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. Without any restrictions on the number of degrees of freedom in the completed matrix this problem is underdetermined since the hidden entries could be assigned arbitrary values. Thus we require some assumption on the matrix to create a well-posed problem, such as assuming it has maximal determinant, is positive definite, or is low-rank. For example, one may assume the matrix has low-rank structure, and then seek to find the lowest rank matrix or, if the rank of the completed matrix is known, a matrix of rank that matches the known entries. The illustration shows that a partially revealed rank-1 matrix (on the left) can be completed with zero-error (on the right) since all the rows with missing entries should be the same as the third row. In the case of the Netflix problem the ratings matrix is expected to be low-rank since user preferences can often be described by a few factors, such as the movie genre and time of release. Other applications include computer vision, where missing pixels in images need to be reconstructed, detecting the global positioning of sensors in a network from partial distance information, and multiclass learning. The matrix completion problem is in general NP-hard, but under additional assumptions there are efficient algorithms that achieve exact reconstruction with high probability. In statistical learning point of view, the matrix completion problem is an application of matrix regularization which is a generalization of vector regularization. For example, in the low-rank matrix completion problem one may apply the regularization penalty taking the form of a nuclear norm (Wikipedia).
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This video shows you how a matrix is constructed from a set of linear equations. It helps you understand where the various elements in a matrix comes from.
From playlist Linear Algebra
How do we add matrices. A matrix is an abstract object that exists in its own right, and in this sense, it is similar to a natural number, or a complex number, or even a polynomial. Each element in a matrix has an address by way of the row in which it is and the column in which it is. Y
From playlist Introducing linear algebra
This is the second video of a series from the Worldwide Center of Mathematics explaining the basics of matrices. This video deals with multiplying two matrices. For more math videos, visit our channel or go to www.centerofmath.org
From playlist Basics: Matrices
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This computer science video is one of a series of lessons about linear algebra for computer scientists. This video introduces the concept of a matrix. A matrix is a rectangular or square, two dimensional array of numbers, symbols, or expressions. A matrix is also classed a second order
From playlist Linear Algebra for Computer Scientists
What is a matrix? Free ebook http://tinyurl.com/EngMathYT
From playlist Intro to Matrices
Matrix Addition and Scalar Multiplication
This is the first video of a series from the Worldwide Center of Mathematics explaining the basics of matrices. This video deals with matrix dimensions, matrix addition, and scalar multiplication. For more math videos, visit our channel or go to www.centerofmath.org
From playlist Basics: Matrices
Matrix Addition, Subtraction, and Scalar Multiplication
This video shows how to add, subtract and perform scalar multiplication with matrices. http://mathispower4u.yolasite.com/ http://mathispower4u.wordpress.com/
From playlist Introduction to Matrices and Matrix Operations
This video explains how to multiply matrices. http://mathispower4u.yolasite.com/ http://mathispower4u.wordpress.com/
From playlist Matrices
We have already looked at the column view of a matrix. In this video lecture I want to expand on this topic to show you that each matrix has a column space. If a matrix is part of a linear system then a linear combination of the columns creates a column space. The vector created by the
From playlist Introducing linear algebra
Low Algebraic Dimension Matrix Completion -Laura Balzano
Virtual Workshop on Missing Data Challenges in Computation Statistics and Applications Topic: Low Algebraic Dimension Matrix Completion Speaker: Laura Balzano Date: September 11, 2020 For more video please visit http://video.ias.edu
From playlist Mathematics
Kaie Kubias: "Rank-one tensor completion"
Tensor Methods and Emerging Applications to the Physical and Data Sciences 2021 Workshop III: Mathematical Foundations and Algorithms for Tensor Computations "Rank-one tensor completion" Kaie Kubias - Aalto University, Department of Mathematics and Systems Analysis Abstract: We study the
From playlist Tensor Methods and Emerging Applications to the Physical and Data Sciences 2021
Ankur Moitra: "Tensor Decompositions and their Applications (Part 2/2)"
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Lecture 30: Completing a Rank-One Matrix, Circulants!
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The famous Lindblad, Kossakowski, Gorini, and Sudarshan's (LKGS) theorem characterizes the generator of a semigroup of completely positive maps. Motivated by this result we study the characterization of the generators of other positive maps e.g. k-positive and k-super positive maps. We pro
From playlist Annual meeting “Arbre de Noël du GDR Géométrie non-commutative”
Low-rank matrix recovery from quantized or count observations - Mark Davenport
Virtual Workshop on Missing Data Challenges in Computation Statistics and Applications Topic: Low-rank matrix recovery from quantized or count observations Speaker: Mark Davenport Date: September 11, 2020 For more video please visit http://video.ias.edu
From playlist Mathematics
NIPS 2011 Sparse Representation & Low-rank Approximation Workshop: Divide-and-Conquer ...
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From playlist NIPS 2011 Sparse Representation & Low-rank Approx Workshop
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From playlist Nexus Trimester - 2016 -Tutorial Week at CIRM
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From playlist IISc Bangalore: Ordinary Differential Equations and Applications | CosmoLearning.org Mathematics
Definition of a matrix | Lecture 1 | Matrix Algebra for Engineers
What is a matrix? Join me on Coursera: https://www.coursera.org/learn/matrix-algebra-engineers Lecture notes at http://www.math.ust.hk/~machas/matrix-algebra-for-engineers.pdf Subscribe to my channel: http://www.youtube.com/user/jchasnov?sub_confirmation=1
From playlist Matrix Algebra for Engineers