Random Walks in Recommender Systems: Exact Computation and Simulations∗

A recommender system uses information about known as-sociations between users and items to compute for a given user an ordered recommendation list of items which this user might be interested in acquiring. We consider ordering rules based on various parameters of random walks on the graph representing associations between users and items. We ex-perimentally compare the quality of recommendations and the required computational resources of two approaches: (i) calculate the exact values of the relevant random walk pa-rameters using matrix algebra; (ii) estimate these values by simulating random walks. In our experiments we include methods proposed by Fouss et al. [8, 9] and Gori and Pucci [11], method P 3, which is based on the distribution of the random walk after three steps, and method P 3α, which gener-alises P 3. We show that the simple method P 3 can outper-form previous methods and method P 3α can offer further im-provements. We show that the time- and memory-efficiency of direct simulation of random walks allows application of these methods to large datasets. We use in our experiments the three MovieLens datasets. 1