leiden clustering explained

& Moore, C. Finding community structure in very large networks. Nonetheless, some networks still show large differences. For higher values of , Leiden finds better partitions than Louvain. As shown in Fig. Once aggregation is complete we restart the local moving phase, and continue to iterate until everything converges down to one node. 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. leiden_clsutering is distributed under a BSD 3-Clause License (see LICENSE). Even though clustering can be applied to networks, it is a broader field in unsupervised machine learning which deals with multiple attribute types. In the case of modularity, communities may have significant substructure both because of the resolution limit and because of the shortcomings of Louvain. 2010. 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. We will use sklearns K-Means implementation looking for 10 clusters in the original 784 dimensional data. 2(b). Newman, M. E. J. Biological sequence clustering is a complicated data clustering problem owing to the high computation costs incurred for pairwise sequence distance calculations through sequence alignments, as well as difficulties in determining parameters for deriving robust clusters. This is very similar to what the smart local moving algorithm does. Louvain can also be quite slow, as it spends a lot of time revisiting nodes that may not have changed neighborhoods. 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. It partitions the data space and identifies the sub-spaces using the Apriori principle. Subset optimality is the strongest guarantee that is provided by the Leiden algorithm. 8, 207218, https://doi.org/10.17706/IJCEE.2016.8.3.207-218 (2016). The quality improvement realised by the Leiden algorithm relative to the Louvain algorithm is larger for empirical networks than for benchmark networks. Crucially, however, the percentage of badly connected communities decreases with each iteration of the Leiden algorithm. Phys. The aggregate network is created based on the partition ${{\mathscr{P}}}_{{\rm{refined}}}$. We consider these ideas to represent the most promising directions in which the Louvain algorithm can be improved, even though we recognise that other improvements have been suggested as well22. Basically, there are two types of hierarchical cluster analysis strategies - 1. All authors conceived the algorithm and contributed to the source code. However, the Louvain algorithm does not consider this possibility, since it considers only individual node movements. 20, 172188, https://doi.org/10.1109/TKDE.2007.190689 (2008). Similarly, in citation networks, such as the Web of Science network, nodes in a community are usually considered to share a common topic26,27. For example, for the Web of Science network, the first iteration takes about 110120 seconds, while subsequent iterations require about 40 seconds. 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. Note that if Leiden finds subcommunities, splitting up the community is guaranteed to increase modularity. Rev. 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. See the documentation on the leidenalg Python module for more information: https://leidenalg.readthedocs.io/en/latest/reference.html. The second iteration of Louvain shows a large increase in the percentage of disconnected communities. The random component also makes the algorithm more explorative, which might help to find better community structures. 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. J. Stat. Wolf, F. A. et al. Soc. Speed of the first iteration of the Louvain and the Leiden algorithm for benchmark networks with increasingly difficult partitions (n=107). First calculate k-nearest neighbors and construct the SNN graph. 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. Rep. 486, 75174, https://doi.org/10.1016/j.physrep.2009.11.002 (2010). Traag, V A. For all networks, Leiden identifies substantially better partitions than Louvain. contrastive-sc works best on datasets with fewer clusters when using the KMeans clustering and conversely for Leiden. Natl. In particular, benchmark networks have a rather simple structure. ADS 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. http://arxiv.org/abs/1810.08473. We now consider the guarantees provided by the Leiden algorithm. Sci. Nature 433, 895900, https://doi.org/10.1038/nature03288 (2005). Scaling of benchmark results for difficulty of the partition. S3. This is not the case when nodes are greedily merged with the community that yields the largest increase in the quality function. 10, 186198, https://doi.org/10.1038/nrn2575 (2009). However, the initial partition for the aggregate network is based on P, just like in the Louvain algorithm. The corresponding results are presented in the Supplementary Fig. Google Scholar. The algorithm may yield arbitrarily badly connected communities, over and above the well-known issue of the resolution limit14. Are you sure you want to create this branch? If nothing happens, download GitHub Desktop and try again. Even worse, the Amazon network has 5% disconnected communities, but 25% badly connected communities. Article Hence, for lower values of , the difference in quality is negligible. Randomness in the selection of a community allows the partition space to be explored more broadly. 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. 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. Phys. CAS An aggregate. 92 (3): 032801. http://dx.doi.org/10.1103/PhysRevE.92.032801. where >0 is a resolution parameter4. 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. E Stat. 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. Data Eng. All experiments were run on a computer with 64 Intel Xeon E5-4667v3 2GHz CPUs and 1TB internal memory. Faster unfolding of communities: Speeding up the Louvain algorithm. This algorithm provides a number of explicit guarantees. Rotta, R. & Noack, A. Multilevel local search algorithms for modularity clustering. Each point corresponds to a certain iteration of an algorithm, with results averaged over 10 experiments. We conclude that the Leiden algorithm is strongly preferable to the Louvain algorithm. E 76, 036106, https://doi.org/10.1103/PhysRevE.76.036106 (2007). Modularity scores of +1 mean that all the edges in a community are connecting nodes within the community. Communities in 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. We study the problem of badly connected communities when using the Louvain algorithm for several empirical networks. They identified an inefficiency in the Louvain algorithm: computes modularity gain for all neighbouring nodes per loop in local moving phase, even though many of these nodes will not have moved. However, it is also possible to start the algorithm from a different partition15. Learn more. As can be seen in Fig. In that case, nodes 16 are all locally optimally assigned, despite the fact that their community has become disconnected. We used the CPM quality function. An overview of the various guarantees is presented in Table1. Cluster cells using Louvain/Leiden community detection Description. Cluster your data matrix with the Leiden algorithm. 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. It therefore does not guarantee -connectivity either. This is similar to ideas proposed recently as pruning16 and in a slightly different form as prioritisation17. Disconnected community. Technol. leidenalg. Provided by the Springer Nature SharedIt content-sharing initiative. The Beginner's Guide to Dimensionality Reduction. Starting from the second iteration, Leiden outperformed Louvain in terms of the percentage of badly connected communities. Scaling of benchmark results for network size. 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. 2016. Int. Conversely, if Leiden does not find subcommunities, there is no guarantee that modularity cannot be increased by splitting up the community. We name our algorithm the Leiden algorithm, after the location of its authors. Raghavan, U., Albert, R. & Kumara, S. Near linear time algorithm to detect community structures in large-scale networks. Then, in order . Ozaki, Naoto, Hiroshi Tezuka, and Mary Inaba. Rev. Phys. We find that the Leiden algorithm commonly finds partitions of higher quality in less time. E 92, 032801, https://doi.org/10.1103/PhysRevE.92.032801 (2015). Later iterations of the Louvain algorithm only aggravate the problem of disconnected communities, even though the quality function (i.e. Communities in ${\mathscr{P}}$ may be split into multiple subcommunities in ${{\mathscr{P}}}_{{\rm{refined}}}$. 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. Random moving can result in some huge speedups, since Louvain spends about 95% of its time computing the modularity gain from moving nodes. The Louvain algorithm guarantees that modularity cannot be increased by merging communities (it finds a locally optimal solution). 63, 23782392, https://doi.org/10.1002/asi.22748 (2012). The problem of disconnected communities has been observed before19,20, also in the context of the label propagation algorithm21. Then the Leiden algorithm can be run on the adjacency matrix. https://doi.org/10.1038/s41598-019-41695-z. Nodes 16 have connections only within this community, whereas node 0 also has many external connections. & Clauset, A. Furthermore, by relying on a fast local move approach, the Leiden algorithm runs faster than 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. Yang, Z., Algesheimer, R. & Tessone, C. J. Modularity optimization. Directed Undirected Homogeneous Heterogeneous Weighted 1. These nodes can be approximately identified based on whether neighbouring nodes have changed communities. B 86, 471, https://doi.org/10.1140/epjb/e2013-40829-0 (2013). 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 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 horizontal axis indicates the cumulative time taken to obtain the quality indicated on the vertical axis. Performance of modularity maximization in practical contexts. 2015. On the other hand, Leiden keeps finding better partitions, especially for higher values of , for which it is more difficult to identify good partitions. However, if communities are badly connected, this may lead to incorrect attributions of shared functionality. 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. Note that this code is designed for Seurat version 2 releases. For example, after four iterations, the Web UK network has 8% disconnected communities, but twice as many badly connected communities. N.J.v.E. to use Codespaces. We thank Lovro Subelj for his comments on an earlier version of this paper. 69 (2 Pt 2): 026113. http://dx.doi.org/10.1103/PhysRevE.69.026113. Clustering algorithms look for similarities or dissimilarities among data points so that similar ones can be grouped together. E 70, 066111, https://doi.org/10.1103/PhysRevE.70.066111 (2004). Nodes 13 should form a community and nodes 46 should form another community. We typically reduce the dimensionality of the data first by running PCA, then construct a neighbor graph in the reduced space. The increase in the percentage of disconnected communities is relatively limited for the Live Journal and Web of Science networks. In the worst case, communities may even be disconnected, especially when running the algorithm iteratively. import leidenalg as la import igraph as ig Example output. The Leiden algorithm is typically iterated: the output of one iteration is used as the input for the next iteration. In the worst case, almost a quarter of the communities are badly connected. MathSciNet Number of iterations until stability. The constant Potts model might give better communities in some cases, as it is not subject to the resolution limit. Waltman, L. & van Eck, N. J. Traag, Vincent, Ludo Waltman, and Nees Jan van Eck. In other words, modularity may hide smaller communities and may yield communities containing significant substructure. 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. SPATA2 currently offers the functions findSeuratClusters (), findMonocleClusters () and findNearestNeighbourClusters () which are wrapper around widely used clustering algorithms. USA 104, 36, https://doi.org/10.1073/pnas.0605965104 (2007). 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 particular, in an attempt to find better partitions, multiple consecutive iterations of the algorithm can be performed, using the partition identified in one iteration as starting point for the next iteration. For each community in a partition that was uncovered by the Louvain algorithm, we determined whether it is internally connected or not. 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. Based on project statistics from the GitHub repository for the PyPI package leiden-clustering, we found that it has been starred 1 times. Consider the partition shown in (a). Phys. Powered by DataCamp DataCamp To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/. J. The Louvain algorithm is illustrated in Fig. The algorithm moves individual nodes from one community to another to find a partition (b), which is then refined (c). This is not too difficult to explain. 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. To find an optimal grouping of cells into communities, we need some way of evaluating different partitions in the graph. The Leiden algorithm has been specifically designed to address the problem of badly connected communities. One may expect that other nodes in the old community will then also be moved to other communities. Leiden algorithm. CAS Traag, V. A., Van Dooren, P. & Nesterov, Y. We use six empirical networks in our analysis. J. In an experiment containing a mixture of cell types, each cluster might correspond to a different cell type. When the Leiden algorithm found that a community could be split into multiple subcommunities, we counted the community as badly connected. This problem is different from the well-known issue of the resolution limit of modularity14. Phys. However, in the case of the Web of Science network, more than 5% of the communities are disconnected in the first iteration. 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. CAS We prove that the new algorithm is guaranteed to produce partitions in which all communities are internally connected. 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. To address this problem, we introduce the Leiden algorithm.

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