Recommendation Engines by Michael Schrage

Author:Michael Schrage [Schrage, Michael]
Language: eng
Format: epub, pdf
Publisher: MIT Press
Published: 2020-08-07T00:00:00+00:00

A = USV′

Where U and V are orthogonal and and S is diagonal. Think of this deconstruction as the rows U reveal how much each user likes a particular “feature” while the columns of V tell us which items have each feature. The diagonal of S “weights” and details the overall importance of each feature. What exactly are these features? We don’t know; they’re what the SVD has determined from the data.

To get a quick sense of how this works, picture that these features are actors, genres, budgets, directors, length, prizes, and so on, for a movie. Different movies would have different mixtures of different features. Different viewers would weight these different features differently. What makes SVD explicitly intriguing is we don’t have to decide or determine what those features are. The SVD does it for us.

Mathematically deconstructing—or dividing—the larger matrix into these smaller matrixes surfaces hidden or “latent” features that measurably influence user ratings. That is, these features weren’t directly observable until the big matrix was broken into the product of the littler matrixes. Dimensionality reduction and decomposition reveal and highlight data-based relationships otherwise concealed in the larger matrix. By definition, these smaller matrixes are less sparse than their parent.

These lower-dimensional matrixes offer intriguing intuitive rationales for inferring tacit user preference. To wit, a user gives good movie ratings to Inception, Edge of Tomorrow, and Arrival. These aren’t presented as three distinct opinions but suggest a strong predilection for high concept “time-twisting” science fiction films. Unlike more specific features—such as actors, budgets, and genre—latent features are expressed by higher-level attributes. Matrix factorization is a powerful mathematical mechanism offering inferential insight into how aligned users may be with latent features and how comfortably movies fit into latent feature sets.

This “similarity” is qualitatively and quantitatively different—and conceptually deeper—than standard nearest neighborhood calculations. Even if two users haven’t rated any of these same movies similarity discovery may still happen if, as these latent features suggest, they share comparable underlying tastes. SVD and other dimensionality reduction approaches such as Principal Component Analysis calculate new dimensions of predictive similarity for recommendation.

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