The topological face of recommendation: models and application to bias detection

Recommendation plays a key role in e-commerce and in the entertainment industry. We propose to consider successive recommendations to users under the form of graphs of recommendations. We give models for this representation. Motivated by the growing interest for algorithmic transparency, we then propose a first application for those graphs, that is the potential detection of introduced recommendation bias by the service provider. This application relies on the analysis of the topology of the extracted graph for a given user; we propose a notion of recommendation coherence with regards to the topological proximity of recommended items (under the measure of items' k-closest neighbors, reminding the "small-world" model by Watts & Stroggatz). We finally illustrate this approach on a model and on Youtube crawls, targeting the prediction of "Recommended for you" links (i.e., biased or not by Youtube).