Dot product latent space embedding is a common form of representation learning in undirected graphs (e.g. social networks, co-occurrence networks). We show that such models have problems dealing with 'intransitive' situations where A is linked to B, B is linked to C but A is not linked to C. Such situations occur in social networks when opposites attract (heterophily) and in co-occurrence networks when there are substitute nodes (e.g. the presence of Pepsi or Coke, but rarely both, in otherwise similar purchase baskets). We present a simple expansion which we call the attract-repel (AR) decomposition: a set of latent attributes on which similar nodes attract and another set of latent attributes on which similar nodes repel. We demonstrate the AR decomposition in real social networks and show that it can be used to measure the amount of latent homophily and heterophily. In addition, it can be applied to co-occurrence networks to discover roles in teams and find substitutable ingredients in recipes.

中文翻译：

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无向网络的吸引-排斥分解

点积潜在空间嵌入是无向图（例如社交网络、共现网络）中表示学习的一种常见形式。我们表明，此类模型在处理“不及物”情况时存在问题，其中 A 与 B 相关联，B 与 C 相关联但 A 与 C 无关。当异性相吸（异性）和共现时，这种情况发生在社交网络中当存在替代节点时的网络（例如百事可乐或可乐的存在，但很少同时存在，在其他类似的购买篮子中）。我们提出了一个简单的扩展，我们称之为吸引-排斥（AR）分解：一组相似节点吸引的潜在属性和另一组相似节点排斥的潜在属性。我们展示了真实社交网络中的 AR 分解，并表明它可用于测量潜在的同质性和异质性的数量。此外，它还可以应用于共现网络以发现团队中的角色并在食谱中找到可替代的成分。