leiden clustering explained leiden clustering explained

The minimum resolvable community size depends on the total size of the network and the degree of interconnectedness of the modules. As shown in Fig. We applied the Louvain and the Leiden algorithm to exactly the same networks, using the same seed for the random number generator. Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. Then optimize the modularity function to determine clusters. 69 (2 Pt 2): 026113. http://dx.doi.org/10.1103/PhysRevE.69.026113. 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). Phys. Note that communities found by the Leiden algorithm are guaranteed to be connected. In this paper, we show that the Louvain algorithm has a major problem, for both modularity and CPM. 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Rev. From Louvain to Leiden: guaranteeing well-connected communities - Nature 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. However, if communities are badly connected, this may lead to incorrect attributions of shared functionality. Sci Rep 9, 5233 (2019). However, so far this problem has never been studied for the Louvain algorithm. We abbreviate the leidenalg package as la and the igraph package as ig in all Python code throughout this documentation. This can be a shared nearest neighbours matrix derived from a graph object. Besides the Louvain algorithm and the Leiden algorithm (see the "Methods" section), there are several widely-used network clustering algorithms, such as the Markov clustering algorithm [], Infomap algorithm [], and label propagation algorithm [].Markov clustering and Infomap algorithm are both based on flow . To elucidate the problem, we consider the example illustrated in Fig. One may expect that other nodes in the old community will then also be moved to other communities. A. Eur. However, the Louvain algorithm does not consider this possibility, since it considers only individual node movements. Starting from the second iteration, Leiden outperformed Louvain in terms of the percentage of badly connected communities. As can be seen in Fig. Sci. Note that this code is designed for Seurat version 2 releases. 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. Klavans, R. & Boyack, K. W. Which Type of Citation Analysis Generates the Most Accurate Taxonomy of Scientific and Technical Knowledge? However, in the case of the Web of Science network, more than 5% of the communities are disconnected in the first iteration. Article We demonstrate the performance of the Leiden algorithm for several benchmark and real-world networks. We show that this algorithm has a major defect that largely went unnoticed until now: the Louvain algorithm may yield arbitrarily badly connected communities. Newman, M. E. J. where >0 is a resolution parameter4. Reichardt, J. 2(a). Figure4 shows how well it does compared to the Louvain algorithm. 8, 207218, https://doi.org/10.17706/IJCEE.2016.8.3.207-218 (2016). There is an entire Leiden package in R-cran here J. However, it is also possible to start the algorithm from a different partition15. http://arxiv.org/abs/1810.08473. 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. However, the initial partition for the aggregate network is based on P, just like in the Louvain algorithm. In terms of the percentage of badly connected communities in the first iteration, Leiden performs even worse than Louvain, as can be seen in Fig. How many iterations of the Leiden clustering algorithm to perform. Leiden is the most recent major development in this space, and highlighted a flaw in the original Louvain algorithm (Traag, Waltman, and Eck 2018). Nat. ML | Hierarchical clustering (Agglomerative and Divisive clustering As the problem of modularity optimization is NP-hard, we need heuristic methods to optimize modularity (or CPM). The R implementation of Leiden can be run directly on the snn igraph object in Seurat. In many complex networks, nodes cluster and form relatively dense groupsoften called communities1,2. In the fast local move procedure in the Leiden algorithm, only nodes whose neighbourhood has changed are visited. Finding communities in large networks is far from trivial: algorithms need to be fast, but they also need to provide high-quality results. We prove that the Leiden algorithm yields communities that are guaranteed to be connected. MathSciNet This amounts to a clustering problem, where we aim to learn an optimal set of groups (communities) from the observed data. The new algorithm integrates several earlier improvements, incorporating a combination of smart local move15, fast local move16,17 and random neighbour move18. Traag, V. A., Van Dooren, P. & Nesterov, Y. Clustering with the Leiden Algorithm in R - cran.microsoft.com As discussed earlier, the Louvain algorithm does not guarantee connectivity. Rep. 6, 30750, https://doi.org/10.1038/srep30750 (2016). As can be seen in Fig. scanpy_04_clustering - GitHub Pages Blondel, V D, J L Guillaume, and R Lambiotte. & Fortunato, S. Community detection algorithms: A comparative analysis. In this case we can solve one of the hard problems for K-Means clustering - choosing the right k value, giving the number of clusters we are looking for. For the results reported below, the average degree was set to \(\langle k\rangle =10\). An iteration of the Leiden algorithm in which the partition does not change is called a stable iteration. These are the same networks that were also studied in an earlier paper introducing the smart local move algorithm15. Cluster cells using Louvain/Leiden community detection Description. We thank Lovro Subelj for his comments on an earlier version of this paper. S3. Hence, the community remains disconnected, unless it is merged with another community that happens to act as a bridge. * (2018). 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. the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in This contrasts with optimisation algorithms such as simulated annealing, which do allow the quality function to decrease4,8. conda install -c conda-forge leidenalg pip install leiden-clustering Used via. In contrast, Leiden keeps finding better partitions in each iteration. Nevertheless, depending on the relative strengths of the different connections, these nodes may still be optimally assigned to their current community. 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. Moreover, Louvain has no mechanism for fixing these communities. to use Codespaces. Clustering algorithms look for similarities or dissimilarities among data points so that similar ones can be grouped together. In practice, this means that small clusters can hide inside larger clusters, making their identification difficult. These steps are repeated until no further improvements can be made. In our experimental analysis, we observe that up to 25% of the communities are badly connected and up to 16% are disconnected. Porter, M. A., Onnela, J.-P. & Mucha, P. J. 10008, 6, https://doi.org/10.1088/1742-5468/2008/10/P10008 (2008). Rev. 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. Cluster your data matrix with the Leiden algorithm. We will use sklearns K-Means implementation looking for 10 clusters in the original 784 dimensional data. A Simple Acceleration Method for the Louvain Algorithm. Int. Similarly, in citation networks, such as the Web of Science network, nodes in a community are usually considered to share a common topic26,27. Phys. This is because Louvain only moves individual nodes at a time. In particular, benchmark networks have a rather simple structure. The count of badly connected communities also included disconnected communities. . A community is subpartition -dense if it can be partitioned into two parts such that: (1) the two parts are well connected to each other; (2) neither part can be separated from its community; and (3) each part is also subpartition -dense itself. For larger networks and higher values of , Louvain is much slower than Leiden. In short, the problem of badly connected communities has important practical consequences. Rev. Raghavan, U., Albert, R. & Kumara, S. Near linear time algorithm to detect community structures in large-scale networks. It maximizes a modularity score for each community, where the modularity quantifies the quality of an assignment of nodes to communities. J. Exp. We name our algorithm the Leiden algorithm, after the location of its authors. 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 . This function takes a cell_data_set as input, clusters the cells using . 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. 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. A new methodology for constructing a publication-level classification system of science. & Arenas, A. Rev. ADS For higher values of , Leiden finds better partitions than Louvain. Node optimality is also guaranteed after a stable iteration of the Louvain algorithm. Traag, V. A. Communities were all of equal size. In this iterative scheme, Louvain provides two guarantees: (1) no communities can be merged and (2) no nodes can be moved. After running local moving, we end up with a set of communities where we cant increase the objective function (eg, modularity) by moving any node to any neighboring community. Article V. A. Traag. The Leiden algorithm starts from a singleton partition (a). The algorithm then moves individual nodes in the aggregate network (d). 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. The algorithm moves individual nodes from one community to another to find a partition (b), which is then refined (c). This is very similar to what the smart local moving algorithm does. There was a problem preparing your codespace, please try again. Phys. This is similar to ideas proposed recently as pruning16 and in a slightly different form as prioritisation17. Community detection in complex networks using extremal optimization. This contrasts with the Leiden algorithm. Google Scholar. The Louvain algorithm is a simple and popular method for community detection (Blondel, Guillaume, and Lambiotte 2008). Contrastive self-supervised clustering of scRNA-seq data As we will demonstrate in our experimental analysis, the problem occurs frequently in practice when using the Louvain algorithm. Rev. We used the CPM quality function. 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. This is similar to what we have seen for benchmark networks. This will compute the Leiden clusters and add them to the Seurat Object Class. Natl. Phys. PubMed Central Louvain community detection algorithm was originally proposed in 2008 as a fast community unfolding method for large networks. Phys. & Moore, C. Finding community structure in very large networks. Crucially, however, the percentage of badly connected communities decreases with each iteration of the Leiden algorithm. Modularity is used most commonly, but is subject to the resolution limit. https://doi.org/10.1038/s41598-019-41695-z, DOI: https://doi.org/10.1038/s41598-019-41695-z. What is Clustering and Different Types of Clustering Methods At some point, the Louvain algorithm may end up in the community structure shown in Fig. Each community in this partition becomes a node in the aggregate network. Some of these nodes may very well act as bridges, similarly to node 0 in the above example. Arguments can be passed to the leidenalg implementation in Python: In particular, the resolution parameter can fine-tune the number of clusters to be detected. 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). On the other hand, after node 0 has been moved to a different community, nodes 1 and 4 have not only internal but also external connections. Contrary to what might be expected, iterating the Louvain algorithm aggravates the problem of badly connected communities, as we will also see in our experimental analysis. ADS GitHub on Feb 15, 2020 Do you think the performance improvements will also be implemented in leidenalg? In an experiment containing a mixture of cell types, each cluster might correspond to a different cell type. Directed Undirected Homogeneous Heterogeneous Weighted 1. While current approaches are successful in reducing the number of sequence alignments performed, the generated clusters are . https://doi.org/10.1038/s41598-019-41695-z. In the Louvain algorithm, an aggregate network is created based on the partition \({\mathscr{P}}\) resulting from the local moving phase. Because the percentage of disconnected communities in the first iteration of the Louvain algorithm usually seems to be relatively low, the problem may have escaped attention from users of the algorithm. Later iterations of the Louvain algorithm only aggravate the problem of disconnected communities, even though the quality function (i.e. For example an SNN can be generated: For Seurat version 3 objects, the Leiden algorithm has been implemented in the Seurat version 3 package with Seurat::FindClusters and algorithm = "leiden"). Source Code (2018). Ph.D. thesis, (University of Oxford, 2016). Modularity is given by. Hierarchical Clustering Explained - Towards Data Science Nevertheless, when CPM is used as the quality function, the Louvain algorithm may still find arbitrarily badly connected communities. Hence, in general, Louvain may find arbitrarily badly connected communities. Computer Syst. Correspondence to By submitting a comment you agree to abide by our Terms and Community Guidelines. Use Git or checkout with SVN using the web URL. 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. In subsequent iterations, the percentage of disconnected communities remains fairly stable. The corresponding results are presented in the Supplementary Fig. Article E 81, 046106, https://doi.org/10.1103/PhysRevE.81.046106 (2010). 10, for the IMDB and Amazon networks, Leiden reaches a stable iteration relatively quickly, presumably because these networks have a fairly simple community structure. Leiden keeps finding better partitions for empirical networks also after the first 10 iterations of the algorithm. From Louvain to Leiden: Guaranteeing Well-Connected Communities, October. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/. In fact, by implementing the refinement phase in the right way, several attractive guarantees can be given for partitions produced by the Leiden algorithm. In this case, refinement does not change the partition (f). The resulting clusters are shown as colors on the 3D model (top) and t -SNE embedding . 63, 23782392, https://doi.org/10.1002/asi.22748 (2012). Source Code (2018). However, after all nodes have been visited once, Leiden visits only nodes whose neighbourhood has changed, whereas Louvain keeps visiting all nodes in the network. Each point corresponds to a certain iteration of an algorithm, with results averaged over 10 experiments. (We ensured that modularity optimisation for the subnetwork was fully consistent with modularity optimisation for the whole network13) The Leiden algorithm was run until a stable iteration was obtained. Unsupervised clustering of cells is a common step in many single-cell expression workflows. It states that there are no communities that can be merged. Rev. Eng. Article J. Comput. By creating the aggregate network based on \({{\mathscr{P}}}_{{\rm{refined}}}\) rather than P, the Leiden algorithm has more room for identifying high-quality partitions. In the meantime, to ensure continued support, we are displaying the site without styles Figure3 provides an illustration of the algorithm. E 78, 046110, https://doi.org/10.1103/PhysRevE.78.046110 (2008). GitHub - MiqG/leiden_clustering: Cluster your data matrix with the Neurosci. The nodes that are more interconnected have been partitioned into separate clusters. E Stat. Discov. In addition, we prove that the algorithm converges to an asymptotically stable partition in which all subsets of all communities are locally optimally assigned. Using UMAP for Clustering umap 0.5 documentation - Read the Docs Node mergers that cause the quality function to decrease are not considered. Inf. Run the code above in your browser using DataCamp Workspace. The refined partition \({{\mathscr{P}}}_{{\rm{refined}}}\) is obtained as follows. and JavaScript. The horizontal axis indicates the cumulative time taken to obtain the quality indicated on the vertical axis. The algorithm is run iteratively, using the partition identified in one iteration as starting point for the next iteration. 20, 172188, https://doi.org/10.1109/TKDE.2007.190689 (2008). In the refinement phase, nodes are not necessarily greedily merged with the community that yields the largest increase in the quality function. U. S. A. To address this important shortcoming, we introduce a new algorithm that is faster, finds better partitions and provides explicit guarantees and bounds. 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. Such a modular structure is usually not known beforehand. The Leiden algorithm is clearly faster than the Louvain algorithm. Two ways of doing this are graph modularity (Newman and Girvan 2004) and the constant Potts model (Ronhovde and Nussinov 2010). Nodes 13 should form a community and nodes 46 should form another community. Each point corresponds to a certain iteration of an algorithm, with results averaged over 10 experiments. 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). The Louvain algorithm is illustrated in Fig. ADS Google Scholar. When the Leiden algorithm found that a community could be split into multiple subcommunities, we counted the community as badly connected. We now consider the guarantees provided by the Leiden algorithm. Traag, Vincent, Ludo Waltman, and Nees Jan van Eck. In doing so, Louvain keeps visiting nodes that cannot be moved to a different community. Class wrapper based on scanpy to use the Leiden algorithm to directly cluster your data matrix with a scikit-learn flavor. Guimer, R. & Nunes Amaral, L. A. Functional cartography of complex metabolic networks. ADS In that case, some optimal partitions cannot be found, as we show in SectionC2 of the Supplementary Information. CPM has the advantage that it is not subject to the resolution limit. Finally, we demonstrate the excellent performance of the algorithm for several benchmark and real-world networks. 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. Basically, there are two types of hierarchical cluster analysis strategies - 1. The horizontal axis indicates the cumulative time taken to obtain the quality indicated on the vertical axis. Google Scholar. Ayan Sinha, David F. Gleich & Karthik Ramani, Marinka Zitnik, Rok Sosi & Jure Leskovec, Zhenqi Lu, Johan Wahlstrm & Arye Nehorai, Natalie Stanley, Roland Kwitt, Peter J. Mucha, Scientific Reports Rather than progress straight to the aggregation stage (as we would for the original Louvain), we next consider each community as a new sub-network and re-apply the local moving step within each community. contrastive-sc works best on datasets with fewer clusters when using the KMeans clustering and conversely for Leiden. Communities may even be internally disconnected. 2 represent stronger connections, while the other edges represent weaker connections. Positive values above 2 define the total number of iterations to perform, -1 has the algorithm run until it reaches its optimal clustering. The triumphs and limitations of computational methods for - Nature We use six empirical networks in our analysis. & Bornholdt, S. Statistical mechanics of community detection. This algorithm provides a number of explicit guarantees. The classic Louvain algorithm should be avoided due to the known problem with disconnected communities. Faster Unfolding of Communities: Speeding up the Louvain Algorithm. Phys. 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. Default behaviour is calling cluster_leiden in igraph with Modularity (for undirected graphs) and CPM cost functions. An overview of the various guarantees is presented in Table1. Inf. Traag, V. A., Waltman, L. & van Eck, N. J. networkanalysis. Google Scholar. Waltman, L. & van Eck, N. J. V.A.T. Zenodo, https://doi.org/10.5281/zenodo.1469357 https://github.com/vtraag/leidenalg. Speed and quality for the first 10 iterations of the Louvain and the Leiden algorithm for benchmark networks (n=106 and n=107). Again, if communities are badly connected, this may lead to incorrect inferences of topics, which will affect bibliometric analyses relying on the inferred topics. How to get started with louvain/leiden algorithm with UMAP in R In this new situation, nodes 2, 3, 5 and 6 have only internal connections. A score of 0 would mean that the community has half its edges connecting nodes within the same community, and half connecting nodes outside the community. MathSciNet bioRxiv, https://doi.org/10.1101/208819 (2018). N.J.v.E. Importantly, the problem of disconnected communities is not just a theoretical curiosity. Phys. According to CPM, it is better to split into two communities when the link density between the communities is lower than the constant. 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. Phys. modularity) increases. 10, 186198, https://doi.org/10.1038/nrn2575 (2009). In this way, the constant acts as a resolution parameter, and setting the constant higher will result in fewer communities. You are using a browser version with limited support for CSS. Newman, M E J, and M Girvan. Ozaki, N., Tezuka, H. & Inaba, M. A Simple Acceleration Method for the Louvain Algorithm. In the worst case, almost a quarter of the communities are badly connected. Centre for Science and Technology Studies, Leiden University, Leiden, The Netherlands, You can also search for this author in E 92, 032801, https://doi.org/10.1103/PhysRevE.92.032801 (2015). 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. Number of iterations until stability. As can be seen in the figure, Louvain quickly reaches a state in which it is unable to find better partitions. 1 and summarised in pseudo-code in AlgorithmA.1 in SectionA of the Supplementary Information. The main ideas of our algorithm are explained in an intuitive way in the main text of the paper. Below we offer an intuitive explanation of these properties. To obtain Sci. Based on project statistics from the GitHub repository for the PyPI package leiden-clustering, we found that it has been starred 1 times. Hence, the Leiden algorithm effectively addresses the problem of badly connected communities. ACM Trans. Additionally, we implemented a Python package, available from https://github.com/vtraag/leidenalg and deposited at Zenodo24). Please The numerical details of the example can be found in SectionB of the Supplementary Information. In the worst case, communities may even be disconnected, especially when running the algorithm iteratively. Clearly, it would be better to split up the community. Randomness in the selection of a community allows the partition space to be explored more broadly. Mech. Local Resolution-Limit-Free Potts Model for Community Detection. Phys. This package requires the 'leidenalg' and 'igraph' modules for python (2) to be installed on your system. One of the most popular algorithms for uncovering community structure is the so-called Louvain algorithm. 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. On Modularity Clustering. PubMed It implies uniform -density and all the other above-mentioned properties. Thank you for visiting nature.com. The Leiden algorithm has been specifically designed to address the problem of badly connected communities. Waltman, Ludo, and Nees Jan van Eck. Usually, the Louvain algorithm starts from a singleton partition, in which each node is in its own community. It is a directed graph if the adjacency matrix is not symmetric. Once aggregation is complete we restart the local moving phase, and continue to iterate until everything converges down to one node. Community detection can then be performed using this graph. While smart local moving and multilevel refinement can improve the communities found, the next two improvements on Louvain that Ill discuss focus on the speed/efficiency of the algorithm. A Smart Local Moving Algorithm for Large-Scale Modularity-Based Community Detection. Eur. SPATA2 currently offers the functions findSeuratClusters (), findMonocleClusters () and findNearestNeighbourClusters () which are wrapper around widely used clustering algorithms. The algorithm moves individual nodes from one community to another to find a partition (b).