Implicit models, latent compression, intrinsic biases, and cheap lunches in community detection
arXiv:2210.09186 · doi:10.1103/PhysRevE.108.024309
Abstract
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.
arXiv comment28 pages, 18 figures
References in corpus (47)
- Modularity and community structure in networks
- Community detection in graphs
- Maps of random walks on complex networks reveal community structure
- Near linear time algorithm to detect community structures in large-scale networks
- Benchmark graphs for testing community detection algorithms
- Resolution limit in community detection
- Community detection algorithms: a comparative analysis
- Statistical Mechanics of Community Detection
- Stochastic blockmodels and community structure in networks
- Community detection in networks: A user guide
- Finding statistically significant communities in networks
- Benchmarks for testing community detection algorithms on directed and weighted graphs with overlapping communities
- Modularity from Fluctuations in Random Graphs and Complex Networks
- An information-theoretic framework for resolving community structure in complex networks
- Missing and spurious interactions and the reconstruction of complex networks
- Asymptotic analysis of the stochastic block model for modular networks and its algorithmic applications
- Spectral redemption: clustering sparse networks
- Detecting fuzzy community structures in complex networks with a Potts model
- Limits of modularity maximization in community detection
- The ground truth about metadata and community detection in networks
- Community detection in networks: Modularity optimization and maximum likelihood are equivalent
- Comparing Community Structure to Characteristics in Online Collegiate Social Networks
- Hierarchical Block Structures and High-resolution Model Selection in Large Networks
- Parsimonious module inference in large networks
- Community detection in networks: Structural communities versus ground truth
- Nonparametric Bayesian inference of the microcanonical stochastic block model
- Scalable detection of statistically significant communities and hierarchies, using message-passing for modularity
- 20 years of network community detection
- Solution of the 2-star model of a network
- Community Structure in Congressional Cosponsorship Networks
- Evaluating Overfit and Underfit in Models of Network Community Structure
- The many facets of community detection in complex networks
- Stacking Models for Nearly Optimal Link Prediction in Complex Networks
- Significant Scales in Community Structure
- Network histograms and universality of blockmodel approximation
- Entropy of stochastic blockmodel ensembles
- When are networks truly modular?
- Deciphering Network Community Structure by Surprise
- Solution for the properties of a clustered network
- Model selection and hypothesis testing for large-scale network models with overlapping groups
- Reconstructing networks with unknown and heterogeneous errors
- Statistical inference of assortative community structures
- Consistencies and inconsistencies between model selection and link prediction in networks
- Revealing consensus and dissensus between network partitions
- Disentangling homophily, community structure and triadic closure in networks
- Universality of the stochastic block model
- Comparative analysis on the selection of number of clusters in community detection