leiden clustering explained

In general, Leiden is both faster than Louvain and finds better partitions. The Leiden community detection algorithm outperforms other clustering methods. Fortunato, S. Community detection in graphs. The horizontal axis indicates the cumulative time taken to obtain the quality indicated on the vertical axis. 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). Hence, the Leiden algorithm effectively addresses the problem of badly connected communities. While current approaches are successful in reducing the number of sequence alignments performed, the generated clusters are . 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. MATH Sci Rep 9, 5233 (2019). The high percentage of badly connected communities attests to this. contrastive-sc works best on datasets with fewer clusters when using the KMeans clustering and conversely for Leiden. You are using a browser version with limited support for CSS. Hence, for lower values of , the difference in quality is negligible. For each network, Table2 reports the maximal modularity obtained using the Louvain and the Leiden algorithm. Phys. S3. The main ideas of our algorithm are explained in an intuitive way in the main text of the paper. Newman, M E J, and M Girvan. We demonstrate the performance of the Leiden algorithm for several benchmark and real-world networks. 20, 172188, https://doi.org/10.1109/TKDE.2007.190689 (2008). In particular, we show that Louvain may identify communities that are internally disconnected. Later iterations of the Louvain algorithm only aggravate the problem of disconnected communities, even though the quality function (i.e. 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. The idea of the refinement phase in the Leiden algorithm is to identify a partition \({{\mathscr{P}}}_{{\rm{refined}}}\) that is a refinement of \({\mathscr{P}}\). 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. By submitting a comment you agree to abide by our Terms and Community Guidelines. In addition, we prove that the algorithm converges to an asymptotically stable partition in which all subsets of all communities are locally optimally assigned. Higher resolutions lead to more communities and lower resolutions lead to fewer communities, similarly to the resolution parameter for modularity. There is an entire Leiden package in R-cran here J. As the problem of modularity optimization is NP-hard, we need heuristic methods to optimize modularity (or CPM). We typically reduce the dimensionality of the data first by running PCA, then construct a neighbor graph in the reduced space. 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. Data 11, 130, https://doi.org/10.1145/2992785 (2017). Each of these can be used as an objective function for graph-based community detection methods, with our goal being to maximize this value. 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. Technol. 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. This will compute the Leiden clusters and add them to the Seurat Object Class. Node optimality is also guaranteed after a stable iteration of the Louvain algorithm. Hence, no further improvements can be made after a stable iteration of the Louvain algorithm. When a disconnected community has become a node in an aggregate network, there are no more possibilities to split up the community. 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 volume9, Articlenumber:5233 (2019) 2010. As such, we scored leiden-clustering popularity level to be Limited. A Simple Acceleration Method for the Louvain Algorithm. Int. Percentage of communities found by the Louvain algorithm that are either disconnected or badly connected compared to percentage of badly connected communities found by the Leiden algorithm. Brandes, U. et al. Each point corresponds to a certain iteration of an algorithm, with results averaged over 10 experiments. This package requires the 'leidenalg' and 'igraph' modules for python (2) to be installed on your system. Importantly, the number of communities discovered is related only to the difference in edge density, and not the total number of nodes in the community. E Stat. 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. Community detection in complex networks using extremal optimization. U. S. A. Source Code (2018). In other words, communities are guaranteed to be well separated. 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. The quality of such an asymptotically stable partition provides an upper bound on the quality of an optimal partition. 63, 23782392, https://doi.org/10.1002/asi.22748 (2012). Article An overview of the various guarantees is presented in Table1. In later stages, most neighbors will belong to the same community, and its very likely that the best move for the node is to the community that most of its neighbors already belong to. This commit does not belong to any branch on this repository, and may belong to a fork outside of the repository. It is a directed graph if the adjacency matrix is not symmetric. B 86 (11): 471. https://doi.org/10.1140/epjb/e2013-40829-0. CAS For higher values of , Leiden finds better partitions than Louvain. This is well illustrated by figure 2 in the Leiden paper: When a community becomes disconnected like this, there is no way for Louvain to easily split it into two separate communities. 2.3. Rev. V.A.T. It states that there are no communities that can be merged. Nonlin. The property of -separation is also guaranteed by the Louvain algorithm. To do this we just sum all the edge weights between nodes of the corresponding communities to get a single weighted edge between them, and collapse each community down to a single new node. 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. The R implementation of Leiden can be run directly on the snn igraph object in Seurat. Cluster your data matrix with the Leiden algorithm. One of the most popular algorithms for uncovering community structure is the so-called Louvain algorithm. In many complex networks, nodes cluster and form relatively dense groupsoften called communities1,2. Iterating the Louvain algorithm can therefore be seen as a double-edged sword: it improves the partition in some way, but degrades it in another way. Using the fast local move procedure, the first visit to all nodes in a network in the Leiden algorithm is the same as in the Louvain algorithm. Leiden is both faster than Louvain and finds better partitions. J. 4. J. Exp. For example, after four iterations, the Web UK network has 8% disconnected communities, but twice as many badly connected communities. E 78, 046110, https://doi.org/10.1103/PhysRevE.78.046110 (2008). Starting from the second iteration, Leiden outperformed Louvain in terms of the percentage of badly connected communities. There was a problem preparing your codespace, please try again. In particular, it yields communities that are guaranteed to be connected. modularity) increases. As can be seen in the figure, Louvain quickly reaches a state in which it is unable to find better partitions. A partition of clusters as a vector of integers Examples ADS 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. It is good at identifying small clusters. In the worst case, almost a quarter of the communities are badly connected. Article Complex brain networks: graph theoretical analysis of structural and functional systems. 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. The algorithm then moves individual nodes in the aggregate network (e). MathSciNet & Bornholdt, S. Statistical mechanics of community detection. Provided by the Springer Nature SharedIt content-sharing initiative. Random moving can result in some huge speedups, since Louvain spends about 95% of its time computing the modularity gain from moving nodes. Crucially, however, the percentage of badly connected communities decreases with each iteration of the Leiden algorithm. 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. The Beginner's Guide to Dimensionality Reduction. AMS 56, 10821097 (2009). The Leiden algorithm is considerably more complex than the Louvain algorithm. 2 represent stronger connections, while the other edges represent weaker connections. It maximizes a modularity score for each community, where the modularity quantifies the quality of an assignment of nodes to communities. There are many different approaches and algorithms to perform clustering tasks. & Arenas, A. In this section, we analyse and compare the performance of the two algorithms in practice. Zenodo, https://doi.org/10.5281/zenodo.1469357 https://github.com/vtraag/leidenalg. In fact, for the Web of Science and Web UK networks, Fig. To elucidate the problem, we consider the example illustrated in Fig. The algorithm is described in pseudo-code in AlgorithmA.2 in SectionA of the Supplementary Information. This is very similar to what the smart local moving algorithm does. However, in the case of the Web of Science network, more than 5% of the communities are disconnected in the first iteration. 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. These nodes are therefore optimally assigned to their current community. The increase in the percentage of disconnected communities is relatively limited for the Live Journal and Web of Science networks. This method tries to maximise the difference between the actual number of edges in a community and the expected number of such edges. For empirical networks, it may take quite some time before the Leiden algorithm reaches its first stable iteration. This continues until the queue is empty. Am. 8, the Leiden algorithm is significantly faster than the Louvain algorithm also in empirical networks. Here we can see partitions in the plotted results. More subtle problems may occur as well, causing Louvain to find communities that are connected, but only in a very weak sense. & Clauset, A. The phase one loop can be greatly accelerated by finding the nodes that have the potential to change community and only revisit those nodes. IEEE Trans. E Stat. Such algorithms are rather slow, making them ineffective for large networks. First, we show that the Louvain algorithm finds disconnected communities, and more generally, badly connected communities in the empirical networks. As shown in Fig. The Leiden algorithm starts from a singleton partition (a). 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. Speed of the first iteration of the Louvain and the Leiden algorithm for six empirical networks. In that case, some optimal partitions cannot be found, as we show in SectionC2 of the Supplementary Information. We applied the Louvain and the Leiden algorithm to exactly the same networks, using the same seed for the random number generator. Modularity is given by. The Louvain algorithm is a simple and popular method for community detection (Blondel, Guillaume, and Lambiotte 2008). We keep removing nodes from the front of the queue, possibly moving these nodes to a different community. The difference in computational time is especially pronounced for larger networks, with Leiden being up to 20 times faster than Louvain in empirical networks. 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. 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. CAS Louvain quickly converges to a partition and is then unable to make further improvements. We name our algorithm the Leiden algorithm, after the location of its authors. leidenalg. Modularity is used most commonly, but is subject to the resolution limit. Badly connected communities. Speed and quality of the Louvain and the Leiden algorithm for benchmark networks of increasing size (two iterations). In this new situation, nodes 2, 3, 5 and 6 have only internal connections. Waltman, Ludo, and Nees Jan van Eck. As can be seen in Fig. Wolf, F. A. et al. Google Scholar. 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. Subpartition -density does not imply that individual nodes are locally optimally assigned. The algorithm then moves individual nodes in the aggregate network (d). . N.J.v.E. At some point, node 0 is considered for moving. Google Scholar. An aggregate network (d) is created based on the refined partition, using the non-refined partition to create an initial partition for the aggregate network. Discov. This aspect of the Louvain algorithm can be used to give information about the hierarchical relationships between communities by tracking at which stage the nodes in the communities were aggregated. When the Leiden algorithm found that a community could be split into multiple subcommunities, we counted the community as badly connected. The nodes that are more interconnected have been partitioned into separate clusters. Blondel, V D, J L Guillaume, and R Lambiotte. We used modularity with a resolution parameter of =1 for the experiments. Usually, the Louvain algorithm starts from a singleton partition, in which each node is in its own community. Faster unfolding of communities: Speeding up the Louvain algorithm. The algorithm moves individual nodes from one community to another to find a partition (b), which is then refined (c). Use Git or checkout with SVN using the web URL. 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. It does not guarantee that modularity cant be increased by moving nodes between communities. The Louvain algorithm10 is very simple and elegant. In contrast, Leiden keeps finding better partitions in each iteration. An aggregate. Below, the quality of a partition is reported as \(\frac{ {\mathcal H} }{2m}\), where H is defined in Eq. 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. This may have serious consequences for analyses based on the resulting partitions. Therefore, clustering algorithms look for similarities or dissimilarities among data points. As discussed earlier, the Louvain algorithm does not guarantee connectivity. The Leiden algorithm has been specifically designed to address the problem of badly connected communities. In our experimental analysis, we observe that up to 25% of the communities are badly connected and up to 16% are disconnected. Four popular community detection algorithms are explained . 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. However, the Louvain algorithm does not consider this possibility, since it considers only individual node movements. * (2018). In practice, this means that small clusters can hide inside larger clusters, making their identification difficult. How many iterations of the Leiden clustering algorithm to perform. In fact, if we keep iterating the Leiden algorithm, it will converge to a partition without any badly connected communities, as discussed earlier. Lancichinetti, A., Fortunato, S. & Radicchi, F. Benchmark graphs for testing community detection algorithms. Trying to fix the problem by simply considering the connected components of communities19,20,21 is unsatisfactory because it addresses only the most extreme case and does not resolve the more fundamental problem. Class wrapper based on scanpy to use the Leiden algorithm to directly cluster your data matrix with a scikit-learn flavor. The algorithm is run iteratively, using the partition identified in one iteration as starting point for the next iteration. Article Rev. One of the best-known methods for community detection is called modularity3. In particular, benchmark networks have a rather simple structure. Value. 81 (4 Pt 2): 046114. http://dx.doi.org/10.1103/PhysRevE.81.046114. Eur. Powered by DataCamp DataCamp Finding communities in large networks is far from trivial: algorithms need to be fast, but they also need to provide high-quality results. leiden_clustering Description Class wrapper based on scanpy to use the Leiden algorithm to directly cluster your data matrix with a scikit-learn flavor. In the most difficult case (=0.9), Louvain requires almost 2.5 days, while Leiden needs fewer than 10 minutes. Get the most important science stories of the day, free in your inbox. The corresponding results are presented in the Supplementary Fig. (2) and m is the number of edges. Slider with three articles shown per slide. bioRxiv, https://doi.org/10.1101/208819 (2018). We here introduce the Leiden algorithm, which guarantees that communities are well connected. Figure6 presents total runtime versus quality for all iterations of the Louvain and the Leiden algorithm. In the initial stage of Louvain (when all nodes belong to their own community), nearly any move will result in a modularity gain, and it doesnt matter too much which move is chosen. Are you sure you want to create this branch? http://iopscience.iop.org/article/10.1088/1742-5468/2008/10/P10008/meta. The above results shows that the problem of disconnected and badly connected communities is quite pervasive in practice. E 81, 046106, https://doi.org/10.1103/PhysRevE.81.046106 (2010). 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. Agglomerative Clustering: Also known as bottom-up approach or hierarchical agglomerative clustering (HAC). The community with which a node is merged is selected randomly18. Note that this code is . MathSciNet the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in 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. J. We now consider the guarantees provided by the Leiden algorithm. Some of these nodes may very well act as bridges, similarly to node 0 in the above example. 9 shows that more than 10 iterations of the Leiden algorithm can be performed before the Louvain algorithm has finished its first iteration. Finally, we compare the performance of the algorithms on the empirical networks. To address this problem, we introduce the Leiden algorithm. E 74, 036104, https://doi.org/10.1103/PhysRevE.74.036104 (2006). where nc is the number of nodes in community c. The interpretation of the resolution parameter is quite straightforward. It means that there are no individual nodes that can be moved to a different community. The second iteration of Louvain shows a large increase in the percentage of disconnected communities.