Graph convolutions, in both their linear and neural network forms, have reached state-of-the-art accuracy on recommender system (RecSys) benchmarks. However, recommendation accuracy is tied with diversity in a delicate trade-off and the potential of graph convolutions to improve the latter is unexplored. Here, we develop a model that learns joint convolutional representations from a nearest neighbor and a furthest neighbor graph to establish a novel accuracy-diversity trade-off for recommender systems. The nearest neighbor graph connects entities (users or items) based on their similarities and is responsible for improving accuracy, while the furthest neighbor graph connects entities based on their dissimilarities and is responsible for diversifying recommendations. The information between the two convolutional modules is balanced already in the training phase through a regularizer inspired by multi-kernel learning. We evaluate the joint convolutional model on three benchmark datasets with different degrees of sparsity. The proposed method can either trade accuracy to improve substantially the catalog coverage or the diversity within the list; or improve both by a lesser amount. Compared with accuracy-oriented graph convolutional approaches, the proposed model shows diversity gains up to seven times by trading as little as $1\%$ in accuracy. Compared with alternative accuracy-diversity trade-off solutions, the joint graph convolutional model retains the highest accuracy while offering a handle to increase diversity. To our knowledge, this is the first work proposing an accuracy-diversity trade-off with graph convolutions and opens the doors to learning over graphs approaches for improving such trade-off.

线性和神经网络形式的图形卷积已达到推荐系统（RecSys）基准的最新精度。但是，推荐精度与多样性之间存在微妙的权衡关系，而图卷积改善后者的潜力尚待探索。在这里，我们开发了一个模型，该模型从最近的邻居和最远的邻居图中学习联合卷积表示，从而为推荐系统建立新颖的精度-多样性折衷方案。最近的邻居图根据实体（用户或项目）的相似性连接实体，并负责提高准确性，而最远的邻居图则根据实体的相似性连接实体，并负责使建议多样化。两个卷积模块之间的信息已经在训练阶段通过受多核学习启发的正则化器得到了平衡。我们在稀疏程度不同的三个基准数据集上评估联合卷积模型。所提出的方法可以牺牲交易准确性来显着提高目录覆盖率，也可以提高列表中的多样性。或两者都减少一点。与面向精度的图卷积方法相比，所提出的模型显示，通过交易少至7 所提出的方法可以牺牲交易准确性来显着提高目录覆盖率，也可以提高列表中的多样性。或两者都减少一点。与面向精度的图卷积方法相比，所提出的模型显示，通过交易少至7 所提出的方法可以牺牲交易准确性来显着提高目录覆盖率，也可以提高列表中的多样性。或两者都减少一点。与面向精度的图卷积方法相比，所提出的模型显示，通过交易少至7$\mathrm{1个}％$准确性。与替代的精度-多样性折衷解决方案相比，联合图卷积模型保留了最高的精度，同时提供了增加多样性的句柄。据我们所知，这是第一项提出利用图卷积进行精度-多样性折衷的工作，并且为改善这种折衷方法打开了学习图方法的大门。