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Glossary
Definition

Matrix Factorization

Approximating a large, mostly unobserved matrix as the product of two smaller matrices, fit only on observed entries so missing ones are filled in for free.

Two small factor matrices are fit so their product approximates the observed entries of a much larger, sparse matrix; the dot product between a row and a column also exists for entries that were never observed, so missing values are filled in without ever being estimated directly.

On a fully observed matrix it converges toward the same structure the SVD gives directly — this generalizes SVD to handle missing data, trading exact optimality for tolerance of sparsity.