leiden clustering explained

Fortunato, S. & Barthlemy, M. Resolution Limit in Community Detection. The Leiden algorithm is clearly faster than the Louvain algorithm. In the aggregation phase, an aggregate network is created based on the partition obtained in the local moving phase. 8 (3): 207. https://pdfs.semanticscholar.org/4ea9/74f0fadb57a0b1ec35cbc5b3eb28e9b966d8.pdf. MATH Directed Undirected Homogeneous Heterogeneous Weighted 1. U. S. A. MathSciNet Therefore, clustering algorithms look for similarities or dissimilarities among data points. 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 . Modularity is given by. This is very similar to what the smart local moving algorithm does. Nodes 13 should form a community and nodes 46 should form another community. J. Exp. Raghavan, U., Albert, R. & Kumara, S. Near linear time algorithm to detect community structures in large-scale networks. Community detection is often used to understand the structure of large and complex networks. Phys. Modularity is a popular objective function used with the Louvain method for community detection. There is an entire Leiden package in R-cran here However, the Louvain algorithm does not consider this possibility, since it considers only individual node movements. 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. Two ways of doing this are graph modularity (Newman and Girvan 2004) and the constant Potts model (Ronhovde and Nussinov 2010). This is very similar to what the smart local moving algorithm does. Hence, the Leiden algorithm effectively addresses the problem of badly connected communities. Nodes 16 have connections only within this community, whereas node 0 also has many external connections. 2010. 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 . A structure that is more informative than the unstructured set of clusters returned by flat clustering. Newman, M. E. J. However, if communities are badly connected, this may lead to incorrect attributions of shared functionality. Subpartition -density does not imply that individual nodes are locally optimally assigned. 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. These nodes can be approximately identified based on whether neighbouring nodes have changed communities. 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. 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. This is not the case when nodes are greedily merged with the community that yields the largest increase in the quality function. Klavans, R. & Boyack, K. W. Which Type of Citation Analysis Generates the Most Accurate Taxonomy of Scientific and Technical Knowledge? Mech. A number of iterations of the Leiden algorithm can be performed before the Louvain algorithm has finished its first iteration. The classic Louvain algorithm should be avoided due to the known problem with disconnected communities. At this point, it is guaranteed that each individual node is optimally assigned. At some point, node 0 is considered for moving. Traag, Vincent, Ludo Waltman, and Nees Jan van Eck. The Louvain algorithm10 is very simple and elegant. Then, in order . This is the crux of the Leiden paper, and the authors show that this exact problem happens frequently in practice. When a disconnected community has become a node in an aggregate network, there are no more possibilities to split up the community. Traag, V. A. leidenalg 0.7.0. When iterating Louvain, the quality of the partitions will keep increasing until the algorithm is unable to make any further improvements. Value. B 86, 471, https://doi.org/10.1140/epjb/e2013-40829-0 (2013). Centre for Science and Technology Studies, Leiden University, Leiden, The Netherlands, You can also search for this author in Performance of modularity maximization in practical contexts. The idea of the refinement phase in the Leiden algorithm is to identify a partition \({{\mathscr{P}}}_{{\rm{refined}}}\) that is a refinement of \({\mathscr{P}}\). CPM does not suffer from this issue13. The Leiden community detection algorithm outperforms other clustering methods. SPATA2 currently offers the functions findSeuratClusters (), findMonocleClusters () and findNearestNeighbourClusters () which are wrapper around widely used clustering algorithms. We abbreviate the leidenalg package as la and the igraph package as ig in all Python code throughout this documentation. Modularity scores of +1 mean that all the edges in a community are connecting nodes within the community. This contrasts with optimisation algorithms such as simulated annealing, which do allow the quality function to decrease4,8. Learn more. In particular, we show that Louvain may identify communities that are internally disconnected. When node 0 is moved to a different community, the red community becomes internally disconnected, as shown in (b). Rev. We generated benchmark networks in the following way. Some of these nodes may very well act as bridges, similarly to node 0 in the above example. Phys. 68, 984998, https://doi.org/10.1002/asi.23734 (2017). The nodes are added to the queue in a random order. CPM has the advantage that it is not subject to the resolution limit. However, so far this problem has never been studied for the Louvain algorithm. 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. 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. Fortunato, S. Community detection in graphs. 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. Such a modular structure is usually not known beforehand. Nature 433, 895900, https://doi.org/10.1038/nature03288 (2005). 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. The main ideas of our algorithm are explained in an intuitive way in the main text of the paper. Lancichinetti, A., Fortunato, S. & Radicchi, F. Benchmark graphs for testing community detection algorithms. reviewed the manuscript. However, Leiden is more than 7 times faster for the Live Journal network, more than 11 times faster for the Web of Science network and more than 20 times faster for the Web UK network. In the fast local move procedure in the Leiden algorithm, only nodes whose neighbourhood has changed are visited. S3. J. Stat. PubMed As can be seen in the figure, Louvain quickly reaches a state in which it is unable to find better partitions. E 92, 032801, https://doi.org/10.1103/PhysRevE.92.032801 (2015). 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. This way of defining the expected number of edges is based on the so-called configuration model. It identifies the clusters by calculating the densities of the cells. 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. 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. 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. Then optimize the modularity function to determine clusters. Louvain quickly converges to a partition and is then unable to make further improvements. Disconnected community. 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. Rev. After a stable iteration of the Leiden algorithm, the algorithm may still be able to make further improvements in later iterations. Obviously, this is a worst case example, showing that disconnected communities may be identified by the Louvain algorithm. IEEE Trans. However, for higher values of , Leiden becomes orders of magnitude faster than Louvain, reaching 10100 times faster runtimes for the largest networks. 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. Below, the quality of a partition is reported as \(\frac{ {\mathcal H} }{2m}\), where H is defined in Eq. PubMed Central In an experiment containing a mixture of cell types, each cluster might correspond to a different cell type. Technol. Nonlin. Conversely, if Leiden does not find subcommunities, there is no guarantee that modularity cannot be increased by splitting up the community. Community detection can then be performed using this graph. 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. Leiden keeps finding better partitions for empirical networks also after the first 10 iterations of the algorithm. This will compute the Leiden clusters and add them to the Seurat Object Class. We now show that the Louvain algorithm may find arbitrarily badly connected communities. The Louvain method for community detection is a popular way to discover communities from single-cell data. The percentage of badly connected communities is less affected by the number of iterations of the Louvain algorithm. In the local moving phase, individual nodes are moved to the community that yields the largest increase in the quality function. We find that the Leiden algorithm is faster than the Louvain algorithm and uncovers better partitions, in addition to providing explicit guarantees. Here is some small debugging code I wrote to find this. Brandes, U. et al. 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. Article Duch, J. In the Louvain algorithm, an aggregate network is created based on the partition \({\mathscr{P}}\) resulting from the local moving phase. Nonlin. E 69, 026113, https://doi.org/10.1103/PhysRevE.69.026113 (2004). These nodes are therefore optimally assigned to their current community. Fast Unfolding of Communities in Large Networks. Journal of Statistical , January. Traag, V.A., Waltman, L. & van Eck, N.J. From Louvain to Leiden: guaranteeing well-connected communities. In the first step of the next iteration, Louvain will again move individual nodes in the network. MATH Rev. Furthermore, by relying on a fast local move approach, the Leiden algorithm runs faster than the Louvain algorithm. Fortunato, Santo, and Marc Barthlemy. To find an optimal grouping of cells into communities, we need some way of evaluating different partitions in the graph. Communities in \({\mathscr{P}}\) may be split into multiple subcommunities in \({{\mathscr{P}}}_{{\rm{refined}}}\). ACM Trans. Google Scholar. This makes sense, because after phase one the total size of the graph should be significantly reduced. I tracked the number of clusters post-clustering at each step. This phenomenon can be explained by the documented tendency KMeans has to identify equal-sized , combined with the significant class imbalance associated with the datasets having more than 8 clusters (Table 1). 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. In general, Leiden is both faster than Louvain and finds better partitions. As can be seen in Fig. Figure4 shows how well it does compared to the Louvain algorithm. For example, for the Web of Science network, the first iteration takes about 110120 seconds, while subsequent iterations require about 40 seconds. 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. Another important difference between the Leiden algorithm and the Louvain algorithm is the implementation of the local moving phase. To address this problem, we introduce the Leiden algorithm. http://iopscience.iop.org/article/10.1088/1742-5468/2008/10/P10008/meta, http://dx.doi.org/10.1073/pnas.0605965104, http://dx.doi.org/10.1103/PhysRevE.69.026113, https://pdfs.semanticscholar.org/4ea9/74f0fadb57a0b1ec35cbc5b3eb28e9b966d8.pdf, http://dx.doi.org/10.1103/PhysRevE.81.046114, http://dx.doi.org/10.1103/PhysRevE.92.032801, https://doi.org/10.1140/epjb/e2013-40829-0, Assign each node to a different community. One may expect that other nodes in the old community will then also be moved to other communities. 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 Louvain algorithm starts from a singleton partition in which each node is in its own community (a). Again, if communities are badly connected, this may lead to incorrect inferences of topics, which will affect bibliometric analyses relying on the inferred topics. Each of these can be used as an objective function for graph-based community detection methods, with our goal being to maximize this value. The R implementation of Leiden can be run directly on the snn igraph object in Seurat. Importantly, the first iteration of the Leiden algorithm is the most computationally intensive one, and subsequent iterations are faster. leidenalg. Traag, V. A., Van Dooren, P. & Nesterov, Y. 8, the Leiden algorithm is significantly faster than the Louvain algorithm also in empirical networks. The algorithm moves individual nodes from one community to another to find a partition (b), which is then refined (c). For this network, Leiden requires over 750 iterations on average to reach a stable iteration. As discussed earlier, the Louvain algorithm does not guarantee connectivity. One of the most popular algorithms for uncovering community structure is the so-called Louvain algorithm. Other networks show an almost tenfold increase in the percentage of disconnected communities. Note that nodes can be revisited several times within a single iteration of the local moving stage, as the possible increase in modularity will change as other nodes are moved to different communities. We also suggested that the Leiden algorithm is faster than the Louvain algorithm, because of the fast local move approach. Table2 provides an overview of the six networks. 92 (3): 032801. http://dx.doi.org/10.1103/PhysRevE.92.032801. In terms of the percentage of badly connected communities in the first iteration, Leiden performs even worse than Louvain, as can be seen in Fig. Local Resolution-Limit-Free Potts Model for Community Detection. Phys. Phys. The constant Potts model might give better communities in some cases, as it is not subject to the resolution limit. MathSciNet 10, for the IMDB and Amazon networks, Leiden reaches a stable iteration relatively quickly, presumably because these networks have a fairly simple community structure. 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. and JavaScript. If nothing happens, download GitHub Desktop and try again. Note that Leiden clustering directly clusters the neighborhood graph of cells, which we already computed in the previous section. The quality of such an asymptotically stable partition provides an upper bound on the quality of an optimal partition. The solution provided by Leiden is based on the smart local moving algorithm. In this iterative scheme, Louvain provides two guarantees: (1) no communities can be merged and (2) no nodes can be moved. At each iteration all clusters are guaranteed to be connected and well-separated. contrastive-sc works best on datasets with fewer clusters when using the KMeans clustering and conversely for Leiden. The Louvain algorithm is a simple and popular method for community detection (Blondel, Guillaume, and Lambiotte 2008). 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 Eng. In addition, we prove that the algorithm converges to an asymptotically stable partition in which all subsets of all communities are locally optimally assigned. In this post Ive mainly focused on the optimisation methods for community detection, rather than the different objective functions that can be used. The Leiden algorithm has been specifically designed to address the problem of badly connected communities. 7, whereas Louvain becomes much slower for more difficult partitions, Leiden is much less affected by the difficulty of the partition. 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. Graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. Google Scholar. N.J.v.E. (2) and m is the number of edges. We therefore require a more principled solution, which we will introduce in the next section. sign in & Fortunato, S. Community detection algorithms: A comparative analysis. We prove that the Leiden algorithm yields communities that are guaranteed to be connected. For each network, we repeated the experiment 10 times. The above results shows that the problem of disconnected and badly connected communities is quite pervasive in practice. the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Phys. to use Codespaces. 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. The inspiration for this method of community detection is the optimization of modularity as the algorithm progresses. import leidenalg as la import igraph as ig Example output. We will use sklearns K-Means implementation looking for 10 clusters in the original 784 dimensional data. 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. Hence, the problem of Louvain outlined above is independent from the issue of the resolution limit. E 80, 056117, https://doi.org/10.1103/PhysRevE.80.056117 (2009). Presumably, many of the badly connected communities in the first iteration of Louvain become disconnected in the second iteration. 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 \({\mathscr{P}}\). This package requires the 'leidenalg' and 'igraph' modules for python (2) to be installed on your system. https://doi.org/10.1038/s41598-019-41695-z. In particular, benchmark networks have a rather simple structure. In practice, this means that small clusters can hide inside larger clusters, making their identification difficult. 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. The solution proposed in smart local moving is to alter how the local moving step in Louvain works. For example, after four iterations, the Web UK network has 8% disconnected communities, but twice as many badly connected communities. The authors act as bibliometric consultants to CWTS B.V., which makes use of community detection algorithms in commercial products and services. In this way, Leiden implements the local moving phase more efficiently than Louvain.

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