Collaborative Filtering (CF) is a popular technique employed by Recommender Systems, a term used to describe intelligent methods that generate personalized recommendations. Some of the most efficient approaches to CF are based on latent factor models and nearest neighbor methods, and have received considerable attention in recent literature. Latent factor models can tackle some fundamental challenges of CF, such as data sparsity and scalability. In this work, we present an optimal scaling framework to address these problems using Categorical Principal Component Analysis (CatPCA) for the low-rank approximation of the user-item ratings matrix, followed by a neighborhood formation step. CatPCA is a versatile technique that utilizes an optimal scaling process where original data are transformed so that their overall variance is maximized. We considered both smooth and non-smooth transformations for the observed variables (items), such as numeric, (spline) ordinal, (spline) nominal and multiple nominal. The method was extended to handle missing data and incorporate differential weighting for items. Experiments were executed on three data sets of different sparsity and size, MovieLens 100k, 1M and Jester, aiming to evaluate the aforementioned options in terms of accuracy. A combined approach with a multiple nominal transformation and a "passive" missing data strategy clearly outperformed the other tested options for all three data sets. The results are comparable with those reported for single methods in the CF literature.
Hierarchical Factor Models for Large Spatially Misaligned Data: A Low-Rank Predictive Process Approach