Alternating Least Squares Regression

Learn how to solve alternate least squares regression using the gradient-solving approach.

Matrix decomposition

Consider a movie recommendation system with nn users and mm movies. Suppose the matrix ARn×mA \in \R^{n \times m} represents the rating matrix where its (i,j)th(i,j)^{th} entry AijA_{ij} represents the rating given by the ithi^{th} user to the jthj^{th} movie. We would like to represent/decompose the matrix AA as a product of the two matrices XRn×r,YRm×rX \in \R^{n \times r}, Y \in \R^{m \times r} as follows:

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