Kernelized Probabilistic Matrix Factorization: Exploiting Graphs and Side Information

We propose a new matrix completion algorithm— Kernelized Probabilistic Matrix Factorization (KPMF), which effectively incorporates external side information into the matrix factorization process. Compared with Probabilistic Matrix Factorization (PMF) [1], which imposes a Gaussian prior for each row of the data matrix, KPMF imposes a Gaussian Process (GP) prior over all rows of the matrix, hence the learned model explicitly captures the underlying correlation among the rows (and the same holds for 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 in...

• Type: Journal
• Year: 2012
• Where: SDM
• Authors: Tinghui Zhou, Hanhuai Shan, Arindam Banerjee, Guillermo Sapiro
• Keywords: Completion Algorithm, Data Mining, Matrix Completion, Matrix Factorization, SDM 2012