ACM Trans. According to CPM, it is better to split into two communities when the link density between the communities is lower than the constant. The algorithm is run iteratively, using the partition identified in one iteration as starting point for the next iteration. Centre for Science and Technology Studies, Leiden University, Leiden, The Netherlands, You can also search for this author in 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. The fast local move procedure can be summarised as follows. Clauset, A., Newman, M. E. J. The property of -connectivity is a slightly stronger variant of ordinary connectivity. 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"). Table2 provides an overview of the six networks. We show that this algorithm has a major defect that largely went unnoticed until now: the Louvain algorithm may yield arbitrarily badly connected communities. 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. All communities are subpartition -dense. Use the Previous and Next buttons to navigate the slides or the slide controller buttons at the end to navigate through each slide. 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. Removing such a node from its old community disconnects the old community. A Simple Acceleration Method for the Louvain Algorithm. Int. Sci. 2.3. The Leiden algorithm is considerably more complex than the Louvain algorithm. That is, one part of such an internally disconnected community can reach another part only through a path going outside the community. SPATA2 currently offers the functions findSeuratClusters (), findMonocleClusters () and findNearestNeighbourClusters () which are wrapper around widely used clustering algorithms. Modularity scores of +1 mean that all the edges in a community are connecting nodes within the community. 2016. Leiden consists of the following steps: The refinement step allows badly connected communities to be split before creating the aggregate network. 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 the worst case, communities may even be disconnected, especially when running the algorithm iteratively. Modularity optimization. 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. Later iterations of the Louvain algorithm only aggravate the problem of disconnected communities, even though the quality function (i.e. MATH 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. 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. Google Scholar. Thank you for visiting nature.com. Subpartition -density is not guaranteed by the Louvain algorithm. Google Scholar. Theory Exp. As can be seen in the figure, Louvain quickly reaches a state in which it is unable to find better partitions. Our analysis is based on modularity with resolution parameter =1. Positive values above 2 define the total number of iterations to perform, -1 has the algorithm run until it reaches its optimal clustering. Local Resolution-Limit-Free Potts Model for Community Detection. Phys. The community with which a node is merged is selected randomly18. This amounts to a clustering problem, where we aim to learn an optimal set of groups (communities) from the observed data. 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. contrastive-sc works best on datasets with fewer clusters when using the KMeans clustering and conversely for Leiden. 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. Rep. 486, 75174, https://doi.org/10.1016/j.physrep.2009.11.002 (2010). We used modularity with a resolution parameter of =1 for the experiments. First, we created a specified number of nodes and we assigned each node to a community. Scaling of benchmark results for network size. Introduction The Louvain method is an algorithm to detect communities in large networks. The Louvain local moving phase consists of the following steps: This process is repeated for every node in the network until no further improvement in modularity is possible. MathSciNet J. The minimum resolvable community size depends on the total size of the network and the degree of interconnectedness of the modules. Electr. However, it is also possible to start the algorithm from a different partition15. This will compute the Leiden clusters and add them to the Seurat Object Class. We conclude that the Leiden algorithm is strongly preferable to the Louvain algorithm. Note that communities found by the Leiden algorithm are guaranteed to be connected. As the use of clustering is highly depending on the biological question it makes sense to use several approaches and algorithms. V. A. Traag. First calculate k-nearest neighbors and construct the SNN graph. When iterating Louvain, the quality of the partitions will keep increasing until the algorithm is unable to make any further improvements. This is similar to ideas proposed recently as pruning16 and in a slightly different form as prioritisation17. Nodes 06 are in the same community. 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 The Beginner's Guide to Dimensionality Reduction. Importantly, the output of the local moving stage will depend on the order that the nodes are considered in. 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. Mech. However, this is not necessarily the case, as the other nodes may still be sufficiently strongly connected to their community, despite the fact that the community has become disconnected. The Louvain algorithm guarantees that modularity cannot be increased by merging communities (it finds a locally optimal solution). The DBLP network is somewhat more challenging, requiring almost 80 iterations on average to reach a stable iteration. 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. Rev. Google Scholar. Natl. For lower values of , the correct partition is easy to find and Leiden is only about twice as fast as Louvain. 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). Similarly, in citation networks, such as the Web of Science network, nodes in a community are usually considered to share a common topic26,27. This package requires the 'leidenalg' and 'igraph' modules for python (2) to be installed on your system. E 92, 032801, https://doi.org/10.1103/PhysRevE.92.032801 (2015). 10, 186198, https://doi.org/10.1038/nrn2575 (2009). Data 11, 130, https://doi.org/10.1145/2992785 (2017). Ozaki, Naoto, Hiroshi Tezuka, and Mary Inaba. Such algorithms are rather slow, making them ineffective for large networks. It therefore does not guarantee -connectivity either. B 86, 471, https://doi.org/10.1140/epjb/e2013-40829-0 (2013). Basically, there are two types of hierarchical cluster analysis strategies - 1. Provided by the Springer Nature SharedIt content-sharing initiative. Percentage of communities found by the Louvain algorithm that are either disconnected or badly connected compared to percentage of badly connected communities found by the Leiden algorithm. The quality improvement realised by the Leiden algorithm relative to the Louvain algorithm is larger for empirical networks than for benchmark networks. partition_type : Optional [ Type [ MutableVertexPartition ]] (default: None) Type of partition to use. Finding communities in large networks is far from trivial: algorithms need to be fast, but they also need to provide high-quality results. How many iterations of the Leiden clustering algorithm to perform. This is not too difficult to explain. Nodes 16 have connections only within this community, whereas node 0 also has many external connections. The two phases are repeated until the quality function cannot be increased further. where nc is the number of nodes in community c. The interpretation of the resolution parameter is quite straightforward. The Leiden algorithm is considerably more complex than the Louvain algorithm. Louvain can also be quite slow, as it spends a lot of time revisiting nodes that may not have changed neighborhoods. Hence, the complex structure of empirical networks creates an even stronger need for the use of the Leiden algorithm. 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. Knowl. We provide the full definitions of the properties as well as the mathematical proofs in SectionD of the Supplementary Information. Ph.D. thesis, (University of Oxford, 2016). Detecting communities in a network is therefore an important problem. 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. Importantly, the problem of disconnected communities is not just a theoretical curiosity. Rev. Number of iterations before the Leiden algorithm has reached a stable iteration for six empirical networks. Soft Matter Phys. Note that Leiden clustering directly clusters the neighborhood graph of cells, which we already computed in the previous section. The authors act as bibliometric consultants to CWTS B.V., which makes use of community detection algorithms in commercial products and services. Again, if communities are badly connected, this may lead to incorrect inferences of topics, which will affect bibliometric analyses relying on the inferred topics. 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. Communities were all of equal size. In doing so, Louvain keeps visiting nodes that cannot be moved to a different community. The random component also makes the algorithm more explorative, which might help to find better community structures. Scientific Reports (Sci Rep) conda install -c conda-forge leidenalg pip install leiden-clustering Used via. The algorithm then moves individual nodes in the aggregate network (d). We will use sklearns K-Means implementation looking for 10 clusters in the original 784 dimensional data. Bullmore, E. & Sporns, O. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/. https://doi.org/10.1038/s41598-019-41695-z. Modularity is a measure of the structure of networks or graphs which measures the strength of division of a network into modules (also called groups, clusters or communities). 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. Sign up for the Nature Briefing newsletter what matters in science, free to your inbox daily. It does not guarantee that modularity cant be increased by moving nodes between communities. In contrast, Leiden keeps finding better partitions in each iteration. Trying to fix the problem by simply considering the connected components of communities19,20,21 is unsatisfactory because it addresses only the most extreme case and does not resolve the more fundamental problem. Nonetheless, some networks still show large differences. Neurosci. These steps are repeated until no further improvements can be made. In particular, we show that Louvain may identify communities that are internally disconnected. 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. For all networks, Leiden identifies substantially better partitions than Louvain. One of the best-known methods for community detection is called modularity3. This package implements the Leiden algorithm in C++ and exposes it to python.It relies on (python-)igraph for it to function. Is modularity with a resolution parameter equivalent to leidenalg.RBConfigurationVertexPartition? Hence, in general, Louvain may find arbitrarily badly connected communities. (We implemented both algorithms in Java, available from https://github.com/CWTSLeiden/networkanalysis and deposited at Zenodo23. The inspiration for this method of community detection is the optimization of modularity as the algorithm progresses. However, modularity suffers from a difficult problem known as the resolution limit (Fortunato and Barthlemy 2007). 81 (4 Pt 2): 046114. http://dx.doi.org/10.1103/PhysRevE.81.046114. 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. However, for higher values of , Leiden becomes orders of magnitude faster than Louvain, reaching 10100 times faster runtimes for the largest networks. PubMed PubMedGoogle Scholar. Phys. https://doi.org/10.1038/s41598-019-41695-z, DOI: https://doi.org/10.1038/s41598-019-41695-z. We name our algorithm the Leiden algorithm, after the location of its authors. Work fast with our official CLI. 4. Inf. Cite this article. 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. 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 \({\mathscr{P}}\). Faster Unfolding of Communities: Speeding up the Louvain Algorithm. Phys. There is an entire Leiden package in R-cran here If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate. As can be seen in Fig. Rep. 6, 30750, https://doi.org/10.1038/srep30750 (2016). Such a modular structure is usually not known beforehand. Each community in this partition becomes a node in the aggregate network. In addition, we prove that the algorithm converges to an asymptotically stable partition in which all subsets of all communities are locally optimally assigned. The horizontal axis indicates the cumulative time taken to obtain the quality indicated on the vertical axis. J. Below we offer an intuitive explanation of these properties. After the first iteration of the Louvain algorithm, some partition has been obtained. You will not need much Python to use it. 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. The main ideas of our algorithm are explained in an intuitive way in the main text of the paper. In that case, some optimal partitions cannot be found, as we show in SectionC2 of the Supplementary Information. 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. These are the same networks that were also studied in an earlier paper introducing the smart local move algorithm15. The count of badly connected communities also included disconnected communities. CPM does not suffer from this issue13. 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. It only implies that individual nodes are well connected to their community.