Mapping preferences into Euclidean space

New approach for a real world problem: preference learning via matrix factorization.Comparison between factorization and SVM tensorial approaches.Visual representation of the solution in an Euclidean space. Understanding and modeling human preferences is one of the key problems in applications ranging from marketing to automated recommendation. In this paper, we focus on learning and analyzing the preferences of consumers regarding food products. In particular, we explore Machine Learning methods that embed consumers and products in an Euclidean space such that their relationship to each other models consumer preferences. In addition to predicting preferences that were not explicitly stated, the Euclidean embedding enables visualization and clustering to understand the overall structure of a population of consumers and their preferences regarding the set of products. Notice that consumers' clusters are market segments, and products clusters can be seen as groups of similar items with respect to consumer tastes. We explore two types of Euclidean embedding of preferences, one based on inner products and other based on distances. Using a real world dataset about consumers of beef meat, we find that both embeddings produce more accurate models than a tensorial approach that uses a SVM to learn preferences. The reason is that the number of parameters to learned in embeddings can be considerably lower than in the tensorial approach. Furthermore, we demonstrate that the visualization of the learned embeddings provides interesting insights into the structure of the consumer and product space, and that it provides a method for qualitatively explaining consumer preferences. In addition, it is important to emphasize that the approach presented here is flexible enough to allow its use with different levels of knowledge about consumers or products; therefore the application field is very wide to grasp an accurate understanding of consumers' preferences.