Moreover, when the algorithm is applied iteratively, it converges to a partition in which all subsets of all communities are guaranteed to be locally optimally assigned. to use Codespaces. V.A.T. Brandes, U. et al. The algorithm moves individual nodes from one community to another to find a partition (b), which is then refined (c). Finding community structure in networks using the eigenvectors of matrices. The increase in the percentage of disconnected communities is relatively limited for the Live Journal and Web of Science networks. The Beginner's Guide to Dimensionality Reduction. Communities in Networks. In doing so, Louvain keeps visiting nodes that cannot be moved to a different community. Therefore, by selecting a community based by choosing randomly from the neighbors, we choose the community to evaluate with probability proportional to the composition of the neighbors communities. To use Leiden with the Seurat pipeline for a Seurat Object object that has an SNN computed (for example with Seurat::FindClusters with save.SNN = TRUE). Such a modular structure is usually not known beforehand. S3. The second iteration of Louvain shows a large increase in the percentage of disconnected communities. Hence, no further improvements can be made after a stable iteration of the Louvain algorithm. Modularity is used most commonly, but is subject to the resolution limit. Speed and quality for the first 10 iterations of the Louvain and the Leiden algorithm for benchmark networks (n=106 and n=107). Then optimize the modularity function to determine clusters. J. Assoc. Soc. In this case we know the answer is exactly 10. Louvain can also be quite slow, as it spends a lot of time revisiting nodes that may not have changed neighborhoods. We now show that the Louvain algorithm may find arbitrarily badly connected communities. In practice, this means that small clusters can hide inside larger clusters, making their identification difficult. For example, after four iterations, the Web UK network has 8% disconnected communities, but twice as many badly connected communities. Presumably, many of the badly connected communities in the first iteration of Louvain become disconnected in the second iteration. In particular, we show that Louvain may identify communities that are internally disconnected. ADS Nevertheless, when CPM is used as the quality function, the Louvain algorithm may still find arbitrarily badly connected communities. Note that communities found by the Leiden algorithm are guaranteed to be connected. Requirements Developed using: scanpy v1.7.2 sklearn v0.23.2 umap v0.4.6 numpy v1.19.2 leidenalg Installation pip pip install leiden_clustering local 2.3. The Leiden algorithm is considerably more complex than the Louvain algorithm. Traag, V A. A number of iterations of the Leiden algorithm can be performed before the Louvain algorithm has finished its first iteration. In the previous section, we showed that the Leiden algorithm guarantees a number of properties of the partitions uncovered at different stages of the algorithm. http://arxiv.org/abs/1810.08473. Google Scholar. Graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. A Smart Local Moving Algorithm for Large-Scale Modularity-Based Community Detection. Eur. It was found to be one of the fastest and best performing algorithms in comparative analyses11,12, and it is one of the most-cited works in the community detection literature. In the aggregation phase, an aggregate network is created based on the partition obtained in the local moving phase. There was a problem preparing your codespace, please try again. Unsupervised clustering of cells is a common step in many single-cell expression workflows. The constant Potts model tries to maximize the number of internal edges in a community, while simultaneously trying to keep community sizes small, and the constant parameter balances these two characteristics. Introduction The Louvain method is an algorithm to detect communities in large networks. I tracked the number of clusters post-clustering at each step. E 80, 056117, https://doi.org/10.1103/PhysRevE.80.056117 (2009). Nonlin. Fortunato, S. Community detection in graphs. It does not guarantee that modularity cant be increased by moving nodes between communities. In our experimental analysis, we observe that up to 25% of the communities are badly connected and up to 16% are disconnected. 20, 172188, https://doi.org/10.1109/TKDE.2007.190689 (2008). The DBLP network is somewhat more challenging, requiring almost 80 iterations on average to reach a stable iteration. This function takes a cell_data_set as input, clusters the cells using . If material is not included in the articles Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. Community detection can then be performed using this graph. It therefore does not guarantee -connectivity either. It only implies that individual nodes are well connected to their community. At each iteration all clusters are guaranteed to be connected and well-separated. Once no further increase in modularity is possible by moving any node to its neighboring community, we move to the second phase of the algorithm: aggregation. Phys. Additionally, we implemented a Python package, available from https://github.com/vtraag/leidenalg and deposited at Zenodo24). The differences are not very large, which is probably because both algorithms find partitions for which the quality is close to optimal, related to the issue of the degeneracy of quality functions29. Lancichinetti, A. Community detection in complex networks using extremal optimization. We provide the full definitions of the properties as well as the mathematical proofs in SectionD of the Supplementary Information. The algorithm optimises a quality function such as modularity or CPM in two elementary phases: (1) local moving of nodes; and (2) aggregation of the network. We conclude that the Leiden algorithm is strongly preferable to the Louvain algorithm. In addition, we prove that the algorithm converges to an asymptotically stable partition in which all subsets of all communities are locally optimally assigned. As we will demonstrate in our experimental analysis, the problem occurs frequently in practice when using the Louvain algorithm. AMS 56, 10821097 (2009). The aggregate network is created based on the partition \({{\mathscr{P}}}_{{\rm{refined}}}\). leiden_clustering Description Class wrapper based on scanpy to use the Leiden algorithm to directly cluster your data matrix with a scikit-learn flavor. MathSciNet A Simple Acceleration Method for the Louvain Algorithm. Int. IEEE Trans. This algorithm provides a number of explicit guarantees. Two ways of doing this are graph modularity (Newman and Girvan 2004) and the constant Potts model (Ronhovde and Nussinov 2010). Nodes 06 are in the same community. Algorithmics 16, 2.1, https://doi.org/10.1145/1963190.1970376 (2011). Later iterations of the Louvain algorithm are very fast, but this is only because the partition remains the same. All communities are subpartition -dense. Perhaps surprisingly, iterating the algorithm aggravates the problem, even though it does increase the quality function. Are you sure you want to create this branch? ADS They show that the original Louvain algorithm that can result in badly connected communities (even communities that are completely disconnected internally) and propose an alternative method, Leiden, that guarantees that communities are well connected. We now compare how the Leiden and the Louvain algorithm perform for the six empirical networks listed in Table2. MathSciNet USA 104, 36, https://doi.org/10.1073/pnas.0605965104 (2007). The Louvain algorithm starts from a singleton partition in which each node is in its own community (a). In this post Ive mainly focused on the optimisation methods for community detection, rather than the different objective functions that can be used. In practical applications, the Leiden algorithm convincingly outperforms the Louvain algorithm, both in terms of speed and in terms of quality of the results, as shown by the experimental analysis presented in this paper. In this post, I will cover one of the common approaches which is hierarchical clustering. The difference in computational time is especially pronounced for larger networks, with Leiden being up to 20 times faster than Louvain in empirical networks. These steps are repeated until no further improvements can be made. Traag, V. A. leidenalg 0.7.0. The Leiden algorithm is partly based on the previously introduced smart local move algorithm15, which itself can be seen as an improvement of the Louvain algorithm. All experiments were run on a computer with 64 Intel Xeon E5-4667v3 2GHz CPUs and 1TB internal memory. The R implementation of Leiden can be run directly on the snn igraph object in Seurat. running Leiden clustering finished: found 16 clusters and added 'leiden_1.0', the cluster labels (adata.obs, categorical) (0:00:00) running Leiden clustering finished: found 12 clusters and added 'leiden_0.6', the cluster labels (adata.obs, categorical) (0:00:00) running Leiden clustering finished: found 9 clusters and added 'leiden_0.4', the Large network community detection by fast label propagation, Representative community divisions of networks, Gausss law for networks directly reveals community boundaries, A Regularized Stochastic Block Model for the robust community detection in complex networks, Community Detection in Complex Networks via Clique Conductance, A generalised significance test for individual communities in networks, Community Detection on Networkswith Ricci Flow, https://github.com/CWTSLeiden/networkanalysis, https://doi.org/10.1016/j.physrep.2009.11.002, https://doi.org/10.1103/PhysRevE.69.026113, https://doi.org/10.1103/PhysRevE.74.016110, https://doi.org/10.1103/PhysRevE.70.066111, https://doi.org/10.1103/PhysRevE.72.027104, https://doi.org/10.1103/PhysRevE.74.036104, https://doi.org/10.1088/1742-5468/2008/10/P10008, https://doi.org/10.1103/PhysRevE.80.056117, https://doi.org/10.1103/PhysRevE.84.016114, https://doi.org/10.1140/epjb/e2013-40829-0, https://doi.org/10.17706/IJCEE.2016.8.3.207-218, https://doi.org/10.1103/PhysRevE.92.032801, https://doi.org/10.1103/PhysRevE.76.036106, https://doi.org/10.1103/PhysRevE.78.046110, https://doi.org/10.1103/PhysRevE.81.046106, http://creativecommons.org/licenses/by/4.0/, A robust and accurate single-cell data trajectory inference method using ensemble pseudotime, Batch alignment of single-cell transcriptomics data using deep metric learning, ViralCC retrieves complete viral genomes and virus-host pairs from metagenomic Hi-C data, Community detection in brain connectomes with hybrid quantum computing. As shown in Fig. It is good at identifying small clusters. Scaling of benchmark results for network size. Data 11, 130, https://doi.org/10.1145/2992785 (2017). In contrast, Leiden keeps finding better partitions in each iteration. For the results reported below, the average degree was set to \(\langle k\rangle =10\). The Leiden algorithm is considerably more complex than the Louvain algorithm. In single-cell biology we often use graph-based community detection methods to do this, as these methods are unsupervised, scale well, and usually give good results.
leiden clustering explained