Collaborative Filtering through SVD-Based and Hierarchical Nonlinear PCA

In this paper, we describe and compare two distinct algorithms aiming at the low-rank approximation of a user-item ratings matrix in the context of Collaborative Filtering (CF). The first one implements standard Principal Component Analysis (PCA) of an association matrix formed from the original data. The second algorithm is based on h-NLPCA, a nonlinear generalization of standard PCA, which utilizes an autoassociative network, and constrains the nonlinear components to have the same hierarchical order as the linear components in standard PCA. We examine the impact of the aforementioned approaches on the quality of the generated predictions through a series of experiments. Experimental results show that the latter approach outperforms the standard PCA approach for most values of the retained dimensions.