Cross-domain sequential recommendation is an important development direction of recommender systems. It combines the characteristics of sequential recommender systems and cross-domain recommender systems, which can capture the dynamic preferences of users and alleviate the problem of cold-start users. However, in recent years, people pay more and more attention to their privacy. They do not want other people to know what they just bought, what videos they just watched, and where they just came from. How to protect the users' privacy has become an urgent problem to be solved. In this paper, we propose a novel privacy-preserving cross-domain sequential recommender system (PriCDSR), which can provide users with recommendation services while preserving their privacy at the same time. Specifically, we define a new differential privacy on the data, taking into account both the ID information and the order information. Then, we design a random mechanism that satisfies this differential privacy and provide its theoretical proof. Our PriCDSR is a non-invasive method that can adopt any cross-domain sequential recommender system as a base model without any modification to it. To the best of our knowledge, our PriCDSR is the first work to investigate privacy issues in cross-domain sequential recommender systems. We conduct experiments on three domains, and the results demonstrate that our PriCDSR, despite introducing noise, still outperforms recommender systems that only use data from a single domain.
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