Kernelized matrix factorization for collaborative filtering

Abstract

Matrix factorization (MF) methods have shown great promise in collaborative filtering (CF). Conventional MF methods usually assume that the correlated data is distributed on a linear hyperplane, which is not always the case. Kernel methods are used widely in SVMs to classify linearly non-separable data, as well as in PCA to discover the non-linear embeddings of data. In this paper, we present a novel method to kernelize matrix factorization for collaborative filtering, which is equivalent to performing the low-rank matrix factorization in a possibly much higher dimensional space that is implicitly defined by the kernel function. Inspired by the success of multiple kernel learning (MKL) methods, we also explore the approach of learning multiple kernels from the rating matrix to further improve the accuracy of prediction. Since the right choice of kernel is usually unknown, our proposed multiple kernel matrix factorization method helps to select effective kernel functions from the candidates. Through extensive experiments on real-world datasets, we show that our proposed method captures the nonlinear correlations among data, which results in improved prediction accuracy compared to the state-of-art CF models.