We applied the Louvain and the Leiden algorithm to exactly the same networks, using the same seed for the random number generator. Performance of modularity maximization in practical contexts. The algorithm continues to move nodes in the rest of the network. Fortunato, S. & Barthlemy, M. Resolution Limit in Community Detection. To find an optimal grouping of cells into communities, we need some way of evaluating different partitions in the graph. Communities were all of equal size. For example, for the Web of Science network, the first iteration takes about 110120 seconds, while subsequent iterations require about 40 seconds. However, Leiden is more than 7 times faster for the Live Journal network, more than 11 times faster for the Web of Science network and more than 20 times faster for the Web UK network. The classic Louvain algorithm should be avoided due to the known problem with disconnected communities. Fortunato, S. Community detection in graphs. As can be seen in Fig. After a stable iteration of the Leiden algorithm, the algorithm may still be able to make further improvements in later iterations. 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. Speed and quality for the first 10 iterations of the Louvain and the Leiden algorithm for six empirical networks. The Leiden algorithm is typically iterated: the output of one iteration is used as the input for the next iteration. https://doi.org/10.1038/s41598-019-41695-z. Moreover, the deeper significance of the problem was not recognised: disconnected communities are merely the most extreme manifestation of the problem of arbitrarily badly connected communities. Leiden consists of the following steps: Local moving of nodes Partition refinement Network aggregation The refinement step allows badly connected communities to be split before creating the aggregate network. From Louvain to Leiden: guaranteeing well-connected communities, $$ {\mathcal H} =\frac{1}{2m}\,{\sum }_{c}({e}_{c}-{\rm{\gamma }}\frac{{K}_{c}^{2}}{2m}),$$, $$ {\mathcal H} ={\sum }_{c}[{e}_{c}-\gamma (\begin{array}{c}{n}_{c}\\ 2\end{array})],$$, https://doi.org/10.1038/s41598-019-41695-z. We denote by ec the actual number of edges in community c. The expected number of edges can be expressed as \(\frac{{K}_{c}^{2}}{2m}\), where Kc is the sum of the degrees of the nodes in community c and m is the total number of edges in the network. If we move the node to a different community, we add to the rear of the queue all neighbours of the node that do not belong to the nodes new community and that are not yet in the queue. Lancichinetti, A., Fortunato, S. & Radicchi, F. Benchmark graphs for testing community detection algorithms. Therefore, clustering algorithms look for similarities or dissimilarities among data points. In the Louvain algorithm, a node may be moved to a different community while it may have acted as a bridge between different components of its old community. The authors show that the total computational time for Louvain depends a lot on the number of phase one loops (loops during the first local moving stage). where nc is the number of nodes in community c. The interpretation of the resolution parameter is quite straightforward. In our experimental analysis, we observe that up to 25% of the communities are badly connected and up to 16% are disconnected. Louvain has two phases: local moving and aggregation. (We implemented both algorithms in Java, available from https://github.com/CWTSLeiden/networkanalysis and deposited at Zenodo23. Phys. J. Comput. Scanpy Tutorial - 65k PBMCs - Parse Biosciences This continues until the queue is empty. 10008, 6, https://doi.org/10.1088/1742-5468/2008/10/P10008 (2008). The Louvain method for community detection is a popular way to discover communities from single-cell data. Modules smaller than the minimum size may not be resolved through modularity optimization, even in the extreme case where they are only connected to the rest of the network through a single edge. The authors act as bibliometric consultants to CWTS B.V., which makes use of community detection algorithms in commercial products and services. The Leiden algorithm has been specifically designed to address the problem of badly connected communities. For example, the red community in (b) is refined into two subcommunities in (c), which after aggregation become two separate nodes in (d), both belonging to the same community. Acad. To address this problem, we introduce the Leiden algorithm. Zenodo, https://doi.org/10.5281/zenodo.1469357 https://github.com/vtraag/leidenalg. the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in At some point, the Louvain algorithm may end up in the community structure shown in Fig. In the local moving phase, individual nodes are moved to the community that yields the largest increase in the quality function. CPM is defined as. MATH As can be seen in Fig. It states that there are no communities that can be merged. The percentage of badly connected communities is less affected by the number of iterations of the Louvain algorithm. Two ways of doing this are graph modularity (Newman and Girvan 2004) and the constant Potts model (Ronhovde and Nussinov 2010). Four popular community detection algorithms are explained . It starts clustering by treating the individual data points as a single cluster then it is merged continuously based on similarity until it forms one big cluster containing all objects. ADS It is a directed graph if the adjacency matrix is not symmetric. A score of -1 means that there are no edges connecting nodes within the community, and they instead all connect nodes outside the community. Waltman, Ludo, and Nees Jan van Eck. U. S. A. There is an entire Leiden package in R-cran here From Louvain to Leiden: guaranteeing well-connected communities - Nature 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). With one exception (=0.2 and n=107), all results in Fig. To install the development version: The current release on CRAN can be installed with: First set up a compatible adjacency matrix: An adjacency matrix is any binary matrix representing links between nodes (column and row names). A Comparative Analysis of Community Detection Algorithms on Artificial Networks. Is modularity with a resolution parameter equivalent to leidenalg.RBConfigurationVertexPartition? In the first step of the next iteration, Louvain will again move individual nodes in the network. Optimising modularity is NP-hard5, and consequentially many heuristic algorithms have been proposed, such as hierarchical agglomeration6, extremal optimisation7, simulated annealing4,8 and spectral9 algorithms. Clustering with the Leiden Algorithm in R This package allows calling the Leiden algorithm for clustering on an igraph object from R. See the Python and Java implementations for more details: https://github.com/CWTSLeiden/networkanalysis https://github.com/vtraag/leidenalg Install Natl. Hierarchical Clustering Explained - Towards Data Science For those wanting to read more, I highly recommend starting with the Leiden paper (Traag, Waltman, and Eck 2018) or the smart local moving paper (Waltman and Eck 2013). We gratefully acknowledge computational facilities provided by the LIACS Data Science Lab Computing Facilities through Frank Takes. Community Detection Algorithms - Towards Data Science The triumphs and limitations of computational methods for - Nature 6 show that Leiden outperforms Louvain in terms of both computational time and quality of the partitions. These are the same networks that were also studied in an earlier paper introducing the smart local move algorithm15. CPM does not suffer from this issue13. Nat. Figure3 provides an illustration of the algorithm. Hence, for lower values of , the difference in quality is negligible. Traag, V. A. leidenalg 0.7.0. It means that there are no individual nodes that can be moved to a different community. & Bornholdt, S. Statistical mechanics of community detection. Soft Matter Phys. An alternative quality function is the Constant Potts Model (CPM)13, which overcomes some limitations of modularity. Additionally, we implemented a Python package, available from https://github.com/vtraag/leidenalg and deposited at Zenodo24). Phys. Importantly, mergers are performed only within each community of the partition \({\mathscr{P}}\). E 81, 046106, https://doi.org/10.1103/PhysRevE.81.046106 (2010). Sci Rep 9, 5233 (2019). Cluster Determination FindClusters Seurat - Satija Lab HiCBin: binning metagenomic contigs and recovering metagenome-assembled Leiden is both faster than Louvain and finds better partitions. The Louvain local moving phase consists of the following steps: This process is repeated for every node in the network until no further improvement in modularity is possible. Resolution Limit in Community Detection. Proc. Directed Undirected Homogeneous Heterogeneous Weighted 1. 10, for the IMDB and Amazon networks, Leiden reaches a stable iteration relatively quickly, presumably because these networks have a fairly simple community structure. Phys. Note that this code is designed for Seurat version 2 releases. When the Leiden algorithm found that a community could be split into multiple subcommunities, we counted the community as badly connected. The above results shows that the problem of disconnected and badly connected communities is quite pervasive in practice. 1 and summarised in pseudo-code in AlgorithmA.1 in SectionA of the Supplementary Information. In an experiment containing a mixture of cell types, each cluster might correspond to a different cell type. Somewhat stronger guarantees can be obtained by iterating the algorithm, using the partition obtained in one iteration of the algorithm as starting point for the next iteration. Article When iterating Louvain, the quality of the partitions will keep increasing until the algorithm is unable to make any further improvements. Complex brain networks: graph theoretical analysis of structural and functional systems. Hence, by counting the number of communities that have been split up, we obtained a lower bound on the number of communities that are badly connected. 104 (1): 3641. When a sufficient number of neighbours of node 0 have formed a community in the rest of the network, it may be optimal to move node 0 to this community, thus creating the situation depicted in Fig. Some of these nodes may very well act as bridges, similarly to node 0 in the above example. Again, if communities are badly connected, this may lead to incorrect inferences of topics, which will affect bibliometric analyses relying on the inferred topics. This is similar to ideas proposed recently as pruning16 and in a slightly different form as prioritisation17. cluster_leiden: Finding community structure of a graph using the Leiden Int. Modularity optimization. By submitting a comment you agree to abide by our Terms and Community Guidelines. The Leiden algorithm also takes advantage of the idea of speeding up the local moving of nodes16,17 and the idea of moving nodes to random neighbours18. Then, in order . We find that the Leiden algorithm is faster than the Louvain algorithm and uncovers better partitions, in addition to providing explicit guarantees. 7, whereas Louvain becomes much slower for more difficult partitions, Leiden is much less affected by the difficulty of the partition. Google Scholar. The corresponding results are presented in the Supplementary Fig. We can guarantee a number of properties of the partitions found by the Leiden algorithm at various stages of the iterative process. Technol. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/. 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. You signed in with another tab or window. Rev. Besides the relative flexibility of the implementation, it also scales well, and can be run on graphs of millions of nodes (as long as they can fit in memory). On Modularity Clustering. Ozaki, Naoto, Hiroshi Tezuka, and Mary Inaba. partition_type : Optional [ Type [ MutableVertexPartition ]] (default: None) Type of partition to use. Phys. leidenalg. For each community, modularity measures the number of edges within the community and the number of edges going outside the community, and gives a value between -1 and +1. In the case of the Louvain algorithm, after a stable iteration, all subsequent iterations will be stable as well. Here we can see partitions in the plotted results. Elect. J. bioRxiv, https://doi.org/10.1101/208819 (2018). Sci. Scientific Reports (Sci Rep) J. We name our algorithm the Leiden algorithm, after the location of its authors. Porter, M. A., Onnela, J.-P. & Mucha, P. J. We prove that the new algorithm is guaranteed to produce partitions in which all communities are internally connected. These steps are repeated until the quality cannot be increased further. Run the code above in your browser using DataCamp Workspace. In the local move procedure in the Leiden algorithm, only nodes whose neighborhood . The parameter functions as a sort of threshold: communities should have a density of at least , while the density between communities should be lower than . For example: If you do not have root access, you can use pip install --user or pip install --prefix to install these in your user directory (which you have write permissions for) and ensure that this directory is in your PATH so that Python can find it. and JavaScript. Both conda and PyPI have leiden clustering in Python which operates via iGraph. However, in the case of the Web of Science network, more than 5% of the communities are disconnected in the first iteration. As far as I can tell, Leiden seems to essentially be smart local moving with the additional improvements of random moving and Louvain pruning added. Number of iterations until stability. For lower values of , the correct partition is easy to find and Leiden is only about twice as fast as Louvain. Edges were created in such a way that an edge fell between two communities with a probability and within a community with a probability 1. DBSCAN Clustering Explained Detailed theorotical explanation and scikit-learn implementation Clustering is a way to group a set of data points in a way that similar data points are grouped together. Finally, we demonstrate the excellent performance of the algorithm for several benchmark and real-world networks. Similarly, in citation networks, such as the Web of Science network, nodes in a community are usually considered to share a common topic26,27. Obviously, this is a worst case example, showing that disconnected communities may be identified by the Louvain algorithm. GitHub on Feb 15, 2020 Do you think the performance improvements will also be implemented in leidenalg? The Louvain algorithm starts from a singleton partition in which each node is in its own community (a). leiden: Run Leiden clustering algorithm in leiden: R Implementation of leiden function - RDocumentation For example, after four iterations, the Web UK network has 8% disconnected communities, but twice as many badly connected communities. The horizontal axis indicates the cumulative time taken to obtain the quality indicated on the vertical axis. We will use sklearns K-Means implementation looking for 10 clusters in the original 784 dimensional data. (2) and m is the number of edges. In addition, we prove that, when the Leiden algorithm is applied iteratively, it converges to a partition in which all subsets of all communities are locally optimally assigned. Nonlin. http://iopscience.iop.org/article/10.1088/1742-5468/2008/10/P10008/meta. This function takes a cell_data_set as input, clusters the cells using . Finding communities in large networks is far from trivial: algorithms need to be fast, but they also need to provide high-quality results. As such, we scored leiden-clustering popularity level to be Limited. In the worst case, almost a quarter of the communities are badly connected. In fact, by implementing the refinement phase in the right way, several attractive guarantees can be given for partitions produced by the Leiden algorithm. Uniform -density means that no matter how a community is partitioned into two parts, the two parts will always be well connected to each other. If you cant use Leiden, choosing Smart Local Moving will likely give very similar results, but might be a bit slower as it doesnt include some of the simple speedups to Louvain like random moving and Louvain pruning. For higher values of , Leiden finds better partitions than Louvain. We demonstrate the performance of the Leiden algorithm for several benchmark and real-world networks. Phys. In fact, for the Web of Science and Web UK networks, Fig. Rep. 6, 30750, https://doi.org/10.1038/srep30750 (2016). For empirical networks, it may take quite some time before the Leiden algorithm reaches its first stable iteration. After each iteration of the Leiden algorithm, it is guaranteed that: In these properties, refers to the resolution parameter in the quality function that is optimised, which can be either modularity or CPM. Internet Explorer). Ronhovde, Peter, and Zohar Nussinov. Algorithmics 16, 2.1, https://doi.org/10.1145/1963190.1970376 (2011). Importantly, the problem of disconnected communities is not just a theoretical curiosity. Here is some small debugging code I wrote to find this. The fast local move procedure can be summarised as follows. E 72, 027104, https://doi.org/10.1103/PhysRevE.72.027104 (2005). Traag, Vincent, Ludo Waltman, and Nees Jan van Eck. The Leiden algorithm starts from a singleton partition (a). Am. Not. Note that Leiden clustering directly clusters the neighborhood graph of cells, which we already computed in the previous section. To overcome the problem of arbitrarily badly connected communities, we introduced a new algorithm, which we refer to as the Leiden algorithm. As shown in Fig. The percentage of disconnected communities is more limited, usually around 1%. Natl. 8 (3): 207. https://pdfs.semanticscholar.org/4ea9/74f0fadb57a0b1ec35cbc5b3eb28e9b966d8.pdf. See the documentation on the leidenalg Python module for more information: https://leidenalg.readthedocs.io/en/latest/reference.html. Modularity is used most commonly, but is subject to the resolution limit. Mech. In addition, we prove that the algorithm converges to an asymptotically stable partition in which all subsets of all communities are locally optimally assigned. Even worse, the Amazon network has 5% disconnected communities, but 25% badly connected communities. Finding community structure in networks using the eigenvectors of matrices. Contrastive self-supervised clustering of scRNA-seq data The refined partition \({{\mathscr{P}}}_{{\rm{refined}}}\) is obtained as follows. B 86, 471, https://doi.org/10.1140/epjb/e2013-40829-0 (2013). Introduction The Louvain method is an algorithm to detect communities in large networks. 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. However, for higher values of , Leiden becomes orders of magnitude faster than Louvain, reaching 10100 times faster runtimes for the largest networks. This amounts to a clustering problem, where we aim to learn an optimal set of groups (communities) from the observed data. We generated benchmark networks in the following way. They identified an inefficiency in the Louvain algorithm: computes modularity gain for all neighbouring nodes per loop in local moving phase, even though many of these nodes will not have moved. E 74, 036104, https://doi.org/10.1103/PhysRevE.74.036104 (2006). Agglomerative clustering is a bottom-up approach. E 80, 056117, https://doi.org/10.1103/PhysRevE.80.056117 (2009). Disconnected community. For example, nodes in a community in biological or neurological networks are often assumed to share similar functions or behaviour25. Bae, S., Halperin, D., West, J. D., Rosvall, M. & Howe, B. Scalable and Efficient Flow-Based Community Detection for Large-Scale Graph Analysis. This contrasts to benchmark networks, for which Leiden often converges after a few iterations. Due to the resolution limit, modularity may cause smaller communities to be clustered into larger communities. Unsupervised clustering of cells is a common step in many single-cell expression workflows. The algorithm is run iteratively, using the partition identified in one iteration as starting point for the next iteration. Nodes 16 have connections only within this community, whereas node 0 also has many external connections. Biological sequence clustering is a complicated data clustering problem owing to the high computation costs incurred for pairwise sequence distance calculations through sequence alignments, as well as difficulties in determining parameters for deriving robust clusters. DBSCAN Clustering Explained. Detailed theorotical explanation and Clustering algorithms look for similarities or dissimilarities among data points so that similar ones can be grouped together. This package allows calling the Leiden algorithm for clustering on an igraph object from R. See the Python and Java implementations for more details: https://github.com/CWTSLeiden/networkanalysis. We used the CPM quality function. Faster unfolding of communities: Speeding up the Louvain algorithm. Ozaki, N., Tezuka, H. & Inaba, M. A Simple Acceleration Method for the Louvain Algorithm. However, it is also possible to start the algorithm from a different partition15. conda install -c conda-forge leidenalg pip install leiden-clustering Used via. ADS Each community in this partition becomes a node in the aggregate network. Cluster cells using Louvain/Leiden community detection Description. To elucidate the problem, we consider the example illustrated in Fig. Community detection is often used to understand the structure of large and complex networks. Centre for Science and Technology Studies, Leiden University, Leiden, The Netherlands, You can also search for this author in Source Code (2018). & Moore, C. Finding community structure in very large networks. In that case, nodes 16 are all locally optimally assigned, despite the fact that their community has become disconnected. Phys. Nonetheless, some networks still show large differences. Below, the quality of a partition is reported as \(\frac{ {\mathcal H} }{2m}\), where H is defined in Eq. In this case we know the answer is exactly 10. Excluding node mergers that decrease the quality function makes the refinement phase more efficient. E 69, 026113, https://doi.org/10.1103/PhysRevE.69.026113 (2004). Cluster your data matrix with the Leiden algorithm. For each set of parameters, we repeated the experiment 10 times.