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SVD Recommendation System in Ruby

Sounds familiar, right? In fact, recommendation systems are a billion-dollar industry, and growing. In academic jargon this problem is known as Collaborative Filtering, and a lot of ink has been spilled on the matter. Netflix, for one, announced a 1 million dollar competition last year for a system that beats their algorithm by +10% percent. It goes without saying that a lot of different systems have been proposed and explored in theory and practice. However, one of the most successful and widely used approaches to this day also happens to be one of the simplest: Singular Value Decomposition (SVD), also affectionately referred to in the literature as LSI (Latent Semantic Indexing), dimensionality reduction, or projection.