Performing SVD on Matrices and Its Extensions
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In this chapter, we describe singular value decomposition (SVD), which is applied on recommender systems. We discuss in detail the method’s mathematical background and present (step by step) the SVD method using a toy example of a recommender system. We also describe in detail UV decomposition. This method is an instance of SVD, as we mathematically prove. We minimize an objective function, which captures the error between the predicted and real value of a user’s rating. We also provide a step-by-step implementation of UV decomposition using a toy example, which is followed by a short representation of the algorithm in pseudocode form. Finally, an additional constraint of friendship is added to the objective function to leverage the quality of recommendations.
KeywordsSingular value decomposition UV decomposition
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