Duch, J. ADS A Comparative Analysis of Community Detection Algorithms on Artificial Networks. It therefore does not guarantee -connectivity either. MATH We now consider the guarantees provided by the Leiden algorithm. cluster_cells: Cluster cells using Louvain/Leiden community detection & Arenas, A. The Leiden algorithm is clearly faster than the Louvain algorithm. 4. To obtain See the documentation on the leidenalg Python module for more information: https://leidenalg.readthedocs.io/en/latest/reference.html. An alternative quality function is the Constant Potts Model (CPM)13, which overcomes some limitations of modularity. Disconnected community. Then optimize the modularity function to determine clusters. At this point, it is guaranteed that each individual node is optimally assigned. 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. Cluster your data matrix with the Leiden algorithm. This may have serious consequences for analyses based on the resulting partitions. HiCBin: binning metagenomic contigs and recovering metagenome-assembled Acad. The second iteration of Louvain shows a large increase in the percentage of disconnected communities. 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. PubMedGoogle Scholar. Communities may even be internally disconnected. The corresponding results are presented in the Supplementary Fig. As we will demonstrate in our experimental analysis, the problem occurs frequently in practice when using the Louvain algorithm. The above results shows that the problem of disconnected and badly connected communities is quite pervasive in practice. Hence, in general, Louvain may find arbitrarily badly connected communities. 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. This method tries to maximise the difference between the actual number of edges in a community and the expected number of such edges. Data 11, 130, https://doi.org/10.1145/2992785 (2017). Zenodo, https://doi.org/10.5281/zenodo.1466831 https://github.com/CWTSLeiden/networkanalysis. In a stable iteration, the partition is guaranteed to be node optimal and subpartition -dense. 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. Get the most important science stories of the day, free in your inbox. This is the crux of the Leiden paper, and the authors show that this exact problem happens frequently in practice. The Louvain algorithm10 is very simple and elegant. As can be seen in Fig. Modularity optimization. A. Waltman, L. & van Eck, N. J. Newman, M. E. J. This will compute the Leiden clusters and add them to the Seurat Object Class. In the refinement phase, nodes are not necessarily greedily merged with the community that yields the largest increase in the quality function. 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. 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. Neurosci. Rev. In the case of modularity, communities may have significant substructure both because of the resolution limit and because of the shortcomings of Louvain. I tracked the number of clusters post-clustering at each step. E 74, 016110, https://doi.org/10.1103/PhysRevE.74.016110 (2006). Ph.D. thesis, (University of Oxford, 2016). However, as shown in this paper, the Louvain algorithm has a major shortcoming: the algorithm yields communities that may be arbitrarily badly connected. After a stable iteration of the Leiden algorithm, the algorithm may still be able to make further improvements in later iterations. Use Git or checkout with SVN using the web URL. 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 According to CPM, it is better to split into two communities when the link density between the communities is lower than the constant. The horizontal axis indicates the cumulative time taken to obtain the quality indicated on the vertical axis. bioRxiv, https://doi.org/10.1101/208819 (2018). 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). However, focussing only on disconnected communities masks the more fundamental issue: Louvain finds arbitrarily badly connected communities. CPM is defined as. A number of iterations of the Leiden algorithm can be performed before the Louvain algorithm has finished its first iteration. Rather than evaluating the modularity gain for moving a node to each neighboring communities, we choose a neighboring node at random and evaluate whether there is a gain in modularity if we were to move the node to that neighbors community. 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. U. S. A. For each community in a partition that was uncovered by the Louvain algorithm, we determined whether it is internally connected or not. You are using a browser version with limited support for CSS. Run the code above in your browser using DataCamp Workspace. This is not too difficult to explain. This algorithm provides a number of explicit guarantees. In addition, we prove that the algorithm converges to an asymptotically stable partition in which all subsets of all communities are locally optimally assigned. Unsupervised clustering of cells is a common step in many single-cell expression workflows. The DBLP network is somewhat more challenging, requiring almost 80 iterations on average to reach a stable iteration. Node mergers that cause the quality function to decrease are not considered. Am. Thank you for visiting nature.com. Value. Positive values above 2 define the total number of iterations to perform, -1 has the algorithm run until it reaches its optimal clustering. This represents the following graph structure. The numerical details of the example can be found in SectionB of the Supplementary Information. We gratefully acknowledge computational facilities provided by the LIACS Data Science Lab Computing Facilities through Frank Takes. 69 (2 Pt 2): 026113. http://dx.doi.org/10.1103/PhysRevE.69.026113. It implies uniform -density and all the other above-mentioned properties. Cite this article. Technol. Importantly, the first iteration of the Leiden algorithm is the most computationally intensive one, and subsequent iterations are faster. A structure that is more informative than the unstructured set of clusters returned by flat clustering. Other networks show an almost tenfold increase in the percentage of disconnected communities. A Smart Local Moving Algorithm for Large-Scale Modularity-Based Community Detection. Eur. 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). Instead, a node may be merged with any community for which the quality function increases. 2. Perhaps surprisingly, iterating the algorithm aggravates the problem, even though it does increase the quality function. Ronhovde, Peter, and Zohar Nussinov. The algorithm moves individual nodes from one community to another to find a partition (b), which is then refined (c). Based on this partition, an aggregate network is created (c). In fact, for the Web of Science and Web UK networks, Fig. MATH Weights for edges an also be passed to the leiden algorithm either as a separate vector or weights or a weighted adjacency matrix. However, nodes 16 are still locally optimally assigned, and therefore these nodes will stay in the red community. Then the Leiden algorithm can be run on the adjacency matrix. E 84, 016114, https://doi.org/10.1103/PhysRevE.84.016114 (2011). The algorithm is described in pseudo-code in AlgorithmA.2 in SectionA of the Supplementary Information. Phys. The Louvain algorithm is illustrated in Fig. 2016. Ozaki, N., Tezuka, H. & Inaba, M. A Simple Acceleration Method for the Louvain Algorithm. Importantly, the output of the local moving stage will depend on the order that the nodes are considered in. modularity) increases. 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 idea of the refinement phase in the Leiden algorithm is to identify a partition \({{\mathscr{P}}}_{{\rm{refined}}}\) that is a refinement of \({\mathscr{P}}\). In particular, benchmark networks have a rather simple structure. J. This phenomenon can be explained by the documented tendency KMeans has to identify equal-sized , combined with the significant class imbalance associated with the datasets having more than 8 clusters (Table 1). The Leiden algorithm starts from a singleton partition (a). Fortunato, Santo, and Marc Barthlemy. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/. We conclude that the Leiden algorithm is strongly preferable to the Louvain algorithm. 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. The Leiden algorithm guarantees all communities to be connected, but it may yield badly connected communities. E 72, 027104, https://doi.org/10.1103/PhysRevE.72.027104 (2005). Rep. 486, 75174, https://doi.org/10.1016/j.physrep.2009.11.002 (2010). Complex brain networks: graph theoretical analysis of structural and functional systems. Phys. 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. This is similar to what we have seen for benchmark networks. Nodes 06 are in the same community. We now compare how the Leiden and the Louvain algorithm perform for the six empirical networks listed in Table2. In the Louvain algorithm, an aggregate network is created based on the partition \({\mathscr{P}}\) resulting from the local moving phase. Some of these nodes may very well act as bridges, similarly to node 0 in the above example. Narrow scope for resolution-limit-free community detection. Note that this code is designed for Seurat version 2 releases. Random moving can result in some huge speedups, since Louvain spends about 95% of its time computing the modularity gain from moving nodes. Electr. Indeed, the percentage of disconnected communities becomes more comparable to the percentage of badly connected communities in later iterations. We find that the Leiden algorithm is faster than the Louvain algorithm and uncovers better partitions, in addition to providing explicit guarantees. 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. After the refinement phase is concluded, communities in \({\mathscr{P}}\) often will have been split into multiple communities in \({{\mathscr{P}}}_{{\rm{refined}}}\), but not always. Class wrapper based on scanpy to use the Leiden algorithm to directly cluster your data matrix with a scikit-learn flavor. In this new situation, nodes 2, 3, 5 and 6 have only internal connections. In other words, communities are guaranteed to be well separated. The quality improvement realised by the Leiden algorithm relative to the Louvain algorithm is larger for empirical networks than for benchmark networks. Nonetheless, some networks still show large differences. Leiden keeps finding better partitions for empirical networks also after the first 10 iterations of the algorithm. This is not the case when nodes are greedily merged with the community that yields the largest increase in the quality function. 2 represent stronger connections, while the other edges represent weaker connections. The quality of such an asymptotically stable partition provides an upper bound on the quality of an optimal partition. Here is some small debugging code I wrote to find this. The current state of the art when it comes to graph-based community detection is Leiden, which incorporates about 10 years of algorithmic improvements to the original Louvain method. Introduction The Louvain method is an algorithm to detect communities in large networks. 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 The nodes that are more interconnected have been partitioned into separate clusters. This contrasts with the Leiden algorithm. Community detection - Tim Stuart 81 (4 Pt 2): 046114. http://dx.doi.org/10.1103/PhysRevE.81.046114. Traag, V A. o CLIQUE (Clustering in Quest): - CLIQUE is a combination of density-based and grid-based clustering algorithm. 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. In this case, refinement does not change the partition (f). First, we created a specified number of nodes and we assigned each node to a community. We consider these ideas to represent the most promising directions in which the Louvain algorithm can be improved, even though we recognise that other improvements have been suggested as well22. Publishers note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Article It is good at identifying small clusters. We find that the Leiden algorithm commonly finds partitions of higher quality in less time. and JavaScript. The algorithm moves individual nodes from one community to another to find a partition (b). E 78, 046110, https://doi.org/10.1103/PhysRevE.78.046110 (2008). Not. V.A.T. 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. In the local moving phase, individual nodes are moved to the community that yields the largest increase in the quality function. leiden_clsutering is distributed under a BSD 3-Clause License (see LICENSE). Additionally, we implemented a Python package, available from https://github.com/vtraag/leidenalg and deposited at Zenodo24). Random moving is a very simple adjustment to Louvain local moving proposed in 2015 (Traag 2015). How to get started with louvain/leiden algorithm with UMAP in R An iteration of the Leiden algorithm in which the partition does not change is called a stable iteration. It is a directed graph if the adjacency matrix is not symmetric. Modularity is a measure of the structure of networks or graphs which measures the strength of division of a network into modules (also called groups, clusters or communities). However, as increases, the Leiden algorithm starts to outperform the Louvain algorithm. See the documentation for these functions. Hence, the problem of Louvain outlined above is independent from the issue of the resolution limit. When iterating Louvain, the quality of the partitions will keep increasing until the algorithm is unable to make any further improvements. Newman, M E J, and M Girvan. The algorithm then locally merges nodes in \({{\mathscr{P}}}_{{\rm{refined}}}\): nodes that are on their own in a community in \({{\mathscr{P}}}_{{\rm{refined}}}\) can be merged with a different community. As the problem of modularity optimization is NP-hard, we need heuristic methods to optimize modularity (or CPM). The resolution limit describes a limitation where there is a minimum community size able to be resolved by optimizing modularity (or other related functions). Sci. Clustering with the Leiden Algorithm in R - cran.microsoft.com E 76, 036106, https://doi.org/10.1103/PhysRevE.76.036106 (2007). All communities are subpartition -dense. The horizontal axis indicates the cumulative time taken to obtain the quality indicated on the vertical axis. There is an entire Leiden package in R-cran here 9 shows that more than 10 iterations of the Leiden algorithm can be performed before the Louvain algorithm has finished its first iteration. Higher resolutions lead to more communities, while lower resolutions lead to fewer communities. Source Code (2018). Rev. 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. Fast Unfolding of Communities in Large Networks. Journal of Statistical , January. ISSN 2045-2322 (online). The fast local move procedure can be summarised as follows. 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. 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. The refined partition \({{\mathscr{P}}}_{{\rm{refined}}}\) is obtained as follows. 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. 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. Traag, Vincent, Ludo Waltman, and Nees Jan van Eck. There was a problem preparing your codespace, please try again. You will not need much Python to use it. We typically reduce the dimensionality of the data first by running PCA, then construct a neighbor graph in the reduced space. Eur. Traag, V. A., Waltman, L. & van Eck, N. J. networkanalysis. That is, one part of such an internally disconnected community can reach another part only through a path going outside the community. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate. 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 10, 186198, https://doi.org/10.1038/nrn2575 (2009). Nat. Article Louvain - Neo4j Graph Data Science Here we can see partitions in the plotted results. leidenalg. For each set of parameters, we repeated the experiment 10 times. Source Code (2018). To elucidate the problem, we consider the example illustrated in Fig. In the first iteration, Leiden is roughly 220 times faster than Louvain. However, for higher values of , Leiden becomes orders of magnitude faster than Louvain, reaching 10100 times faster runtimes for the largest networks. To find an optimal grouping of cells into communities, we need some way of evaluating different partitions in the graph. As can be seen in Fig. Furthermore, by relying on a fast local move approach, the Leiden algorithm runs faster than the Louvain algorithm. Hence, for lower values of , the difference in quality is negligible. 2010. Inf. AMS 56, 10821097 (2009). 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. 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. Finally, we compare the performance of the algorithms on the empirical networks. As can be seen in Fig. Louvain community detection algorithm was originally proposed in 2008 as a fast community unfolding method for large networks. Subpartition -density does not imply that individual nodes are locally optimally assigned. We prove that the Leiden algorithm yields communities that are guaranteed to be connected. After the first iteration of the Louvain algorithm, some partition has been obtained. The percentage of disconnected communities is more limited, usually around 1%. Louvain pruning is another improvement to Louvain proposed in 2016, and can reduce the computational time by as much as 90% while finding communities that are almost as good as Louvain (Ozaki, Tezuka, and Inaba 2016). Nodes 16 have connections only within this community, whereas node 0 also has many external connections. Louvain algorithm. MathSciNet The new algorithm integrates several earlier improvements, incorporating a combination of smart local move15, fast local move16,17 and random neighbour move18. However, in the case of the Web of Science network, more than 5% of the communities are disconnected in the first iteration. Subpartition -density is not guaranteed by the Louvain algorithm. In this case we know the answer is exactly 10. The Leiden algorithm starts from a singleton partition (a). 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. 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. DBSCAN Clustering Explained. Detailed theorotical explanation and 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. 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 . This contrasts to benchmark networks, for which Leiden often converges after a few iterations. Algorithmics 16, 2.1, https://doi.org/10.1145/1963190.1970376 (2011). However, if communities are badly connected, this may lead to incorrect attributions of shared functionality. The constant Potts model might give better communities in some cases, as it is not subject to the resolution limit. Again, if communities are badly connected, this may lead to incorrect inferences of topics, which will affect bibliometric analyses relying on the inferred topics. Rev. In many complex networks, nodes cluster and form relatively dense groupsoften called communities1,2. 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. On the other hand, Leiden keeps finding better partitions, especially for higher values of , for which it is more difficult to identify good partitions. CAS Phys. Zenodo, https://doi.org/10.5281/zenodo.1469357 https://github.com/vtraag/leidenalg. The images or other third party material in this article are included in the articles Creative Commons license, unless indicated otherwise in a credit line to the material. Centre for Science and Technology Studies, Leiden University, Leiden, The Netherlands, You can also search for this author in E 70, 066111, https://doi.org/10.1103/PhysRevE.70.066111 (2004). The high percentage of badly connected communities attests to this. Crucially, however, the percentage of badly connected communities decreases with each iteration of the Leiden algorithm. E 69, 026113, https://doi.org/10.1103/PhysRevE.69.026113 (2004). One may expect that other nodes in the old community will then also be moved to other communities. 2004. PubMed Each community in this partition becomes a node in the aggregate network. leiden-clustering - Python Package Health Analysis | Snyk Therefore, clustering algorithms look for similarities or dissimilarities among data points. Traag, V. A., Van Dooren, P. & Nesterov, Y. http://iopscience.iop.org/article/10.1088/1742-5468/2008/10/P10008/meta, http://dx.doi.org/10.1073/pnas.0605965104, http://dx.doi.org/10.1103/PhysRevE.69.026113, https://pdfs.semanticscholar.org/4ea9/74f0fadb57a0b1ec35cbc5b3eb28e9b966d8.pdf, http://dx.doi.org/10.1103/PhysRevE.81.046114, http://dx.doi.org/10.1103/PhysRevE.92.032801, https://doi.org/10.1140/epjb/e2013-40829-0, Assign each node to a different community. Leiden now included in python-igraph #1053 - Github 8 (3): 207. https://pdfs.semanticscholar.org/4ea9/74f0fadb57a0b1ec35cbc5b3eb28e9b966d8.pdf. The solution provided by Leiden is based on the smart local moving algorithm. contrastive-sc works best on datasets with fewer clusters when using the KMeans clustering and conversely for Leiden. Speed of the first iteration of the Louvain and the Leiden algorithm for six empirical networks. Google Scholar. Modularity scores of +1 mean that all the edges in a community are connecting nodes within the community. Phys. Hence, no further improvements can be made after a stable iteration of the Louvain algorithm. For this network, Leiden requires over 750 iterations on average to reach a stable iteration. The algorithm continues to move nodes in the rest of the network. Phys. Phys. E 81, 046106, https://doi.org/10.1103/PhysRevE.81.046106 (2010). 2.3. V. A. Traag. 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. The two phases are repeated until the quality function cannot be increased further. This continues until the queue is empty. You signed in with another tab or window. All experiments were run on a computer with 64 Intel Xeon E5-4667v3 2GHz CPUs and 1TB internal memory. Nonlin. Fortunato, S. Community detection in graphs. We used modularity with a resolution parameter of =1 for the experiments. wrote the manuscript. J. First, we show that the Louvain algorithm finds disconnected communities, and more generally, badly connected communities in the empirical networks. This is similar to ideas proposed recently as pruning16 and in a slightly different form as prioritisation17. Number of iterations until stability. Nevertheless, depending on the relative strengths of the different connections, these nodes may still be optimally assigned to their current community. Later iterations of the Louvain algorithm only aggravate the problem of disconnected communities, even though the quality function (i.e. 10008, 6, https://doi.org/10.1088/1742-5468/2008/10/P10008 (2008). J. 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. For larger networks and higher values of , Louvain is much slower than Leiden. In the aggregation phase, an aggregate network is created based on the partition obtained in the local moving phase. Louvain quickly converges to a partition and is then unable to make further improvements. 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.