leiden clustering explained leiden clustering explained

We applied the Louvain and the Leiden algorithm to exactly the same networks, using the same seed for the random number generator. In addition, to analyse whether a community is badly connected, we ran the Leiden algorithm on the subnetwork consisting of all nodes belonging to the community. bioRxiv, https://doi.org/10.1101/208819 (2018). In the fast local move procedure in the Leiden algorithm, only nodes whose neighbourhood has changed are visited. We here introduce the Leiden algorithm, which guarantees that communities are well connected. Guimer, R. & Nunes Amaral, L. A. Functional cartography of complex metabolic networks. In an experiment containing a mixture of cell types, each cluster might correspond to a different cell type. One of the most widely used algorithms is the Louvain algorithm10, which is reported to be among the fastest and best performing community detection algorithms11,12. Use Git or checkout with SVN using the web URL. E 70, 066111, https://doi.org/10.1103/PhysRevE.70.066111 (2004). Soc. Nonlin. GitHub on Feb 15, 2020 Do you think the performance improvements will also be implemented in leidenalg? Preprocessing and clustering 3k PBMCs Scanpy documentation Nonlin. In particular, we show that Louvain may identify communities that are internally disconnected. From Louvain to Leiden: guaranteeing well-connected communities, $$ {\mathcal H} =\frac{1}{2m}\,{\sum }_{c}({e}_{c}-{\rm{\gamma }}\frac{{K}_{c}^{2}}{2m}),$$, $$ {\mathcal H} ={\sum }_{c}[{e}_{c}-\gamma (\begin{array}{c}{n}_{c}\\ 2\end{array})],$$, https://doi.org/10.1038/s41598-019-41695-z. The new algorithm integrates several earlier improvements, incorporating a combination of smart local move15, fast local move16,17 and random neighbour move18. Bullmore, E. & Sporns, O. In the first step of the next iteration, Louvain will again move individual nodes in the network. Louvain has two phases: local moving and aggregation. Two ways of doing this are graph modularity (Newman and Girvan 2004) and the constant Potts model (Ronhovde and Nussinov 2010). As shown in Fig. However, modularity suffers from a difficult problem known as the resolution limit (Fortunato and Barthlemy 2007). We find that the Leiden algorithm is faster than the Louvain algorithm and uncovers better partitions, in addition to providing explicit guarantees. Louvain method - Wikipedia However, the initial partition for the aggregate network is based on P, just like in the Louvain algorithm. The difference in computational time is especially pronounced for larger networks, with Leiden being up to 20 times faster than Louvain in empirical networks. * (2018). In practice, this means that small clusters can hide inside larger clusters, making their identification difficult. When node 0 is moved to a different community, the red community becomes internally disconnected, as shown in (b). Moreover, when no more nodes can be moved, the algorithm will aggregate the network. The algorithm optimises a quality function such as modularity or CPM in two elementary phases: (1) local moving of nodes; and (2) aggregation of the network. Electr. 2015. MathSciNet This is very similar to what the smart local moving algorithm does. CPM is defined as. Modularity is used most commonly, but is subject to the resolution limit. One of the best-known methods for community detection is called modularity3. The Leiden algorithm provides several guarantees. In the Louvain algorithm, a node may be moved to a different community while it may have acted as a bridge between different components of its old 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. In this post, I will cover one of the common approaches which is hierarchical clustering. Theory Exp. To elucidate the problem, we consider the example illustrated in Fig. The algorithm moves individual nodes from one community to another to find a partition (b), which is then refined (c). The solution proposed in smart local moving is to alter how the local moving step in Louvain works. Louvain can also be quite slow, as it spends a lot of time revisiting nodes that may not have changed neighborhoods. This continues until the queue is empty. After a stable iteration of the Leiden algorithm, the algorithm may still be able to make further improvements in later iterations. By creating the aggregate network based on \({{\mathscr{P}}}_{{\rm{refined}}}\) rather than P, the Leiden algorithm has more room for identifying high-quality partitions. In contrast, Leiden keeps finding better partitions in each iteration. Soft Matter Phys. Louvain algorithm. Phys. Not. We therefore require a more principled solution, which we will introduce in the next section. Clustering with the Leiden Algorithm in R Leiden is the most recent major development in this space, and highlighted a flaw in the original Louvain algorithm (Traag, Waltman, and Eck 2018). 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. The quality improvement realised by the Leiden algorithm relative to the Louvain algorithm is larger for empirical networks than for benchmark networks. The algorithm moves individual nodes from one community to another to find a partition (b), which is then refined (c). In that case, nodes 16 are all locally optimally assigned, despite the fact that their community has become disconnected. Importantly, the first iteration of the Leiden algorithm is the most computationally intensive one, and subsequent iterations are faster. At each iteration all clusters are guaranteed to be connected and well-separated. When a disconnected community has become a node in an aggregate network, there are no more possibilities to split up the community. Other networks show an almost tenfold increase in the percentage of disconnected communities. As can be seen in Fig. Finding and Evaluating Community Structure in Networks. Phys. 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. The resolution limit describes a limitation where there is a minimum community size able to be resolved by optimizing modularity (or other related functions). In this new situation, nodes 2, 3, 5 and 6 have only internal connections. For larger networks and higher values of , Louvain is much slower than Leiden. Importantly, mergers are performed only within each community of the partition \({\mathscr{P}}\). 2004. Conversely, if Leiden does not find subcommunities, there is no guarantee that modularity cannot be increased by splitting up the community. Node mergers that cause the quality function to decrease are not considered. Traag, V. A., Van Dooren, P. & Nesterov, Y. The phase one loop can be greatly accelerated by finding the nodes that have the potential to change community and only revisit those nodes. Speed and quality of the Louvain and the Leiden algorithm for benchmark networks of increasing size (two iterations). Subset optimality is the strongest guarantee that is provided by the Leiden algorithm. 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). (We implemented both algorithms in Java, available from https://github.com/CWTSLeiden/networkanalysis and deposited at Zenodo23. Cluster Determination FindClusters Seurat - Satija Lab Hence, the Leiden algorithm effectively addresses the problem of badly connected communities. However, if communities are badly connected, this may lead to incorrect attributions of shared functionality. Complex brain networks: graph theoretical analysis of structural and functional systems. Knowl. This amounts to a clustering problem, where we aim to learn an optimal set of groups (communities) from the observed data. Hence, the problem of Louvain outlined above is independent from the issue of the resolution limit. Segmentation & Clustering SPATA2 - GitHub Pages Hence, the community remains disconnected, unless it is merged with another community that happens to act as a bridge. To address this important shortcoming, we introduce a new algorithm that is faster, finds better partitions and provides explicit guarantees and bounds. 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). Finally, we demonstrate the excellent performance of the algorithm for several benchmark and real-world networks. Sci. Duch, J. Inf. Is modularity with a resolution parameter equivalent to leidenalg.RBConfigurationVertexPartition? An alternative quality function is the Constant Potts Model (CPM)13, which overcomes some limitations of modularity. The Louvain algorithm is illustrated in Fig. The horizontal axis indicates the cumulative time taken to obtain the quality indicated on the vertical axis. Moreover, when the algorithm is applied iteratively, it converges to a partition in which all subsets of all communities are guaranteed to be locally optimally assigned. Finding communities in large networks is far from trivial: algorithms need to be fast, but they also need to provide high-quality results. The triumphs and limitations of computational methods for - Nature Communities may even be internally disconnected. We name our algorithm the Leiden algorithm, after the location of its authors. Traag, V.A., Waltman, L. & van Eck, N.J. From Louvain to Leiden: guaranteeing well-connected communities. Rather than progress straight to the aggregation stage (as we would for the original Louvain), we next consider each community as a new sub-network and re-apply the local moving step within each community. Nat. 4. After a stable iteration of the Leiden algorithm, it is guaranteed that: All nodes are locally optimally assigned. Such a modular structure is usually not known beforehand. See the documentation for these functions. The numerical details of the example can be found in SectionB of the Supplementary Information. 4, in the first iteration of the Louvain algorithm, the percentage of badly connected communities can be quite high. Weights for edges an also be passed to the leiden algorithm either as a separate vector or weights or a weighted adjacency matrix. It implies uniform -density and all the other above-mentioned properties. Google Scholar. It partitions the data space and identifies the sub-spaces using the Apriori principle. Both conda and PyPI have leiden clustering in Python which operates via iGraph. It only implies that individual nodes are well connected to their community. MathSciNet http://iopscience.iop.org/article/10.1088/1742-5468/2008/10/P10008/meta. Anyone you share the following link with will be able to read this content: Sorry, a shareable link is not currently available for this article. Soft Matter Phys. Louvain keeps visiting all nodes in a network until there are no more node movements that increase the quality function. On the other hand, Leiden keeps finding better partitions, especially for higher values of , for which it is more difficult to identify good partitions. Number of iterations before the Leiden algorithm has reached a stable iteration for six empirical networks. To overcome the problem of arbitrarily badly connected communities, we introduced a new algorithm, which we refer to as the Leiden algorithm. Article That is, no subset can be moved to a different community. The algorithm then moves individual nodes in the aggregate network (e). The algorithm moves individual nodes from one community to another to find a partition (b). In the meantime, to ensure continued support, we are displaying the site without styles 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. A score of -1 means that there are no edges connecting nodes within the community, and they instead all connect nodes outside the community. In the case of the Louvain algorithm, after a stable iteration, all subsequent iterations will be stable as well. Instead, a node may be merged with any community for which the quality function increases. 6 show that Leiden outperforms Louvain in terms of both computational time and quality of the partitions. Google Scholar. What is Clustering and Different Types of Clustering Methods Provided by the Springer Nature SharedIt content-sharing initiative. 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. These steps are repeated until no further improvements can be made. Am. 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. Phys. For each set of parameters, we repeated the experiment 10 times. Faster Unfolding of Communities: Speeding up the Louvain Algorithm. Phys. Rev. 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. Fortunato, Santo, and Marc Barthlemy. Agglomerative clustering is a bottom-up approach. In our experimental analysis, we observe that up to 25% of the communities are badly connected and up to 16% are disconnected. By moving these nodes, Louvain creates badly connected communities. Initially, \({{\mathscr{P}}}_{{\rm{refined}}}\) is set to a singleton partition, in which each node is in its own community. (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. Fortunato, S. Community detection in graphs. In this way, Leiden implements the local moving phase more efficiently than Louvain. 68, 984998, https://doi.org/10.1002/asi.23734 (2017). Neurosci. As we will demonstrate in our experimental analysis, the problem occurs frequently in practice when using the Louvain algorithm. DBSCAN Clustering Explained. Detailed theorotical explanation and 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. In this case we know the answer is exactly 10. Acad. We use six empirical networks in our analysis. You are using a browser version with limited support for CSS. & Clauset, A. 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 Rev. Unsupervised clustering of cells is a common step in many single-cell expression workflows. To find an optimal grouping of cells into communities, we need some way of evaluating different partitions in the graph. 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. That is, one part of such an internally disconnected community can reach another part only through a path going outside the community. 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. Figure3 provides an illustration of the algorithm. Modularity is given by. 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. volume9, Articlenumber:5233 (2019) Int. Leiden keeps finding better partitions for empirical networks also after the first 10 iterations of the algorithm. 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. 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). The community with which a node is merged is selected randomly18. the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Resolution Limit in Community Detection. Proc. Here we can see partitions in the plotted results. Leiden consists of the following steps: The refinement step allows badly connected communities to be split before creating the aggregate network. 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. Nature 433, 895900, https://doi.org/10.1038/nature03288 (2005). 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 inspiration for this method of community detection is the optimization of modularity as the algorithm progresses. 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. E 78, 046110, https://doi.org/10.1103/PhysRevE.78.046110 (2008). However, so far this problem has never been studied for the Louvain algorithm. This is not too difficult to explain. Google Scholar. As such, we scored leiden-clustering popularity level to be Limited. GitHub - vtraag/leidenalg: Implementation of the Leiden algorithm for In this stage we essentially collapse communities down into a single representative node, creating a new simplified graph. How to get started with louvain/leiden algorithm with UMAP in R Raghavan, U., Albert, R. & Kumara, S. Near linear time algorithm to detect community structures in large-scale networks. The algorithm continues to move nodes in the rest of the network. cluster_cells: Cluster cells using Louvain/Leiden community detection Waltman, L. & van Eck, N. J. The algorithm then moves individual nodes in the aggregate network (d). We start by initialising a queue with all nodes in the network. We generated networks with n=103 to n=107 nodes. Google Scholar. Starting from the second iteration, Leiden outperformed Louvain in terms of the percentage of badly connected communities. The Leiden algorithm is typically iterated: the output of one iteration is used as the input for the next iteration. 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 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. ADS These nodes are therefore optimally assigned to their current community. This is similar to ideas proposed recently as pruning16 and in a slightly different form as prioritisation17. Phys. This contrasts with the Leiden algorithm. 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. igraph R manual pages Again, if communities are badly connected, this may lead to incorrect inferences of topics, which will affect bibliometric analyses relying on the inferred topics. In fact, for the Web of Science and Web UK networks, Fig. Rev. Runtime versus quality for empirical networks. 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. Phys. leiden: Run Leiden clustering algorithm in leiden: R Implementation of Four popular community detection algorithms are explained . Excluding node mergers that decrease the quality function makes the refinement phase more efficient. Traag, V. A., Waltman, L. & van Eck, N. J. networkanalysis. 2018. To address this problem, we introduce the Leiden algorithm. The refined partition \({{\mathscr{P}}}_{{\rm{refined}}}\) is obtained as follows. We thank Lovro Subelj for his comments on an earlier version of this paper. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate. In many complex networks, nodes cluster and form relatively dense groupsoften called communities1,2. A new methodology for constructing a publication-level classification system of science. Then the Leiden algorithm can be run on the adjacency matrix. Note that the object for Seurat version 3 has changed. First iteration runtime for empirical networks. Narrow scope for resolution-limit-free community detection. Local Resolution-Limit-Free Potts Model for Community Detection. Phys. Are you sure you want to create this branch? Traag, V. A. 2016. Higher resolutions lead to more communities, while lower resolutions lead to fewer communities. 10, for the IMDB and Amazon networks, Leiden reaches a stable iteration relatively quickly, presumably because these networks have a fairly simple community structure. Get the most important science stories of the day, free in your inbox. The PyPI package leiden-clustering receives a total of 15 downloads a week. 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. Scientific Reports (Sci Rep) modularity) increases. Clustering algorithms look for similarities or dissimilarities among data points so that similar ones can be grouped together. 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. Agglomerative Clustering: Also known as bottom-up approach or hierarchical agglomerative clustering (HAC). & Arenas, A. Each community in this partition becomes a node in the aggregate network. ISSN 2045-2322 (online). In particular, benchmark networks have a rather simple structure. Class wrapper based on scanpy to use the Leiden algorithm to directly cluster your data matrix with a scikit-learn flavor. Phys. It means that there are no individual nodes that can be moved to a different community. Below, the quality of a partition is reported as \(\frac{ {\mathcal H} }{2m}\), where H is defined in Eq. There was a problem preparing your codespace, please try again. 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. Knowl. PubMed More subtle problems may occur as well, causing Louvain to find communities that are connected, but only in a very weak sense. 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. & Girvan, M. Finding and evaluating community structure in networks. All communities are subpartition -dense.