leiden clustering explained

Blondel, V D, J L Guillaume, and R Lambiotte. The classic Louvain algorithm should be avoided due to the known problem with disconnected communities. In all experiments reported here, we used a value of 0.01 for the parameter that determines the degree of randomness in the refinement phase of the Leiden algorithm. 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. In practical applications, the Leiden algorithm convincingly outperforms the Louvain algorithm, both in terms of speed and in terms of quality of the results, as shown by the experimental analysis presented in this paper. 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 algorithm is described in pseudo-code in AlgorithmA.2 in SectionA of the Supplementary Information. Google Scholar. In the most difficult case (=0.9), Louvain requires almost 2.5 days, while Leiden needs fewer than 10 minutes. 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. 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. We first applied the Scanpy pipeline, including its clustering method (Leiden clustering), on the PBMC dataset. There was a problem preparing your codespace, please try again. 2007. As we prove in SectionC1 of the Supplementary Information, even when node mergers that decrease the quality function are excluded, the optimal partition of a set of nodes can still be uncovered. As shown in Fig. For example, nodes in a community in biological or neurological networks are often assumed to share similar functions or behaviour25. Importantly, the output of the local moving stage will depend on the order that the nodes are considered in. Blondel, V. D., Guillaume, J.-L., Lambiotte, R. & Lefebvre, E. Fast unfolding of communities in large networks. Get the most important science stories of the day, free in your inbox. Other networks show an almost tenfold increase in the percentage of disconnected communities. Acad. As can be seen in Fig. A Smart Local Moving Algorithm for Large-Scale Modularity-Based Community Detection. Eur. ISSN 2045-2322 (online). Removing such a node from its old community disconnects the old community. E Stat. As far as I can tell, Leiden seems to essentially be smart local moving with the additional improvements of random moving and Louvain pruning added. E 80, 056117, https://doi.org/10.1103/PhysRevE.80.056117 (2009). 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. 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). Article where nc is the number of nodes in community c. The interpretation of the resolution parameter is quite straightforward. The inspiration for this method of community detection is the optimization of modularity as the algorithm progresses. Complex brain networks: graph theoretical analysis of structural and functional systems. However, the initial partition for the aggregate network is based on P, just like in the Louvain algorithm. The algorithm is run iteratively, using the partition identified in one iteration as starting point for the next iteration. Higher resolutions lead to more communities, while lower resolutions lead to fewer communities. In our experimental analysis, we observe that up to 25% of the communities are badly connected and up to 16% are disconnected. (2) and m is the number of edges. Moreover, when no more nodes can be moved, the algorithm will aggregate the network. Community detection is an important task in the analysis of complex networks. Sci. You are using a browser version with limited support for CSS. However, as increases, the Leiden algorithm starts to outperform the Louvain algorithm. The numerical details of the example can be found in SectionB of the Supplementary Information. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/. 2018. 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. This is similar to ideas proposed recently as pruning16 and in a slightly different form as prioritisation17. Sci. The resolution limit describes a limitation where there is a minimum community size able to be resolved by optimizing modularity (or other related functions). 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. Rev. Rev. Finding and Evaluating Community Structure in Networks. Phys. It means that there are no individual nodes that can be moved to a different community. Performance of modularity maximization in practical contexts. Soft Matter Phys. Traag, V. A. leidenalg 0.7.0. That is, one part of such an internally disconnected community can reach another part only through a path going outside the community. In the local moving phase, individual nodes are moved to the community that yields the largest increase in the quality function. Nature 433, 895900, https://doi.org/10.1038/nature03288 (2005). Luecken, M. D. Application of multi-resolution partitioning of interaction networks to the study of complex disease. Phys. Communities were all of equal size. Louvain algorithm. https://leidenalg.readthedocs.io/en/latest/reference.html. This algorithm provides a number of explicit guarantees. Importantly, the first iteration of the Leiden algorithm is the most computationally intensive one, and subsequent iterations are faster. 8, the Leiden algorithm is significantly faster than the Louvain algorithm also in empirical networks. Speed and quality for the first 10 iterations of the Louvain and the Leiden algorithm for six empirical networks. After a stable iteration of the Leiden algorithm, the algorithm may still be able to make further improvements in later iterations. However, focussing only on disconnected communities masks the more fundamental issue: Louvain finds arbitrarily badly connected communities. The resulting clusters are shown as colors on the 3D model (top) and t -SNE embedding . The Beginner's Guide to Dimensionality Reduction. Value. The algorithm may yield arbitrarily badly connected communities, over and above the well-known issue of the resolution limit14. Note that if Leiden finds subcommunities, splitting up the community is guaranteed to increase modularity. Runtime versus quality for empirical networks. 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). and L.W. 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. However, nodes 16 are still locally optimally assigned, and therefore these nodes will stay in the red community. In the first iteration, Leiden is roughly 220 times faster than Louvain. Detecting communities in a network is therefore an important problem. Both conda and PyPI have leiden clustering in Python which operates via iGraph. PubMedGoogle Scholar. One of the most popular algorithms to optimise modularity is the so-called Louvain algorithm10, named after the location of its authors. Discov. When the Leiden algorithm found that a community could be split into multiple subcommunities, we counted the community as badly connected. 2015. A number of iterations of the Leiden algorithm can be performed before the Louvain algorithm has finished its first iteration. Four popular community detection algorithms are explained . Learn more. Perhaps surprisingly, iterating the algorithm aggravates the problem, even though it does increase the quality function. An overview of the various guarantees is presented in Table1. Even worse, the Amazon network has 5% disconnected communities, but 25% badly connected communities. This will compute the Leiden clusters and add them to the Seurat Object Class. https://doi.org/10.1038/s41598-019-41695-z, DOI: https://doi.org/10.1038/s41598-019-41695-z. 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. 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. This way of defining the expected number of edges is based on the so-called configuration model. Here is some small debugging code I wrote to find this. The constant Potts model (CPM), so called due to the use of a constant value in the Potts model, is an alternative objective function for community detection. Runtime versus quality for benchmark networks. Soft Matter Phys. Communities in Networks. Elect. 81 (4 Pt 2): 046114. http://dx.doi.org/10.1103/PhysRevE.81.046114. The Leiden algorithm is considerably more complex than the Louvain algorithm. CAS Algorithmics 16, 2.1, https://doi.org/10.1145/1963190.1970376 (2011). This problem is different from the well-known issue of the resolution limit of modularity14. You signed in with another tab or window. Clustering the neighborhood graph As with Seurat and many other frameworks, we recommend the Leiden graph-clustering method (community detection based on optimizing modularity) by Traag *et al. We used modularity with a resolution parameter of =1 for the experiments. This is similar to what we have seen for benchmark networks. bioRxiv, https://doi.org/10.1101/208819 (2018). In the first step of the next iteration, Louvain will again move individual nodes in the network. Furthermore, if all communities in a partition are uniformly -dense, the quality of the partition is not too far from optimal, as shown in SectionE of the Supplementary Information. . However, values of within a range of roughly [0.0005, 0.1] all provide reasonable results, thus allowing for some, but not too much randomness. We then created a certain number of edges such that a specified average degree \(\langle k\rangle \) was obtained. http://iopscience.iop.org/article/10.1088/1742-5468/2008/10/P10008/meta. This contrasts to benchmark networks, for which Leiden often converges after a few iterations. B 86 (11): 471. https://doi.org/10.1140/epjb/e2013-40829-0. We now compare how the Leiden and the Louvain algorithm perform for the six empirical networks listed in Table2. We applied the Louvain and the Leiden algorithm to exactly the same networks, using the same seed for the random number generator. Default behaviour is calling cluster_leiden in igraph with Modularity (for undirected graphs) and CPM cost functions. Google Scholar. Clustering is the task of grouping a set of objects with similar characteristics into one bucket and differentiating them from the rest of the group. Newman, M. E. J. Good, B. H., De Montjoye, Y. We conclude that the Leiden algorithm is strongly preferable to the Louvain algorithm. It therefore does not guarantee -connectivity either. The PyPI package leiden-clustering receives a total of 15 downloads a week. Moreover, Louvain has no mechanism for fixing these communities. We can guarantee a number of properties of the partitions found by the Leiden algorithm at various stages of the iterative process. Google Scholar. It only implies that individual nodes are well connected to their community. The problem of disconnected communities has been observed before19,20, also in the context of the label propagation algorithm21. The Leiden algorithm starts from a singleton partition (a). The refined partition \({{\mathscr{P}}}_{{\rm{refined}}}\) is obtained as follows. http://dx.doi.org/10.1073/pnas.0605965104. E 74, 016110, https://doi.org/10.1103/PhysRevE.74.016110 (2006). In the meantime, to ensure continued support, we are displaying the site without styles This amounts to a clustering problem, where we aim to learn an optimal set of groups (communities) from the observed data. 2(b). Technol. We find that the Leiden algorithm commonly finds partitions of higher quality in less time. 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. Nat. We start by initialising a queue with all nodes in the network. Leiden is the most recent major development in this space, and highlighted a flaw in the original Louvain algorithm (Traag, Waltman, and Eck 2018). Finally, we compare the performance of the algorithms on the empirical networks. The quality of such an asymptotically stable partition provides an upper bound on the quality of an optimal partition. We gratefully acknowledge computational facilities provided by the LIACS Data Science Lab Computing Facilities through Frank Takes. We generated networks with n=103 to n=107 nodes. 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. In the local move procedure in the Leiden algorithm, only nodes whose neighborhood . Therefore, clustering algorithms look for similarities or dissimilarities among data points. 2013. 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 \({\mathscr{P}}\). Due to the resolution limit, modularity may cause smaller communities to be clustered into larger communities. These are the same networks that were also studied in an earlier paper introducing the smart local move algorithm15. 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. Internet Explorer). MathSciNet 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. Below we offer an intuitive explanation of these properties. Cluster cells using Louvain/Leiden community detection Description. Based on project statistics from the GitHub repository for the PyPI package leiden-clustering, we found that it has been starred 1 times. In general, Leiden is both faster than Louvain and finds better partitions. This can be a shared nearest neighbours matrix derived from a graph object. Consider the partition shown in (a). The DBLP network is somewhat more challenging, requiring almost 80 iterations on average to reach a stable iteration. See the documentation on the leidenalg Python module for more information: https://leidenalg.readthedocs.io/en/latest/reference.html. Once aggregation is complete we restart the local moving phase, and continue to iterate until everything converges down to one node. 2008. The increase in the percentage of disconnected communities is relatively limited for the Live Journal and Web of Science networks. We will use sklearns K-Means implementation looking for 10 clusters in the original 784 dimensional data. Communities in \({\mathscr{P}}\) may be split into multiple subcommunities in \({{\mathscr{P}}}_{{\rm{refined}}}\). Eng. E 81, 046106, https://doi.org/10.1103/PhysRevE.81.046106 (2010). Leiden is both faster than Louvain and finds better partitions. Klavans, R. & Boyack, K. W. Which Type of Citation Analysis Generates the Most Accurate Taxonomy of Scientific and Technical Knowledge? In this stage we essentially collapse communities down into a single representative node, creating a new simplified graph. Acad. J. Comput. The idea of the refinement phase in the Leiden algorithm is to identify a partition \({{\mathscr{P}}}_{{\rm{refined}}}\) that is a refinement of \({\mathscr{P}}\). 2 represent stronger connections, while the other edges represent weaker connections. In the case of modularity, communities may have significant substructure both because of the resolution limit and because of the shortcomings of Louvain. The algorithm continues to move nodes in the rest of the network. For the results reported below, the average degree was set to \(\langle k\rangle =10\). This is because Louvain only moves individual nodes at a time. 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 Louvain algorithm is illustrated in Fig. This package implements the Leiden algorithm in C++ and exposes it to python.It relies on (python-)igraph for it to function. (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. In this post, I will cover one of the common approaches which is hierarchical clustering. Provided by the Springer Nature SharedIt content-sharing initiative. An aggregate. Ozaki, N., Tezuka, H. & Inaba, M. A Simple Acceleration Method for the Louvain Algorithm. Newman, M. E. J. V. A. Traag. When node 0 is moved to a different community, the red community becomes internally disconnected, as shown in (b). On the other hand, Leiden keeps finding better partitions, especially for higher values of , for which it is more difficult to identify good partitions. Phys. Soft Matter Phys. The solution provided by Leiden is based on the smart local moving algorithm. At some point, node 0 is considered for moving. 92 (3): 032801. http://dx.doi.org/10.1103/PhysRevE.92.032801. Please The property of -separation is also guaranteed by the Louvain algorithm. Weights for edges an also be passed to the leiden algorithm either as a separate vector or weights or a weighted adjacency matrix. 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. For each set of parameters, we repeated the experiment 10 times. 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. The value of the resolution parameter was determined based on the so-called mixing parameter 13. By moving these nodes, Louvain creates badly connected communities. J. Assoc. The Leiden algorithm is considerably more complex than the Louvain algorithm. Nodes 13 should form a community and nodes 46 should form another community. Clustering is a machine learning technique in which similar data points are grouped into the same cluster based on their attributes. J. Stat. At some point, the Louvain algorithm may end up in the community structure shown in Fig. In fact, for the Web of Science and Web UK networks, Fig. Article Graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. Rev. http://arxiv.org/abs/1810.08473. It identifies the clusters by calculating the densities of the cells. We use six empirical networks in our analysis. Phys. E 70, 066111, https://doi.org/10.1103/PhysRevE.70.066111 (2004). Crucially, however, the percentage of badly connected communities decreases with each iteration of the Leiden algorithm. Sign up for the Nature Briefing newsletter what matters in science, free to your inbox daily. conda install -c conda-forge leidenalg pip install leiden-clustering Used via. 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. To install the development version: The current release on CRAN can be installed with: First set up a compatible adjacency matrix: An adjacency matrix is any binary matrix representing links between nodes (column and row names). The minimum resolvable community size depends on the total size of the network and the degree of interconnectedness of the modules. 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. USA 104, 36, https://doi.org/10.1073/pnas.0605965104 (2007). Use the Previous and Next buttons to navigate the slides or the slide controller buttons at the end to navigate through each slide. CAS For a full specification of the fast local move procedure, we refer to the pseudo-code of the Leiden algorithm in AlgorithmA.2 in SectionA of the Supplementary Information. ADS The algorithm moves individual nodes from one community to another to find a partition (b), which is then refined (c). Class wrapper based on scanpy to use the Leiden algorithm to directly cluster your data matrix with a scikit-learn flavor. Centre for Science and Technology Studies, Leiden University, Leiden, The Netherlands, You can also search for this author in J. Exp. This represents the following graph structure. leiden_clustering Description Class wrapper based on scanpy to use the Leiden algorithm to directly cluster your data matrix with a scikit-learn flavor. This commit does not belong to any branch on this repository, and may belong to a fork outside of the repository. https://doi.org/10.1038/s41598-019-41695-z. This will compute the Leiden clusters and add them to the Seurat Object Class. Introduction The Louvain method is an algorithm to detect communities in large networks. 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 84, 016114, https://doi.org/10.1103/PhysRevE.84.016114 (2011). E 78, 046110, https://doi.org/10.1103/PhysRevE.78.046110 (2008). In this new situation, nodes 2, 3, 5 and 6 have only internal connections. 4, in the first iteration of the Louvain algorithm, the percentage of badly connected communities can be quite high. It is a directed graph if the adjacency matrix is not symmetric. The community with which a node is merged is selected randomly18. It maximizes a modularity score for each community, where the modularity quantifies the quality of an assignment of nodes to communities. J. The Leiden community detection algorithm outperforms other clustering methods. Rotta, R. & Noack, A. Multilevel local search algorithms for modularity clustering. These nodes can be approximately identified based on whether neighbouring nodes have changed communities. Subpartition -density does not imply that individual nodes are locally optimally assigned.

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