Abstract—We investigate dimensionality reduction methods from the perspective of their ability to produce a low-rank customer-product matrix representation. We analyze the results of using collaborative filtering based on SVD, RI, Reflective Random Indexing (RRI) and Randomized Singular Value Decomposition (RSVD) from the perspective of selected algebraic (i.e. application-independent) properties. We show that the Frobenius-norm optimality of SVD does not correspond to the optimal recommendation accuracy, when measured in terms of F1. On the other hand, a high collaborative filtering quality is achievable when a matrix decomposition – based on a combination of RRI and SVD referred to as RSVD-RRI – leads to increased diversity of low-dimensional eigenvectors. The diversity is observable from the perspective of cosine similarities analyzed in comparison to the analogical case of SVD. Such a feature is more desirable than the fidelity of the input matrix spectrum representation, despite the MSE-optimality of SVD.
Index Terms—dimensionality reduction, random indexing, recommender system, singular value decomposition.
Michal Ciesielczyk is with the Institute of Control and Information Engineering, Poznan University of Technology, Poznan, Poland (e-mail: Michal.Ciesielczyk@put.poznan.pl). Andrzej Szwabe is with the Institute of Control and Information Engineering, Poznan University of Technology, Poznan, Poland (e-mail: Andrzej.Szwabe@put.poznan.pl).
Cite: Michal Ciesielczyk and Andrzej Szwabe, "RSVD-based Dimensionality Reduction for Recommender Systems," International Journal of Machine Learning and Computing vol. 1, no. 2, pp. 170-175, 2011.