Everything about Matrix completion
Filling in missing entries of a matrix
Matrix completion is the task of filling in the missing entries of a partially observed matrix, which is equivalent to performing data imputation in statistics. A wide range of datasets are naturally organized in matrix form. One example is the movie-ratings matrix, as appears in the Netflix problem: Given a ratings matrix in which each entry represents the rating of movie by customer, if customer has watched movie and is otherwise missing, we would like to predict the remaining entries in order to make good recommendations to customers on what to watch next. Another example is the document-term matrix: The frequencies of words used in a collection of documents can be represented as a matrix, where each entry corresponds to the number of times the associated term appears in the indicated document. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Matrix completionA 5-minute orientation
- Skim a recent paper: Matrix effects demystified: Strategies for resolving challenges in analytical separations of complex samplesInfluential work since 2022
- Pick up a classic book: TensorsThe most-reprinted book on the subject
- Read the landmark paper: A Singular Value Thresholding Algorithm for Matrix CompletionCited 4,799 times
- Go sideways: Monge–Ampère equationA closely related topic
- Go sideways: Menter's Shear Stress TransportA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🏆 Landmark papers (most cited)
A Singular Value Thresholding Algorithm for Matrix Completion
A complete active space SCF method (CASSCF) using a density matrix formulated super-CI approach
Exact Matrix Completion via Convex Optimization
Matrix Completion With Noise
Exact matrix completion via convex optimization
Phase Retrieval via Matrix Completion
Phase Retrieval via Matrix Completion
Matrix completion by deep matrix factorization
🆕 Influential since 2022
Matrix effects demystified: Strategies for resolving challenges in analytical separations of complex samples
Propagation Map Reconstruction via Interpolation Assisted Matrix Completion
A review on matrix completion for recommender systems
Prediction of Henry's law constants by matrix completion
MiRNA-Disease association prediction via non-negative matrix factorization based matrix completion
📚 Books worth reading
- 📕TensorsJ. M. Landsberg · 2011
New aspects in interpolation and completion theoriesGohberg, I. · 1993- 📕Completion Problems on Operator MatricesDragana S. Cvetkovic Ilic · 2022
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
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