The task of community detection, which aims to partition a network into clusters of nodes to summarize its large-scale structure, has spawned the development of many competing algorithms with varying objectives. Some community detection methods are inferential, explicitly deriving the clustering objective through a probabilistic generative model, while other methods are descriptive, dividing a network according to an objective motivated by a particular application, making it challenging to compare these methods on the same scale. Here we present a solution to this problem that associates any community detection objective, inferential or descriptive, with its corresponding implicit network generative model. This allows us to compute the description length of a network and its partition under arbitrary objectives, providing a principled measure to compare the performance of different algorithms without the need for "ground truth" labels. Our approach also gives access to instances of the community detection problem that are optimal to any given algorithm, and in this way reveals intrinsic biases in popular descriptive methods, explaining their tendency to overfit. Using our framework, we compare a number of community detection methods on artificial networks, and on a corpus of over 500 structurally diverse empirical networks. We find that more expressive community detection methods exhibit consistently superior compression performance on structured data instances, without having degraded performance on a minority of situations where more specialized algorithms perform optimally. Our results undermine the implications of the "no free lunch" theorem for community detection, both conceptually and in practice, since it is confined to unstructured data instances, unlike relevant community detection problems which are structured by requirement.

翻译：群落检测任务旨在将网络划分为节点簇以总结其大规模结构，这一目标催生了诸多目标各异的竞争性算法。部分群落检测方法具有推断性，通过概率生成模型显式推导聚类目标；另一些方法则属描述性，依据特定应用场景的动机划分网络，这使得难以在同一尺度上比较这些方法。本文提出一种解决方案，将任意群落检测目标（无论是推断性还是描述性）与其对应的隐式网络生成模型相关联。由此，我们可在任意目标下计算网络及其划分的描述长度，为无需“真实标记”的比较不同算法性能提供原则性度量。该方法还能为给定算法生成最优的群落检测问题实例，从而揭示流行描述性方法的内在偏差，解释其过度拟合倾向。利用该框架，我们在人工网络及涵盖500余个结构多样性的真实网络语料库上比较了多种群落检测方法。研究发现，更具表达力的群落检测方法在处理结构化数据实例时始终展现出更优的压缩性能，而在少数因专精算法表现最优的情境中也未出现性能退化。本研究成果从概念与实践层面动摇了群落检测中“无免费午餐定理”的适用性——该定理仅适用于非结构化数据实例，而相关群落检测问题本质上具有结构化特征。