Spectral Regularization Algorithms for Recommender Systems with Large Implicit Datasets

Recommender systems are a class of algorithms that help customers to overcome their choice problem by recommending products that they are likely to be interested in. Most recommender systems are developed for datasets where users explicitly provide feedback in the form of ratings. In practice, such datasets are often unavailable and companies have to resort to implicit datasets, where feedback is distilled from different sorts of user’s behavior, such as click through data or purchases. There exists some models that are specifically suited for implicit datasets and that can be estimated with alternating least squares (ALS) and stochastic gradient descent methods. The main goal of this research is to develop convex spectral regularization algorithms that are able to solve these implicit models. Until now, such algorithms are only designed for explicit context and cannot be applied to solve implicit models. The advantage of these algorithms is that they are computationally very efficient and need fewer observations than their ALS counterparts. We develop three algorithms that optimize three different implicit data models. One of these models is newly developed and based on a squared hinge loss function. All algorithms scale linearly in complexity with the size of the data. From a simulation study, we find evidence that the algorithms perform well for large datasets. We successfully apply the algorithms to an empirical dataset of an e-commerce company and show that they compare favourably to competing methods. We find no evidence for superior performance of our newly developed one-sided squared hinge loss model.