Matrix completion under interval uncertainty: highlights

J. Mareček, P. Richtárik, M. Takáč
Lecture Notes in Computer Science, ECML-PKDD, (2018)

Matrix completion under interval uncertainty: highlights


Matrix completion, Dimensions of a matrix


Matrix completion is a well-known problem: Given dimensions of a matrix X and some of its elements Xi,j, (i,j)∈ E, the goal is to find the remaining elements. Without imposing any further requirements on X , there are infinitely many solutions. In many applications, however, the matrix completion that minimizes the rank:

min Y rank(Y), subject to Yi,j=Xi,j, (i,j)∈E,

often works as well as the best known solvers for problems in the particular domain. There are literally hundreds of applications of matrix completion, especially in recommender systems [3], where the matrix is composed of ratings, with a row per user and column per product.





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