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Performing SVD on Matrices and Its Extensions

  • Panagiotis SymeonidisEmail author
  • Andreas Zioupos
Chapter
  • 1.4k Downloads
Part of the SpringerBriefs in Computer Science book series (BRIEFSCOMPUTER)

Abstract

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.

Keywords

Singular value decomposition UV decomposition 

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Copyright information

© The Author(s) 2016

Authors and Affiliations

  1. 1.Faculty of Computer ScienceFree University of Bozen-BolzanoBozen-BolzanoItaly
  2. 2.ThessalonikiGreece

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