Rev. Article To obtain 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. Publishers note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. The percentage of disconnected communities even jumps to 16% for the DBLP network. Sci. When iterating Louvain, the quality of the partitions will keep increasing until the algorithm is unable to make any further improvements. 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. Technol. While current approaches are successful in reducing the number of sequence alignments performed, the generated clusters are . & Moore, C. Finding community structure in very large networks. Bae, S., Halperin, D., West, J. D., Rosvall, M. & Howe, B. Scalable and Efficient Flow-Based Community Detection for Large-Scale Graph Analysis. In the refinement phase, nodes are not necessarily greedily merged with the community that yields the largest increase in the quality function. Default behaviour is calling cluster_leiden in igraph with Modularity (for undirected graphs) and CPM cost functions. 10, for the IMDB and Amazon networks, Leiden reaches a stable iteration relatively quickly, presumably because these networks have a fairly simple community structure. To address this problem, we introduce the Leiden algorithm. Google Scholar. Each point corresponds to a certain iteration of an algorithm, with results averaged over 10 experiments. Below we offer an intuitive explanation of these properties. 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. Complex brain networks: graph theoretical analysis of structural and functional systems. A structure that is more informative than the unstructured set of clusters returned by flat clustering. We start by initialising a queue with all nodes in the network. contrastive-sc works best on datasets with fewer clusters when using the KMeans clustering and conversely for Leiden. Traag, V. A., Waltman, L. & van Eck, N. J. networkanalysis. Rev. J. Stat. Mech. An aggregate. and L.W. 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. * (2018). The value of the resolution parameter was determined based on the so-called mixing parameter 13. In this post Ive mainly focused on the optimisation methods for community detection, rather than the different objective functions that can be used. b, The elephant graph (in a) is clustered using the Leiden clustering algorithm 51 (resolution r = 0.5). Nodes 16 have connections only within this community, whereas node 0 also has many external connections. Lancichinetti, A. In that case, some optimal partitions cannot be found, as we show in SectionC2 of the Supplementary Information. Google Scholar. In fact, when we keep iterating the Leiden algorithm, it will converge to a partition for which it is guaranteed that: A community is uniformly -dense if there are no subsets of the community that can be separated from the community. These nodes are therefore optimally assigned to their current community. Google Scholar. Hence, the problem of Louvain outlined above is independent from the issue of the resolution limit. Random moving is a very simple adjustment to Louvain local moving proposed in 2015 (Traag 2015). The two phases are repeated until the quality function cannot be increased further. 1 I am using the leiden algorithm implementation in iGraph, and noticed that when I repeat clustering using the same resolution parameter, I get different results. 2(a). 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 . Google Scholar. This is similar to ideas proposed recently as pruning16 and in a slightly different form as prioritisation17. Leiden is faster than Louvain especially for larger networks. Consider the partition shown in (a). Four popular community detection algorithms are explained . modularity) increases. ACM Trans. In the local move procedure in the Leiden algorithm, only nodes whose neighborhood . E 84, 016114, https://doi.org/10.1103/PhysRevE.84.016114 (2011). and JavaScript. Note that this code is designed for Seurat version 2 releases. performed the experimental analysis. 2015. In this case, refinement does not change the partition (f). Node mergers that cause the quality function to decrease are not considered. . Sci. In an experiment containing a mixture of cell types, each cluster might correspond to a different cell type. 2013. In contrast, Leiden keeps finding better partitions in each iteration. The Web of Science network is the most difficult one. Rev. 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. Even worse, the Amazon network has 5% disconnected communities, but 25% badly connected communities. 1 and summarised in pseudo-code in AlgorithmA.1 in SectionA of the Supplementary Information. Article Technol. The algorithm moves individual nodes from one community to another to find a partition (b), which is then refined (c). Electr. Please 2.3. bioRxiv, https://doi.org/10.1101/208819 (2018). https://doi.org/10.1038/s41598-019-41695-z, DOI: https://doi.org/10.1038/s41598-019-41695-z. Perhaps surprisingly, iterating the algorithm aggravates the problem, even though it does increase the quality function. Inf. Higher resolutions lead to more communities and lower resolutions lead to fewer communities, similarly to the resolution parameter for modularity. Note that nodes can be revisited several times within a single iteration of the local moving stage, as the possible increase in modularity will change as other nodes are moved to different communities. In particular, in an attempt to find better partitions, multiple consecutive iterations of the algorithm can be performed, using the partition identified in one iteration as starting point for the next iteration. Our analysis is based on modularity with resolution parameter =1. Agglomerative clustering is a bottom-up approach. In particular, it yields communities that are guaranteed to be connected. Phys. 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. V. A. Traag. Hence, the Leiden algorithm effectively addresses the problem of badly connected communities. The Louvain algorithm starts from a singleton partition in which each node is in its own community (a). 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. Louvain pruning keeps track of a list of nodes that have the potential to change communities, and only revisits nodes in this list, which is much smaller than the total number of nodes. Then, in order . Removing such a node from its old community disconnects the old community. 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. For all networks, Leiden identifies substantially better partitions than Louvain. In fact, if we keep iterating the Leiden algorithm, it will converge to a partition without any badly connected communities, as discussed earlier. Other networks show an almost tenfold increase in the percentage of disconnected communities. 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. However, if communities are badly connected, this may lead to incorrect attributions of shared functionality. https://leidenalg.readthedocs.io/en/latest/reference.html. 8, 207218, https://doi.org/10.17706/IJCEE.2016.8.3.207-218 (2016). Detecting communities in a network is therefore an important problem. Google Scholar. The count of badly connected communities also included disconnected communities. Modularity is given by. The speed difference is especially large for larger networks. Clustering is a machine learning technique in which similar data points are grouped into the same cluster based on their attributes. The Leiden algorithm consists of three phases: (1) local moving of nodes, (2) refinement of the partition and (3) aggregation of the network based on the refined partition, using the non-refined partition to create an initial partition for the aggregate network. In the local moving phase, individual nodes are moved to the community that yields the largest increase in the quality function. Finding community structure in networks using the eigenvectors of matrices. Instead, a node may be merged with any community for which the quality function increases. To overcome the problem of arbitrarily badly connected communities, we introduced a new algorithm, which we refer to as the Leiden algorithm. We therefore require a more principled solution, which we will introduce in the next section. For each network, we repeated the experiment 10 times. The horizontal axis indicates the cumulative time taken to obtain the quality indicated on the vertical axis. The solution proposed in smart local moving is to alter how the local moving step in Louvain works. The algorithm may yield arbitrarily badly connected communities, over and above the well-known issue of the resolution limit14. Subpartition -density is not guaranteed by 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. 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. If nothing happens, download Xcode and try again. Package 'leiden' October 13, 2022 Type Package Title R Implementation of Leiden Clustering Algorithm Version 0.4.3 Date 2022-09-10 Description Implements the 'Python leidenalg' module to be called in R. Enables clustering using the leiden algorithm for partition a graph into communities. The inspiration for this method of community detection is the optimization of modularity as the algorithm progresses. Modularity is a scale value between 0.5 (non-modular clustering) and 1 (fully modular clustering) that measures the relative density of edges inside communities with respect to edges outside communities. Additionally, we implemented a Python package, available from https://github.com/vtraag/leidenalg and deposited at Zenodo24). The community with which a node is merged is selected randomly18. A smart local moving algorithm for large-scale modularity-based community detection. The algorithm then moves individual nodes in the aggregate network (d). 9, the Leiden algorithm also performs better than the Louvain algorithm in terms of the quality of the partitions that are obtained. Presumably, many of the badly connected communities in the first iteration of Louvain become disconnected in the second iteration. Acad. 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. The nodes that are more interconnected have been partitioned into separate clusters. Sci. J. A tag already exists with the provided branch name. Importantly, the output of the local moving stage will depend on the order that the nodes are considered in. 7, whereas Louvain becomes much slower for more difficult partitions, Leiden is much less affected by the difficulty of the partition. Subpartition -density does not imply that individual nodes are locally optimally assigned. Faster unfolding of communities: Speeding up the Louvain algorithm. In the meantime, to ensure continued support, we are displaying the site without styles In addition, a node is merged with a community in \({{\mathscr{P}}}_{{\rm{refined}}}\) only if both are sufficiently well connected to their community in \({\mathscr{P}}\). Note that the object for Seurat version 3 has changed. The constant Potts model might give better communities in some cases, as it is not subject to the resolution limit. Leiden algorithm. In the worst case, communities may even be disconnected, especially when running the algorithm iteratively. However, this is not necessarily the case, as the other nodes may still be sufficiently strongly connected to their community, despite the fact that the community has become disconnected. It was originally developed for modularity optimization, although the same method can be applied to optimize CPM. J. First iteration runtime for empirical networks. CPM is defined as. MATH This will compute the Leiden clusters and add them to the Seurat Object Class. E 69, 026113, https://doi.org/10.1103/PhysRevE.69.026113 (2004). E 76, 036106, https://doi.org/10.1103/PhysRevE.76.036106 (2007). Run the code above in your browser using DataCamp Workspace. 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). 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. J. This amounts to a clustering problem, where we aim to learn an optimal set of groups (communities) from the observed data. The smart local moving algorithm (Waltman and Eck 2013) identified another limitation in the original Louvain method: it isnt able to split communities once theyre merged, even when it may be very beneficial to do so. Louvain keeps visiting all nodes in a network until there are no more node movements that increase the quality function. We then remove the first node from the front of the queue and we determine whether the quality function can be increased by moving this node from its current community to a different one. Usually, the Louvain algorithm starts from a singleton partition, in which each node is in its own community. There is an entire Leiden package in R-cran here This function takes a cell_data_set as input, clusters the cells using . Agglomerative Clustering: Also known as bottom-up approach or hierarchical agglomerative clustering (HAC). Phys. These nodes can be approximately identified based on whether neighbouring nodes have changed communities. Louvain has two phases: local moving and aggregation. Ozaki, N., Tezuka, H. & Inaba, M. A Simple Acceleration Method for the Louvain Algorithm. As can be seen in Fig. 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. The Louvain algorithm guarantees that modularity cannot be increased by merging communities (it finds a locally optimal solution). All authors conceived the algorithm and contributed to the source code. The problem of disconnected communities has been observed before19,20, also in the context of the label propagation algorithm21. This enables us to find cases where its beneficial to split a community. 63, 23782392, https://doi.org/10.1002/asi.22748 (2012). It states that there are no communities that can be merged. For lower values of , the correct partition is easy to find and Leiden is only about twice as fast as Louvain. Finding and Evaluating Community Structure in Networks. Phys. 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 ). This makes sense, because after phase one the total size of the graph should be significantly reduced. 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.
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