An Optimal Scaling Approach to Collaborative Filtering Using Categorical Principal Component Analysis and Neighborhood Formation

Collaborative Filtering (CF) is a popular technique employed by Recommender Systems, a term used to describe intelligent methods that generate personalized recommendations. The most common and accurate approaches to CF are based on latent factor models. Latent factor models can tackle two fundamental problems of CF, data sparsity and scalability and have received considerable attention in recent literature. In this work, we present an optimal scaling approach to address both of these problems using Categorical Principal Component Analysis for the low-rank approximation of the user-item ratings matrix, followed by a neighborhood formation step. The optimal scaling approach has the advantage that it can be easily extended to the case when there are missing data and restrictions for ordinal and numerical variables can be easily imposed. We considered different measurement levels for the user ratings on items, starting with a multiple nominal and consecutively applying nominal, ordinal and numeric levels. Experiments were executed on the MovieLens dataset, aiming to evaluate the aforementioned options in terms of accuracy. Results indicated that a combined approach (multiple nominal measurement level, “passive” missing data strategy) clearly outperformed the other tested options.