Collaborative filtering by PSO-based MMMF

Matrix factorization (MF) techniques are one of the most succesful realisations of recommender systems based on collaborative filtering/prediction (CF). For instance, in a movie recommender system based on CF, the inputs to the system are user ratings on movies (items) the users have already seen. To predict user preferences on movies they have not yet watched one needs to understand the patterns in the partially observed rating matrix. It is possible to visualize this setting as a matrix completion problem, i.e., completing entries in a partially observed data matrix. Then the objective is to compute user latent factor and item latent factor such that the rating matrix is completed. The factorization is usually accomplished by minimizing an objective function using gradient descent or its variants such as conjugate gradient or stochastic gradient descent. In this paper we make use of a particular MF technique called Maximum Margin Matrix Factorization (MMMF) and show that it is suitable for multi-level discrete rating matrix. The factorization is accomplished by minimizing the hinge loss objective function. We propose to improve the gradient search by combining a component of particle Swarm Optimisation (PSO) search. Though earlier attempts of improving PSO search by adding gradient information exist, the main objective of the present work is to improvise gradient/stochastic-gradient search. Our proposed algorithm finds better minimizing points early (fewer number of iterations) not only for the loss function but also for other performance metrics of collaborative filtering such as RMSE and MAE. There has not been any earlier attempt to combine particle swarm optimisation with maximum margin matrix factorisation for collaborative filtering.