Explainability of recommender systems has become essential to ensure users' trust and satisfaction. Various types of explainable recommender systems have been proposed including explainable graph-based recommender systems. This review paper discusses state-of-the-art approaches of these systems and categorizes them based on three aspects: learning methods, explaining methods, and explanation types. It also explores the commonly used datasets, explainability evaluation methods, and future directions of this research area. Compared with the existing review papers, this paper focuses on explainability based on graphs and covers the topics required for developing novel explainable graph-based recommender systems.

Recent progress in Graph Neural Networks has resulted in wide adoption by many applications, including recommendation systems. The reason for Graph Neural Networks' superiority over other approaches is that many problems in recommendation systems can be naturally modeled as graphs, where nodes can be either users or items and edges represent preference relationships. In current Graph Neural Network approaches, nodes are represented with a static vector learned at training time. This static vector might only be suitable to capture some of the nuances of users or items they define. To overcome this limitation, we propose using a recently proposed model inspired by category theory: Sheaf Neural Networks. Sheaf Neural Networks, and its connected Laplacian, can address the previous problem by associating every node (and edge) with a vector space instead than a single vector. The vector space representation is richer and allows picking the proper representation at inference time. This approach can be generalized for different related tasks on graphs and achieves state-of-the-art performance in terms of F1-Score@N in collaborative filtering and Hits@20 in link prediction. For collaborative filtering, the approach is evaluated on the MovieLens 100K with a 5.1% improvement, on MovieLens 1M with a 5.4% improvement and on Book-Crossing with a 2.8% improvement, while for link prediction on the ogbl-ddi dataset with a 1.6% refinement with respect to the respective baselines.

Recommender system is an important component of many web services to help users locate items that match their interests. Several studies showed that recommender systems are vulnerable to poisoning attacks, in which an attacker injects fake data to a given system such that the system makes recommendations as the attacker desires. However, these poisoning attacks are either agnostic to recommendation algorithms or optimized to recommender systems that are not graph-based. Like association-rule-based and matrix-factorization-based recommender systems, graph-based recommender system is also deployed in practice, e.g., eBay, Huawei App Store. However, how to design optimized poisoning attacks for graph-based recommender systems is still an open problem. In this work, we perform a systematic study on poisoning attacks to graph-based recommender systems. Due to limited resources and to avoid detection, we assume the number of fake users that can be injected into the system is bounded. The key challenge is how to assign rating scores to the fake users such that the target item is recommended to as many normal users as possible. To address the challenge, we formulate the poisoning attacks as an optimization problem, solving which determines the rating scores for the fake users. We also propose techniques to solve the optimization problem. We evaluate our attacks and compare them with existing attacks under white-box (recommendation algorithm and its parameters are known), gray-box (recommendation algorithm is known but its parameters are unknown), and black-box (recommendation algorithm is unknown) settings using two real-world datasets. Our results show that our attack is effective and outperforms existing attacks for graph-based recommender systems. For instance, when 1% fake users are injected, our attack can make a target item recommended to 580 times more normal users in certain scenarios.