparse representations, via a singular value decomposition…
- Basis pursuit denoising In applied mathematics and statistics, basis pursuit denoising (BPDN) refers to a mathematical optimization problem of the form min x ( 1 2 ‖ y − A x ‖…
- Matching pursuit Matching pursuit (MP) is a sparse approximation algorithm which finds the "best matching" projections of multidimensional data onto the span of an over-complete…
- Sparse dictionary learning Sparse dictionary learning (also known as sparse coding or SDL) is a representation learning method which aims to find a sparse representation of the input…
- Mutual coherence (linear algebra) In linear algebra, mutual coherence (or simply coherence) measures the maximum similarity between any two columns of a matrix, defined as the largest absolute…
- Manifold regularization In machine learning, manifold regularization is a technique for using the shape of a dataset to constrain the functions that should be learned on that…
- Frank–Wolfe algorithm The Frank–Wolfe algorithm is an iterative first-order optimization algorithm for constrained convex optimization. Also known as the conditional gradient…
- Structured sparsity regularization Structured sparsity regularization is a class of methods, and an area of research in statistical learning theory, that extend and generalize sparsity regulariza…