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Everything about Matrix regularization
In the field of statistical learning theory, matrix regularization generalizes notions of vector regularization to cases where the object to be learned is a matrix. The purpose of regularization is to enforce conditions, for example sparsity or smoothness, that can produce stable predictive functions. For example, in the more common vector framework, Tikhonov regularization optimizes over to find a vector that is a stable solution to the regression problem. When the system is described by a matrix rather than a vector, this problem can be written as where the vector norm enforcing a regularization penalty on has been extended to a matrix norm on. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Matrix regularizationA 5-minute orientation
- Skim a recent paper: Robust graph regularization nonnegative matrix factorization for link prediction in attributed networksInfluential work since 2022
- Pick up a classic book: Mathematical structures for computer scienceThe most-reprinted book on the subject
- Read the landmark paper: Matrix Metalloproteinases: Regulators of the Tumor MicroenvironmentCited 4,543 times
- Go sideways: Regularized least squaresA closely related topic
- Go sideways: Regularization (mathematics)A closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
Matrix Metalloproteinases: Regulators of the Tumor Microenvironment
How Matrix Metalloproteinases Regulate Cell Behavior
Matrix metalloproteinases and the regulation of tissue remodelling
Low-Rank Matrix Approximation with Manifold Regularization
Regularization of one-matrix models
Regularization in Matrix Relevance Learning
Error Analysis for Matrix Elastic-Net Regularization Algorithms
Robust nonnegative matrix factorization with structure regularization
🆕 Influential since 2022
Robust graph regularization nonnegative matrix factorization for link prediction in attributed networks
Diverse Deep Matrix Factorization with Hypergraph Regularization for Multi-View Data Representation
Adaptive graph nonnegative matrix factorization with the self-paced regularization
Nonredundancy regularization based nonnegative matrix factorization with manifold learning for multiview data representation
Noise-tolerant clustering via joint doubly stochastic matrix regularization and dual sparse coding
📚 Books worth reading
Mathematical structures for computer scienceJudith L. Gersting · 1982
The Elements of Statistical LearningTrevor Hastie, Robert Tibshirani · 2001
Gaussian processes for machine learningCarl Edward Rasmussen · 2005
An Introduction to Probability Theory and Its Applications [2/2]William Feller · 1966
Parallel Programming in C with MPI and OpenMPMichael J. Quinn · 2003
Data science from scratchJoel Grus · 2015
Programming Massively Parallel ProcessorsDavid Kirk, Wen-Mei W. Hwu · 2010- 📕Structural Aspects of Quantum Field Theory and Noncommutative GeometryGerhard Grensing · 2013
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Regularized least squares Regularized least squares (RLS) is a family of methods for solving the least-squares problem while using regularization to further constrain the resulting…
- Regularization (mathematics) In mathematics, statistics, finance, and computer science, particularly in machine learning and inverse problems, regularization is a process that converts…
- 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…
- Ridge regression Ridge regression (also known as Tikhonov regularization, named for Andrey Tikhonov) is a method of estimating the coefficients of multiple-regression models…
- Lasso (statistics) In statistics and machine learning, lasso (least absolute shrinkage and selection operator; also Lasso, LASSO or L1 regularization) is a regression analysis…
- Multi-task learning Multi-task learning (MTL) is a subfield of machine learning in which multiple learning tasks are solved at the same time, while exploiting commonalities…
- Elastic net regularization In statistics and, in particular, in the fitting of linear or logistic regression models, the elastic net is a regularized regression method that linearly…
- Support vector machine In machine learning, a support vector machine (SVM) or support vector network is a supervised max-margin model with associated learning algorithms that…