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：社区检测任务旨在将网络划分为节点簇以总结其大规模结构，由此催生了众多目标各异的竞争算法。部分社区检测方法基于推断性框架，通过概率生成模型明确推导聚类目标；另一些方法则属于描述性框架，根据特定应用场景的目标划分网络，这使得在统一尺度下比较这些方法颇具挑战。本文为解决该问题提出方案，将任何社区检测目标（无论推断性或描述性）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，提供无需“真实”标签即可比较不同算法性能的规范化度量。该方法还能生成对特定算法最优的社区检测问题实例，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，我们比较了多类社区检测方法在人工网络及500余个结构多样的实证网络语料库中的表现。结果表明，更具表达力的社区检测方法在结构化数据实例中持续展现更优的压缩性能，且在少数专用算法表现最优的情境下也未出现性能退化。这些发现从概念与实践层面动摇了“无免费午餐”定理对社区检测的适用性——该定理仅限于非结构化数据实例，而现实社区检测问题必然要求结构化特性。