This paper proposes a method to generate a synthetic rating matrix based on user’s rational behavior, with the aim of generating a large-scale rating matrix at low cost. Collaborative filtering is one of the major techniques for recommender systems, which is widely used because it can recommend items using only a history of ratings given to the items by users. However, collaborative filtering has some problems such as the cold-start problem and the sparsity problem, both of which are caused by the shortage of ratings in a database (rating matrix). This problem is particularly serious for services that have just started operation or do not have a large number of users. The proposed method generates a rating matrix without missing values using users’ rating probabilities, which are obtained from the distribution of their actual ratings. The final synthetic rating matrix is generated after adjusting its sparsity by introducing missing values. The validity of the proposed method is evaluated by comparing the synthetic rating matrix in terms of the similarity of the distribution of several statistics with that of the real data. The synthetic rating matrix is also evaluated by applying it to recommendation to actual users. The experimental results show that the proposed method can generate the synthetic rating matrix that has similar statistics to the real data, and recommendation models trained with the synthetic data achieve comparable recall to that trained with the real data when using the real data as test data. Based on the results of these experiments, this paper also tries to generate the synthetic rating matrix that contains richer information than the real data by increasing the number of users or reducing the sparsity of the rating matrix. The results of these experiments show the possibility that increasing the information contained in a rating matrix could improve recall.

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