leiden clustering explained leiden clustering explained

We now compare how the Leiden and the Louvain algorithm perform for the six empirical networks listed in Table2. See the documentation on the leidenalg Python module for more information: https://leidenalg.readthedocs.io/en/latest/reference.html. Neurosci. reviewed the manuscript. 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. E 78, 046110, https://doi.org/10.1103/PhysRevE.78.046110 (2008). Louvain keeps visiting all nodes in a network until there are no more node movements that increase the quality function. It therefore does not guarantee -connectivity either. & Arenas, A. 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Rep. 486, 75174, https://doi.org/10.1016/j.physrep.2009.11.002 (2010). to use Codespaces. Bullmore, E. & Sporns, O. 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. A. Modularity optimization. The value of the resolution parameter was determined based on the so-called mixing parameter 13. A Smart Local Moving Algorithm for Large-Scale Modularity-Based Community Detection. Eur. (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. 69 (2 Pt 2): 026113. http://dx.doi.org/10.1103/PhysRevE.69.026113. The inspiration for this method of community detection is the optimization of modularity as the algorithm progresses. AMS 56, 10821097 (2009). 104 (1): 3641. As far as I can tell, Leiden seems to essentially be smart local moving with the additional improvements of random moving and Louvain pruning added. ADS The second iteration of Louvain shows a large increase in the percentage of disconnected communities. Run the code above in your browser using DataCamp Workspace. Google Scholar. Google Scholar. 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. Phys. 10008, 6, https://doi.org/10.1088/1742-5468/2008/10/P10008 (2008). The images or other third party material in this article are included in the articles Creative Commons license, unless indicated otherwise in a credit line to the material. The docs are here. Importantly, mergers are performed only within each community of the partition \({\mathscr{P}}\). We generated networks with n=103 to n=107 nodes. Louvain community detection algorithm was originally proposed in 2008 as a fast community unfolding method for large networks. To address this problem, we introduce the Leiden algorithm. In the worst case, almost a quarter of the communities are badly connected. This is not the case when nodes are greedily merged with the community that yields the largest increase in the quality function. The increase in the percentage of disconnected communities is relatively limited for the Live Journal and Web of Science networks. MATH In this way, the constant acts as a resolution parameter, and setting the constant higher will result in fewer communities. Finally, we compare the performance of the algorithms on the empirical networks. Cluster Determination Source: R/generics.R, R/clustering.R Identify clusters of cells by a shared nearest neighbor (SNN) modularity optimization based clustering algorithm. B 86 (11): 471. https://doi.org/10.1140/epjb/e2013-40829-0. You signed in with another tab or window. the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Leiden algorithm. For all networks, Leiden identifies substantially better partitions than Louvain. 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. Speed of the first iteration of the Louvain and the Leiden algorithm for benchmark networks with increasingly difficult partitions (n=107). Hence, the Leiden algorithm effectively addresses the problem of badly connected communities. Then optimize the modularity function to determine clusters. In the Louvain algorithm, an aggregate network is created based on the partition \({\mathscr{P}}\) resulting from the local moving phase. 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 because Louvain only moves individual nodes at a time. The algorithm moves individual nodes from one community to another to find a partition (b). 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. 2018. Then, in order . This contrasts with the Leiden algorithm. 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. Speed and quality of the Louvain and the Leiden algorithm for benchmark networks of increasing size (two iterations). 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. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/. Knowl. 68, 984998, https://doi.org/10.1002/asi.23734 (2017). A Simple Acceleration Method for the Louvain Algorithm. Int. Rev. I tracked the number of clusters post-clustering at each step. 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. 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 . 4. These steps are repeated until the quality cannot be increased further. 2 represent stronger connections, while the other edges represent weaker connections. 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 algorithm moves individual nodes from one community to another to find a partition (b), which is then refined (c). 2004. A community is subset optimal if all subsets of the community are locally optimally assigned. We now show that the Louvain algorithm may find arbitrarily badly connected communities. 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. Similarly, in citation networks, such as the Web of Science network, nodes in a community are usually considered to share a common topic26,27. First, we show that the Louvain algorithm finds disconnected communities, and more generally, badly connected communities in the empirical networks. The idea of the refinement phase in the Leiden algorithm is to identify a partition \({{\mathscr{P}}}_{{\rm{refined}}}\) that is a refinement of \({\mathscr{P}}\). A major goal of single-cell analysis is to study the cell-state heterogeneity within a sample by discovering groups within the population of cells. The corresponding results are presented in the Supplementary Fig. Rev. Faster Unfolding of Communities: Speeding up the Louvain Algorithm. Phys. (We implemented both algorithms in Java, available from https://github.com/CWTSLeiden/networkanalysis and deposited at Zenodo23. Lancichinetti, A., Fortunato, S. & Radicchi, F. Benchmark graphs for testing community detection algorithms. To ensure readability of the paper to the broadest possible audience, we have chosen to relegate all technical details to the Supplementary Information. and JavaScript. contrastive-sc works best on datasets with fewer clusters when using the KMeans clustering and conversely for Leiden. 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. Weights for edges an also be passed to the leiden algorithm either as a separate vector or weights or a weighted adjacency matrix. For both algorithms, 10 iterations were performed. J. Comput. The Leiden algorithm starts from a singleton partition (a). Iterating the Louvain algorithm can therefore be seen as a double-edged sword: it improves the partition in some way, but degrades it in another way. The algorithm then moves individual nodes in the aggregate network (d). The degree of randomness in the selection of a community is determined by a parameter >0. 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. Google Scholar. Traag, V A. 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). Hence, for lower values of , the difference in quality is negligible. Community detection is an important task in the analysis of complex networks. & Bornholdt, S. Statistical mechanics of community detection. In doing so, Louvain keeps visiting nodes that cannot be moved to a different community. Eng. Use Git or checkout with SVN using the web URL. Centre for Science and Technology Studies, Leiden University, Leiden, The Netherlands, You can also search for this author in 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. Rather than progress straight to the aggregation stage (as we would for the original Louvain), we next consider each community as a new sub-network and re-apply the local moving step within each community. Performance of modularity maximization in practical contexts. The minimum resolvable community size depends on the total size of the network and the degree of interconnectedness of the modules. Rev. It states that there are no communities that can be merged. It was originally developed for modularity optimization, although the same method can be applied to optimize CPM. Waltman, L. & van Eck, N. J. In a stable iteration, the partition is guaranteed to be node optimal and subpartition -dense. 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. 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. Modularity is a popular objective function used with the Louvain method for community detection. Blondel, V D, J L Guillaume, and R Lambiotte. 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. Ph.D. thesis, (University of Oxford, 2016). Even worse, the Amazon network has 5% disconnected communities, but 25% badly connected communities. Raghavan, U., Albert, R. & Kumara, S. Near linear time algorithm to detect community structures in large-scale networks. An aggregate. In this case, refinement does not change the partition (f). The solution proposed in smart local moving is to alter how the local moving step in Louvain works. Community detection is often used to understand the structure of large and complex networks. Figure6 presents total runtime versus quality for all iterations of the Louvain and the Leiden algorithm. To address this important shortcoming, we introduce a new algorithm that is faster, finds better partitions and provides explicit guarantees and bounds. The algorithm continues to move nodes in the rest of the network. After a stable iteration of the Leiden algorithm, the algorithm may still be able to make further improvements in later iterations. 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. To find an optimal grouping of cells into communities, we need some way of evaluating different partitions in the graph. Article performed the experimental analysis. The phase one loop can be greatly accelerated by finding the nodes that have the potential to change community and only revisit those nodes. However, if communities are badly connected, this may lead to incorrect attributions of shared functionality. First, we created a specified number of nodes and we assigned each node to a community. Phys. Speed and quality for the first 10 iterations of the Louvain and the Leiden algorithm for benchmark networks (n=106 and n=107). Rev. Soft Matter Phys. Correspondence to When the Leiden algorithm found that a community could be split into multiple subcommunities, we counted the community as badly connected. For each set of parameters, we repeated the experiment 10 times. 10, for the IMDB and Amazon networks, Leiden reaches a stable iteration relatively quickly, presumably because these networks have a fairly simple community structure. 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. 7, whereas Louvain becomes much slower for more difficult partitions, Leiden is much less affected by the difficulty of the partition. To overcome the problem of arbitrarily badly connected communities, we introduced a new algorithm, which we refer to as the Leiden algorithm. We gratefully acknowledge computational facilities provided by the LIACS Data Science Lab Computing Facilities through Frank Takes.