TY - GEN

T1 - Kernelized probabilistic matrix factorization

T2 - 12th SIAM International Conference on Data Mining, SDM 2012

AU - Zhou, Tinghui

AU - Shan, Hanhuai

AU - Banerjee, Arindam

AU - Sapiro, Guillermo

PY - 2012

Y1 - 2012

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84880250677&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84880250677&partnerID=8YFLogxK

U2 - 10.1137/1.9781611972825.35

DO - 10.1137/1.9781611972825.35

M3 - Conference contribution

AN - SCOPUS:84880250677

SN - 9781611972320

T3 - Proceedings of the 12th SIAM International Conference on Data Mining, SDM 2012

SP - 403

EP - 414

BT - Proceedings of the 12th SIAM International Conference on Data Mining, SDM 2012

PB - Society for Industrial and Applied Mathematics Publications

Y2 - 26 April 2012 through 28 April 2012

ER -