Tikhonov and Sobolev regularisers compared to user-based KNN collaborative filtering

Abstract

Collaborative filtering is used to predict the preference or rating of a user for a certain item. Collaborative filtering is based on the notion that similar users rate similarly. A lot of research is done on how to improve this algorithm, mostly with deep learning. A less investigated field for recommender systems is graph signal processing. Graph signal processing is used to reconstruct a graph signal based on the surrounding nodes. The item ratings of a user can be represented as a graph signal. So it is possible to use graph signal processing as a recommender system. In this paper we investigate how the Tikhonov and Sobolev graph regularisers perform for user-based KNN collaborative filtering. We investigated this by comparing the performance of the collaborative filtering algorithm with the two graph regularisers. We found that the Tikhonov regulariser and the Sobolev regulariser performed very similar to user-based KNN collaborative filtering. This means that the added complexity of the graph regularisers did not increase the quality of predictions we can already make with collaborative filtering.