leiden clustering explained

Performance of modularity maximization in practical contexts. Clearly, it would be better to split up the community. Leiden keeps finding better partitions for empirical networks also after the first 10 iterations of the algorithm. The aggregate network is created based on the partition \({{\mathscr{P}}}_{{\rm{refined}}}\). J. Article We also suggested that the Leiden algorithm is faster than the Louvain algorithm, because of the fast local move approach. It only implies that individual nodes are well connected to their community. See the documentation for these functions. The R implementation of Leiden can be run directly on the snn igraph object in Seurat. 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. Note that the object for Seurat version 3 has changed. See the documentation on the leidenalg Python module for more information: https://leidenalg.readthedocs.io/en/latest/reference.html. Cluster your data matrix with the Leiden algorithm. 8, the Leiden algorithm is significantly faster than the Louvain algorithm also in empirical networks. In this case we know the answer is exactly 10. The R implementation of Leiden can be run directly on the snn igraph object in Seurat. The corresponding results are presented in the Supplementary Fig. 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. A Simple Acceleration Method for the Louvain Algorithm. Int. 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. A community is subset optimal if all subsets of the community are locally optimally assigned. U. S. A. Eng. N.J.v.E. In general, Leiden is both faster than Louvain and finds better partitions. Elect. Louvain can also be quite slow, as it spends a lot of time revisiting nodes that may not have changed neighborhoods. An alternative quality function is the Constant Potts Model (CPM)13, which overcomes some limitations of modularity. Note that if Leiden finds subcommunities, splitting up the community is guaranteed to increase modularity. As the problem of modularity optimization is NP-hard, we need heuristic methods to optimize modularity (or CPM). As can be seen in Fig. Wolf, F. A. et al. & Moore, C. Finding community structure in very large networks. For each network, Table2 reports the maximal modularity obtained using the Louvain and the Leiden algorithm. This can be a shared nearest neighbours matrix derived from a graph object. ACM Trans. (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. Are you sure you want to create this branch? We used modularity with a resolution parameter of =1 for the experiments. 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. Agglomerative clustering is a bottom-up approach. 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 This method tries to maximise the difference between the actual number of edges in a community and the expected number of such edges. to use Codespaces. & Bornholdt, S. Statistical mechanics of community detection. Phys. 2016. 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. Leiden is the most recent major development in this space, and highlighted a flaw in the original Louvain algorithm (Traag, Waltman, and Eck 2018). Hence, for lower values of , the difference in quality is negligible. 1 and summarised in pseudo-code in AlgorithmA.1 in SectionA of the Supplementary Information. To ensure readability of the paper to the broadest possible audience, we have chosen to relegate all technical details to the Supplementary Information. The algorithm may yield arbitrarily badly connected communities, over and above the well-known issue of the resolution limit14. Article Many Git commands accept both tag and branch names, so creating this branch may cause unexpected behavior. Directed Undirected Homogeneous Heterogeneous Weighted 1. The Leiden community detection algorithm outperforms other clustering methods. 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. Number of iterations until stability. & Girvan, M. Finding and evaluating community structure in networks. The leidenalg package facilitates community detection of networks and builds on the package igraph. J. E 81, 046106, https://doi.org/10.1103/PhysRevE.81.046106 (2010). Each point corresponds to a certain iteration of an algorithm, with results averaged over 10 experiments. V.A.T. The Web of Science network is the most difficult one. Instead, a node may be merged with any community for which the quality function increases. Soft Matter Phys. For those wanting to read more, I highly recommend starting with the Leiden paper (Traag, Waltman, and Eck 2018) or the smart local moving paper (Waltman and Eck 2013). The parameter functions as a sort of threshold: communities should have a density of at least , while the density between communities should be lower than . The algorithm moves individual nodes from one community to another to find a partition (b). 5, for lower values of the partition is well defined, and neither the Louvain nor the Leiden algorithm has a problem in determining the correct partition in only two iterations. 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. Local Resolution-Limit-Free Potts Model for Community Detection. Phys. However, the Louvain algorithm does not consider this possibility, since it considers only individual node movements. Nodes 16 have connections only within this community, whereas node 0 also has many external connections. 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. Finally, we demonstrate the excellent performance of the algorithm for several benchmark and real-world networks. Subset optimality is the strongest guarantee that is provided by the Leiden algorithm. Basically, there are two types of hierarchical cluster analysis strategies - 1. We keep removing nodes from the front of the queue, possibly moving these nodes to a different community. Speed of the first iteration of the Louvain and the Leiden algorithm for benchmark networks with increasingly difficult partitions (n=107). In that case, some optimal partitions cannot be found, as we show in SectionC2 of the Supplementary Information. The inspiration for this method of community detection is the optimization of modularity as the algorithm progresses. The idea of the refinement phase in the Leiden algorithm is to identify a partition \({{\mathscr{P}}}_{{\rm{refined}}}\) that is a refinement of \({\mathscr{P}}\). The problem of disconnected communities has been observed before19,20, also in the context of the label propagation algorithm21. 2010. reviewed the manuscript. 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. It means that there are no individual nodes that can be moved to a different community. Finally, we compare the performance of the algorithms on the empirical networks. Community detection is an important task in the analysis of complex networks. The authors act as bibliometric consultants to CWTS B.V., which makes use of community detection algorithms in commercial products and services. As can be seen in Fig. However, as shown in this paper, the Louvain algorithm has a major shortcoming: the algorithm yields communities that may be arbitrarily badly connected. 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. Speed of the first iteration of the Louvain and the Leiden algorithm for six empirical networks. 2004. 63, 23782392, https://doi.org/10.1002/asi.22748 (2012). Zenodo, https://doi.org/10.5281/zenodo.1469357 https://github.com/vtraag/leidenalg. Google Scholar. It identifies the clusters by calculating the densities of the cells. 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. This is not too difficult to explain. Bae, S., Halperin, D., West, J. D., Rosvall, M. & Howe, B. Scalable and Efficient Flow-Based Community Detection for Large-Scale Graph Analysis. This problem is different from the well-known issue of the resolution limit of modularity14. Faster Unfolding of Communities: Speeding up the Louvain Algorithm. Phys. Rep. 6, 30750, https://doi.org/10.1038/srep30750 (2016). On the other hand, Leiden keeps finding better partitions, especially for higher values of , for which it is more difficult to identify good partitions. The fast local move procedure can be summarised as follows. Google Scholar. Random moving is a very simple adjustment to Louvain local moving proposed in 2015 (Traag 2015). Figure6 presents total runtime versus quality for all iterations of the Louvain and the Leiden algorithm. http://arxiv.org/abs/1810.08473. Here we can see partitions in the plotted results. Electr. Soc. Rev. As discussed earlier, the Louvain algorithm does not guarantee connectivity. The 'devtools' package will be used to install 'leiden' and the dependancies (igraph and reticulate). This will compute the Leiden clusters and add them to the Seurat Object Class. It is good at identifying small clusters. However, focussing only on disconnected communities masks the more fundamental issue: Louvain finds arbitrarily badly connected communities. 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. Table2 provides an overview of the six networks. In the Louvain algorithm, an aggregate network is created based on the partition \({\mathscr{P}}\) resulting from the local moving phase. Phys. MATH J. Comput. Communities were all of equal size. 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. & Arenas, A. 2.3. wrote the manuscript. Eur. Rev. Random moving can result in some huge speedups, since Louvain spends about 95% of its time computing the modularity gain from moving nodes. 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. However, if communities are badly connected, this may lead to incorrect attributions of shared functionality. The increase in the percentage of disconnected communities is relatively limited for the Live Journal and Web of Science networks. SPATA2 currently offers the functions findSeuratClusters (), findMonocleClusters () and findNearestNeighbourClusters () which are wrapper around widely used clustering algorithms. Traag, V.A., Waltman, L. & van Eck, N.J. From Louvain to Leiden: guaranteeing well-connected communities. Subpartition -density is not guaranteed by the Louvain algorithm. The Leiden algorithm is clearly faster than the Louvain algorithm. We use six empirical networks in our analysis. Importantly, the output of the local moving stage will depend on the order that the nodes are considered in. If nothing happens, download GitHub Desktop and try again. 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. MATH In a stable iteration, the partition is guaranteed to be node optimal and subpartition -dense. and JavaScript. Rev. We find that the Leiden algorithm commonly finds partitions of higher quality in less time. ADS Clustering algorithms look for similarities or dissimilarities among data points so that similar ones can be grouped together. J. Assoc. 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. Even worse, the Amazon network has 5% disconnected communities, but 25% badly connected communities. Agglomerative Clustering: Also known as bottom-up approach or hierarchical agglomerative clustering (HAC). Then, in order . 2. Ph.D. thesis, (University of Oxford, 2016). Phys. http://iopscience.iop.org/article/10.1088/1742-5468/2008/10/P10008/meta. 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. For example, nodes in a community in biological or neurological networks are often assumed to share similar functions or behaviour25. Figure3 provides an illustration of the algorithm. E 74, 036104, https://doi.org/10.1103/PhysRevE.74.036104 (2006). 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. 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. As can be seen in Fig. However, nodes 16 are still locally optimally assigned, and therefore these nodes will stay in the red community. AMS 56, 10821097 (2009). The count of badly connected communities also included disconnected communities. The speed difference is especially large for larger networks. This may have serious consequences for analyses based on the resulting partitions. Nonetheless, some networks still show large differences. 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. The horizontal axis indicates the cumulative time taken to obtain the quality indicated on the vertical axis. 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. Both conda and PyPI have leiden clustering in Python which operates via iGraph. From Louvain to Leiden: Guaranteeing Well-Connected Communities, October. The Louvain algorithm guarantees that modularity cannot be increased by merging communities (it finds a locally optimal solution). When iterating Louvain, the quality of the partitions will keep increasing until the algorithm is unable to make any further improvements. 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. That is, one part of such an internally disconnected community can reach another part only through a path going outside the community. In other words, modularity may hide smaller communities and may yield communities containing significant substructure. Communities may even be internally disconnected. We now compare how the Leiden and the Louvain algorithm perform for the six empirical networks listed in Table2. 2007. Such algorithms are rather slow, making them ineffective for large networks. After the first iteration of the Louvain algorithm, some partition has been obtained. For the Amazon and IMDB networks, the first iteration of the Leiden algorithm is only about 1.6 times faster than the first iteration of the Louvain algorithm. However, it is also possible to start the algorithm from a different partition15. 2018. Article ADS & Fortunato, S. Community detection algorithms: A comparative analysis. 92 (3): 032801. http://dx.doi.org/10.1103/PhysRevE.92.032801. Phys. Rev. B 86 (11): 471. https://doi.org/10.1140/epjb/e2013-40829-0. Modularity is given by. In the case of the Louvain algorithm, after a stable iteration, all subsequent iterations will be stable as well. Value. Moreover, the deeper significance of the problem was not recognised: disconnected communities are merely the most extreme manifestation of the problem of arbitrarily badly connected communities. In doing so, Louvain keeps visiting nodes that cannot be moved to a different community. On the other hand, after node 0 has been moved to a different community, nodes 1 and 4 have not only internal but also external connections. Use the Previous and Next buttons to navigate the slides or the slide controller buttons at the end to navigate through each slide. These steps are repeated until no further improvements can be made. 10, 186198, https://doi.org/10.1038/nrn2575 (2009). In short, the problem of badly connected communities has important practical consequences. Higher resolutions lead to more communities and lower resolutions lead to fewer communities, similarly to the resolution parameter for modularity. Leiden consists of the following steps: The refinement step allows badly connected communities to be split before creating the aggregate network. 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. We now show that the Louvain algorithm may find arbitrarily badly connected communities. The Leiden algorithm is considerably more complex than the Louvain algorithm. The Leiden algorithm is typically iterated: the output of one iteration is used as the input for the next iteration. Modularity is used most commonly, but is subject to the resolution limit. In fact, by implementing the refinement phase in the right way, several attractive guarantees can be given for partitions produced by the Leiden algorithm. CAS 9 shows that more than 10 iterations of the Leiden algorithm can be performed before the Louvain algorithm has finished its first iteration. Scaling of benchmark results for network size. 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. Google Scholar. 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. leiden_clustering Description Class wrapper based on scanpy to use the Leiden algorithm to directly cluster your data matrix with a scikit-learn flavor. USA 104, 36, https://doi.org/10.1073/pnas.0605965104 (2007). bioRxiv, https://doi.org/10.1101/208819 (2018). Louvain has two phases: local moving and aggregation. sign in 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. 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. 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. This contrasts with the Leiden algorithm. CAS Fortunato, Santo, and Marc Barthlemy. Phys. 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. It was found to be one of the fastest and best performing algorithms in comparative analyses11,12, and it is one of the most-cited works in the community detection literature. ADS 2008. 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. Subpartition -density does not imply that individual nodes are locally optimally assigned. The Leiden algorithm provides several guarantees. E 80, 056117, https://doi.org/10.1103/PhysRevE.80.056117 (2009). The algorithm then moves individual nodes in the aggregate network (e). If nothing happens, download Xcode and try again. In fact, if we keep iterating the Leiden algorithm, it will converge to a partition without any badly connected communities, as discussed earlier. This continues until the queue is empty. In this new situation, nodes 2, 3, 5 and 6 have only internal connections. Initially, \({{\mathscr{P}}}_{{\rm{refined}}}\) is set to a singleton partition, in which each node is in its own community. Analyses based on benchmark networks have only a limited value because these networks are not representative of empirical real-world networks. Sci. The Louvain algorithm is illustrated in Fig. Other networks show an almost tenfold increase in the percentage of disconnected communities. This contrasts with optimisation algorithms such as simulated annealing, which do allow the quality function to decrease4,8. The corresponding results are presented in the Supplementary Fig. Furthermore, by relying on a fast local move approach, the Leiden algorithm runs faster than the Louvain algorithm. Louvain community detection algorithm was originally proposed in 2008 as a fast community unfolding method for large networks. 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). Leiden is faster than Louvain especially for larger networks. PubMed Central Hence, the problem of Louvain outlined above is independent from the issue of the resolution limit. Phys. 69 (2 Pt 2): 026113. http://dx.doi.org/10.1103/PhysRevE.69.026113. In fact, although it may seem that the Louvain algorithm does a good job at finding high quality partitions, in its standard form the algorithm provides only one guarantee: the algorithm yields partitions for which it is guaranteed that no communities can be merged. First calculate k-nearest neighbors and construct the SNN graph. Powered by DataCamp DataCamp The resolution limit describes a limitation where there is a minimum community size able to be resolved by optimizing modularity (or other related functions). However, for higher values of , Leiden becomes orders of magnitude faster than Louvain, reaching 10100 times faster runtimes for the largest networks. It was originally developed for modularity optimization, although the same method can be applied to optimize CPM. As we will demonstrate in our experimental analysis, the problem occurs frequently in practice when using the Louvain algorithm. Nonlin. This enables us to find cases where its beneficial to split a community. This should be the first preference when choosing an algorithm. Each community in this partition becomes a node in the aggregate network. Article 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. Note that this code is . The authors show that the total computational time for Louvain depends a lot on the number of phase one loops (loops during the first local moving stage). 68, 984998, https://doi.org/10.1002/asi.23734 (2017). Google Scholar. Am. 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. For the Amazon, DBLP and Web UK networks, Louvain yields on average respectively 23%, 16% and 14% badly connected communities. volume9, Articlenumber:5233 (2019) In this stage we essentially collapse communities down into a single representative node, creating a new simplified graph. Moreover, Louvain has no mechanism for fixing these communities. and L.W. We study the problem of badly connected communities when using the Louvain algorithm for several empirical networks. Networks with high modularity have dense connections between the nodes within modules but sparse connections between nodes in different modules. It does not guarantee that modularity cant be increased by moving nodes between communities. Speed and quality for the first 10 iterations of the Louvain and the Leiden algorithm for benchmark networks (n=106 and n=107). Weights for edges an also be passed to the leiden algorithm either as a separate vector or weights or a weighted adjacency matrix. Google Scholar. This makes sense, because after phase one the total size of the graph should be significantly reduced. We first applied the Scanpy pipeline, including its clustering method (Leiden clustering), on the PBMC dataset. A number of iterations of the Leiden algorithm can be performed before the Louvain algorithm has finished its first iteration. Our analysis is based on modularity with resolution parameter =1. . This is similar to what we have seen for benchmark networks. 8 (3): 207. https://pdfs.semanticscholar.org/4ea9/74f0fadb57a0b1ec35cbc5b3eb28e9b966d8.pdf. Community detection is often used to understand the structure of large and complex networks. The thick edges in Fig. partition_type : Optional [ Type [ MutableVertexPartition ]] (default: None) Type of partition to use. Theory Exp. Additionally, we implemented a Python package, available from https://github.com/vtraag/leidenalg and deposited at Zenodo24). Brandes, U. et al. A. In particular, benchmark networks have a rather simple structure. E 69, 026113, https://doi.org/10.1103/PhysRevE.69.026113 (2004). 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 Leiden is both faster than Louvain and finds better partitions. Sci. For empirical networks, it may take quite some time before the Leiden algorithm reaches its first stable iteration. Randomness in the selection of a community allows the partition space to be explored more broadly. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/. 7, whereas Louvain becomes much slower for more difficult partitions, Leiden is much less affected by the difficulty of the partition. 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 \({\mathscr{P}}\). All authors conceived the algorithm and contributed to the source code. For example, for the Web of Science network, the first iteration takes about 110120 seconds, while subsequent iterations require about 40 seconds. We generated benchmark networks in the following way. E 70, 066111, https://doi.org/10.1103/PhysRevE.70.066111 (2004). where >0 is a resolution parameter4. Hence, by counting the number of communities that have been split up, we obtained a lower bound on the number of communities that are badly connected. Nodes 06 are in the same community. This is very similar to what the smart local moving algorithm does. Again, if communities are badly connected, this may lead to incorrect inferences of topics, which will affect bibliometric analyses relying on the inferred topics. Traag, V A. Raghavan, U., Albert, R. & Kumara, S. Near linear time algorithm to detect community structures in large-scale networks. PubMed the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in 10, for the IMDB and Amazon networks, Leiden reaches a stable iteration relatively quickly, presumably because these networks have a fairly simple community structure. The property of -separation is also guaranteed by the Louvain algorithm. Soft Matter Phys. However, so far this problem has never been studied for the Louvain algorithm. Scientific Reports (Sci Rep) We prove that the Leiden algorithm yields communities that are guaranteed to be connected. We typically reduce the dimensionality of the data first by running PCA, then construct a neighbor graph in the reduced space. 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 Louvain algorithm is a simple and popular method for community detection (Blondel, Guillaume, and Lambiotte 2008). For example an SNN can be generated: For Seurat version 3 objects, the Leiden algorithm has been implemented in the Seurat version 3 package with Seurat::FindClusters and algorithm = "leiden"). S3. The quality of such an asymptotically stable partition provides an upper bound on the quality of an optimal partition. PubMedGoogle Scholar. 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.