Kernelized probabilistic matrix factorization: Exploiting graphs and side information

Tinghui Zhou, Hanhuai Shan, Arindam Banerjee, Guillermo Sapiro

Research output: Chapter in Book/Report/Conference proceedingConference contribution

101 Scopus citations

Abstract

We propose a new matrix completion algorithm| Kernelized Probabilistic Matrix Factorization (KPMF), which effectively incorporates external side information into the matrix factorization process. Unlike Probabilistic Matrix Factorization (PMF) [14], which assumes an independent latent vector for each row (and each column) with Gaussian priors, KMPF works with latent vectors spanning all rows (and columns) with Gaussian Process (GP) priors. Hence, KPMF explicitly captures the underlying (nonlinear) covariance structures across rows and columns. This crucial difference greatly boosts the performance of KPMF when appropriate side information, e.g., users' social network in recommender systems, is incorporated. Furthermore, GP priors allow the KPMF model to fill in a row that is entirely missing in the original matrix based on the side information alone, which is not feasible for standard PMF formulation. In our paper, we mainly work on the matrix completion problem with a graph among the rows and/or columns as side information, but the proposed framework can be easily used with other types of side information as well. Finally, we demonstrate the efficacy of KPMF through two different applications: 1) recommender systems and 2) image restoration.

Original languageEnglish (US)
Title of host publicationProceedings of the 12th SIAM International Conference on Data Mining, SDM 2012
Pages403-414
Number of pages12
StatePublished - Dec 1 2012
Event12th SIAM International Conference on Data Mining, SDM 2012 - Anaheim, CA, United States
Duration: Apr 26 2012Apr 28 2012

Publication series

NameProceedings of the 12th SIAM International Conference on Data Mining, SDM 2012

Other

Other12th SIAM International Conference on Data Mining, SDM 2012
CountryUnited States
CityAnaheim, CA
Period4/26/124/28/12

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