Graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. Speed and quality of the Louvain and the Leiden algorithm for benchmark networks of increasing size (two iterations). For this network, Leiden requires over 750 iterations on average to reach a stable iteration. Inf. The leidenalg package facilitates community detection of networks and builds on the package igraph. The main ideas of our algorithm are explained in an intuitive way in the main text of the paper. where nc is the number of nodes in community c. The interpretation of the resolution parameter is quite straightforward. Nonetheless, some networks still show large differences. Random moving is a very simple adjustment to Louvain local moving proposed in 2015 (Traag 2015). For example, for the Web of Science network, the first iteration takes about 110120 seconds, while subsequent iterations require about 40 seconds. Modularity optimization. We applied the Louvain and the Leiden algorithm to exactly the same networks, using the same seed for the random number generator. It identifies the clusters by calculating the densities of the cells. Sci. This will compute the Leiden clusters and add them to the Seurat Object Class. Please Acad. Two ways of doing this are graph modularity (Newman and Girvan 2004) and the constant Potts model (Ronhovde and Nussinov 2010). 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 'devtools' package will be used to install 'leiden' and the dependancies (igraph and reticulate). 68, 984998, https://doi.org/10.1002/asi.23734 (2017). After a stable iteration of the Leiden algorithm, the algorithm may still be able to make further improvements in later iterations. HiCBin: binning metagenomic contigs and recovering metagenome-assembled For the results reported below, the average degree was set to \(\langle k\rangle =10\). 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. The algorithm then moves individual nodes in the aggregate network (e). Hence, the Leiden algorithm effectively addresses the problem of badly connected communities. Nodes 06 are in the same community. AMS 56, 10821097 (2009). U. S. A. The second iteration of Louvain shows a large increase in the percentage of disconnected communities. ADS Segmentation & Clustering SPATA2 - GitHub Pages This amounts to a clustering problem, where we aim to learn an optimal set of groups (communities) from the observed data. At some point, node 0 is considered for moving. Besides the Louvain algorithm and the Leiden algorithm (see the "Methods" section), there are several widely-used network clustering algorithms, such as the Markov clustering algorithm [], Infomap algorithm [], and label propagation algorithm [].Markov clustering and Infomap algorithm are both based on flow . Theory Exp. 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. The difference in computational time is especially pronounced for larger networks, with Leiden being up to 20 times faster than Louvain in empirical networks. 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. Rotta, R. & Noack, A. Multilevel local search algorithms for modularity clustering. Electr. Communities may even be disconnected. modularity) increases. In the most difficult case (=0.9), Louvain requires almost 2.5 days, while Leiden needs fewer than 10 minutes. However, as increases, the Leiden algorithm starts to outperform the Louvain algorithm. . Leiden consists of the following steps: The refinement step allows badly connected communities to be split before creating the aggregate network. Moreover, Louvain has no mechanism for fixing these communities. Analyses based on benchmark networks have only a limited value because these networks are not representative of empirical real-world networks. 8, 207218, https://doi.org/10.17706/IJCEE.2016.8.3.207-218 (2016). Preprocessing and clustering 3k PBMCs Scanpy documentation 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. When iterating Louvain, the quality of the partitions will keep increasing until the algorithm is unable to make any further improvements. Note that this code is designed for Seurat version 2 releases. In this stage we essentially collapse communities down into a single representative node, creating a new simplified graph. Random moving can result in some huge speedups, since Louvain spends about 95% of its time computing the modularity gain from moving nodes. As can be seen in Fig. In the worst case, almost a quarter of the communities are badly connected. Article wrote the manuscript. The aggregate network is created based on the partition \({{\mathscr{P}}}_{{\rm{refined}}}\). 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. Article In fact, by implementing the refinement phase in the right way, several attractive guarantees can be given for partitions produced by the Leiden algorithm. Clauset, A., Newman, M. E. J. Perhaps surprisingly, iterating the algorithm aggravates the problem, even though it does increase the quality function. The quality improvement realised by the Leiden algorithm relative to the Louvain algorithm is larger for empirical networks than for benchmark networks. cluster_cells: Cluster cells using Louvain/Leiden community detection Rev. 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. Article Here we can see partitions in the plotted results. For all networks, Leiden identifies substantially better partitions than Louvain. 9, the Leiden algorithm also performs better than the Louvain algorithm in terms of the quality of the partitions that are obtained. At each iteration all clusters are guaranteed to be connected and well-separated. That is, one part of such an internally disconnected community can reach another part only through a path going outside the community. Phys. Hierarchical Clustering Explained - Towards Data Science This function takes a cell_data_set as input, clusters the cells using . The problem of disconnected communities has been observed before19,20, also in the context of the label propagation algorithm21. To ensure readability of the paper to the broadest possible audience, we have chosen to relegate all technical details to the Supplementary Information. We demonstrate the performance of the Leiden algorithm for several benchmark and real-world networks. where >0 is a resolution parameter4. 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 & Clauset, A. It therefore does not guarantee -connectivity either. From Louvain to Leiden: guaranteeing well-connected communities - Nature IEEE Trans. Hence, the problem of Louvain outlined above is independent from the issue of the resolution limit. The Leiden algorithm is partly based on the previously introduced smart local move algorithm15, which itself can be seen as an improvement of the Louvain algorithm. The Louvain algorithm starts from a singleton partition in which each node is in its own community (a). We prove that the Leiden algorithm yields communities that are guaranteed to be connected. J. In our experimental analysis, we observe that up to 25% of the communities are badly connected and up to 16% are disconnected. E 76, 036106, https://doi.org/10.1103/PhysRevE.76.036106 (2007). In the first iteration, Leiden is roughly 220 times faster than Louvain. Community Detection Algorithms - Towards Data Science Fortunato, Santo, and Marc Barthlemy. Basically, there are two types of hierarchical cluster analysis strategies - 1. and JavaScript. 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. the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Hence, the complex structure of empirical networks creates an even stronger need for the use of the Leiden algorithm. The Leiden algorithm is considerably more complex than the Louvain algorithm. Later iterations of the Louvain algorithm only aggravate the problem of disconnected communities, even though the quality function (i.e. One of the most popular algorithms for uncovering community structure is the so-called Louvain algorithm. Source Code (2018). Modularity is a popular objective function used with the Louvain method for community detection. Many Git commands accept both tag and branch names, so creating this branch may cause unexpected behavior. Four popular community detection algorithms are explained . This aspect of the Louvain algorithm can be used to give information about the hierarchical relationships between communities by tracking at which stage the nodes in the communities were aggregated. https://doi.org/10.1038/s41598-019-41695-z. It states that there are no communities that can be merged. Even worse, the Amazon network has 5% disconnected communities, but 25% badly connected communities. You signed in with another tab or window. 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. This problem is different from the well-known issue of the resolution limit of modularity14. For example, after four iterations, the Web UK network has 8% disconnected communities, but twice as many badly connected communities. 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 authors act as bibliometric consultants to CWTS B.V., which makes use of community detection algorithms in commercial products and services. Clustering with the Leiden Algorithm in R - cran.microsoft.com Here is some small debugging code I wrote to find this. scanpy.tl.leiden Scanpy 1.9.3 documentation - Read the Docs Unsupervised clustering of cells is a common step in many single-cell expression workflows. J. In an experiment containing a mixture of cell types, each cluster might correspond to a different cell type. If you cant use Leiden, choosing Smart Local Moving will likely give very similar results, but might be a bit slower as it doesnt include some of the simple speedups to Louvain like random moving and Louvain pruning. 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. GitHub on Feb 15, 2020 Do you think the performance improvements will also be implemented in leidenalg? Leiden keeps finding better partitions for empirical networks also after the first 10 iterations of the algorithm. We keep removing nodes from the front of the queue, possibly moving these nodes to a different community. Raghavan, U., Albert, R. & Kumara, S. Near linear time algorithm to detect community structures in large-scale networks. We provide the full definitions of the properties as well as the mathematical proofs in SectionD of the Supplementary Information. The Leiden community detection algorithm outperforms other clustering methods. 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. The percentage of badly connected communities is less affected by the number of iterations of the Louvain algorithm. leiden_clustering Description Class wrapper based on scanpy to use the Leiden algorithm to directly cluster your data matrix with a scikit-learn flavor. 2015. The degree of randomness in the selection of a community is determined by a parameter >0. J. For the Amazon, DBLP and Web UK networks, Louvain yields on average respectively 23%, 16% and 14% badly connected communities. However, it is also possible to start the algorithm from a different partition15. Leiden is both faster than Louvain and finds better partitions. As shown in Fig. 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. Note that this code is . CPM does not suffer from this issue13. MathSciNet 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. 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. From Louvain to Leiden: Guaranteeing Well-Connected Communities, October. An alternative quality function is the Constant Potts Model (CPM)13, which overcomes some limitations of modularity. Klavans, R. & Boyack, K. W. Which Type of Citation Analysis Generates the Most Accurate Taxonomy of Scientific and Technical Knowledge? Rep. 6, 30750, https://doi.org/10.1038/srep30750 (2016). E Stat. CPM has the advantage that it is not subject to the resolution limit. Luecken, M. D. Application of multi-resolution partitioning of interaction networks to the study of complex disease. We now compare how the Leiden and the Louvain algorithm perform for the six empirical networks listed in Table2. igraph R manual pages Note that Leiden clustering directly clusters the neighborhood graph of cells, which we already computed in the previous section. Eng. Clustering algorithms look for similarities or dissimilarities among data points so that similar ones can be grouped together. The increase in the percentage of disconnected communities is relatively limited for the Live Journal and Web of Science networks. I tracked the number of clusters post-clustering at each step. 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. In general, Leiden is both faster than Louvain and finds better partitions. Rev. The DBLP network is somewhat more challenging, requiring almost 80 iterations on average to reach a stable iteration. In doing so, Louvain keeps visiting nodes that cannot be moved to a different community. When node 0 is moved to a different community, the red community becomes internally disconnected, as shown in (b). Scientific Reports (Sci Rep) If nothing happens, download GitHub Desktop and try again. S3. Clustering with the Leiden Algorithm in R Leiden now included in python-igraph #1053 - Github Proc. In this case we know the answer is exactly 10. The new algorithm integrates several earlier improvements, incorporating a combination of smart local move15, fast local move16,17 and random neighbour move18. Node mergers that cause the quality function to decrease are not considered. 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). According to CPM, it is better to split into two communities when the link density between the communities is lower than the constant. The resulting clusters are shown as colors on the 3D model (top) and t -SNE embedding . J. J. Stat. In many complex networks, nodes cluster and form relatively dense groupsoften called communities1,2. Each point corresponds to a certain iteration of an algorithm, with results averaged over 10 experiments. The nodes that are more interconnected have been partitioned into separate clusters. The Louvain algorithm is illustrated in Fig. Subset optimality is the strongest guarantee that is provided by the Leiden algorithm. The R implementation of Leiden can be run directly on the snn igraph object in Seurat. Nevertheless, when CPM is used as the quality function, the Louvain algorithm may still find arbitrarily badly connected communities. V.A.T. 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. PubMed A community is subset optimal if all subsets of the community are locally optimally assigned. Rev. 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"). Neurosci. conda install -c conda-forge leidenalg pip install leiden-clustering Used via. E 74, 036104, https://doi.org/10.1103/PhysRevE.74.036104 (2006). Such a modular structure is usually not known beforehand. In the refinement phase, nodes are not necessarily greedily merged with the community that yields the largest increase in the quality function. Each community in this partition becomes a node in the aggregate network. 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). This should be the first preference when choosing an algorithm. The Beginner's Guide to Dimensionality Reduction. 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. Then the Leiden algorithm can be run on the adjacency matrix. Ozaki, N., Tezuka, H. & Inaba, M. A Simple Acceleration Method for the Louvain Algorithm. 2(a). Contrary to what might be expected, iterating the Louvain algorithm aggravates the problem of badly connected communities, as we will also see in our experimental analysis. Optimising modularity is NP-hard5, and consequentially many heuristic algorithms have been proposed, such as hierarchical agglomeration6, extremal optimisation7, simulated annealing4,8 and spectral9 algorithms. Traag, V A. For each set of parameters, we repeated the experiment 10 times. Node optimality is also guaranteed after a stable iteration of the Louvain algorithm. We find that the Leiden algorithm is faster than the Louvain algorithm and uncovers better partitions, in addition to providing explicit guarantees. CAS Conversely, if Leiden does not find subcommunities, there is no guarantee that modularity cannot be increased by splitting up the community. In this post, I will cover one of the common approaches which is hierarchical clustering. The refined partition \({{\mathscr{P}}}_{{\rm{refined}}}\) is obtained as follows. While smart local moving and multilevel refinement can improve the communities found, the next two improvements on Louvain that Ill discuss focus on the speed/efficiency of the algorithm. To address this problem, we introduce the Leiden algorithm. 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. Ph.D. thesis, (University of Oxford, 2016). partition_type : Optional [ Type [ MutableVertexPartition ]] (default: None) Type of partition to use. CAS Cluster Determination Source: R/generics.R, R/clustering.R Identify clusters of cells by a shared nearest neighbor (SNN) modularity optimization based clustering algorithm. The Louvain algorithm is a simple and popular method for community detection (Blondel, Guillaume, and Lambiotte 2008). E 72, 027104, https://doi.org/10.1103/PhysRevE.72.027104 (2005). As the problem of modularity optimization is NP-hard, we need heuristic methods to optimize modularity (or CPM). This is similar to what we have seen for benchmark networks. A Smart Local Moving Algorithm for Large-Scale Modularity-Based Community Detection. Eur. 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. Louvain has two phases: local moving and aggregation. Second, to study the scaling of the Louvain and the Leiden algorithm, we use benchmark networks, allowing us to compare the algorithms in terms of both computational time and quality of the partitions. Internet Explorer). The docs are here. A tag already exists with the provided branch name. One of the most popular algorithms to optimise modularity is the so-called Louvain algorithm10, named after the location of its authors. Consider the partition shown in (a). In the Louvain algorithm, an aggregate network is created based on the partition \({\mathscr{P}}\) resulting from the local moving phase. To do this we just sum all the edge weights between nodes of the corresponding communities to get a single weighted edge between them, and collapse each community down to a single new node. cluster_leiden: Finding community structure of a graph using the Leiden 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. In addition, we prove that, when the Leiden algorithm is applied iteratively, it converges to a partition in which all subsets of all communities are locally optimally assigned. Starting from the second iteration, Leiden outperformed Louvain in terms of the percentage of badly connected communities.