9 shows that more than 10 iterations of the Leiden algorithm can be performed before the Louvain algorithm has finished its first iteration. Note that the object for Seurat version 3 has changed. 8, the Leiden algorithm is significantly faster than the Louvain algorithm also in empirical networks. An aggregate. Google Scholar. Google Scholar. V.A.T. CPM does not suffer from this issue13. Sci Rep 9, 5233 (2019). ADS We now consider the guarantees provided by the Leiden algorithm. Louvain community detection algorithm was originally proposed in 2008 as a fast community unfolding method for large networks. We conclude that the Leiden algorithm is strongly preferable to the Louvain algorithm. Louvain quickly converges to a partition and is then unable to make further improvements. Unlike the Louvain algorithm, the Leiden algorithm uses a fast local move procedure in this phase. The aggregate network is created based on the partition \({{\mathscr{P}}}_{{\rm{refined}}}\). A. In the case of modularity, communities may have significant substructure both because of the resolution limit and because of the shortcomings of Louvain. 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. As can be seen in Fig. You will not need much Python to use it. 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. Scientific Reports (Sci Rep) It is good at identifying small clusters. Furthermore, by relying on a fast local move approach, the Leiden algorithm runs faster than the Louvain algorithm. 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 Phys. Porter, M. A., Onnela, J.-P. & Mucha, P. J. E 92, 032801, https://doi.org/10.1103/PhysRevE.92.032801 (2015). 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. Correspondence to We will use sklearns K-Means implementation looking for 10 clusters in the original 784 dimensional data. Centre for Science and Technology Studies, Leiden University, Leiden, The Netherlands, You can also search for this author in B 86 (11): 471. https://doi.org/10.1140/epjb/e2013-40829-0. The second iteration of Louvain shows a large increase in the percentage of disconnected communities. For both algorithms, 10 iterations were performed. 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. In this way, Leiden implements the local moving phase more efficiently than Louvain. For example, for the Web of Science network, the first iteration takes about 110120 seconds, while subsequent iterations require about 40 seconds. Inf. (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. How many iterations of the Leiden clustering algorithm to perform. In particular, we show that Louvain may identify communities that are internally disconnected. There are many different approaches and algorithms to perform clustering tasks. In the initial stage of Louvain (when all nodes belong to their own community), nearly any move will result in a modularity gain, and it doesnt matter too much which move is chosen. Scaling of benchmark results for network size. When the Leiden algorithm found that a community could be split into multiple subcommunities, we counted the community as badly connected. Source Code (2018). At some point, the Louvain algorithm may end up in the community structure shown in Fig. In the case of the Louvain algorithm, after a stable iteration, all subsequent iterations will be stable as well. Note that this code is . For this network, Leiden requires over 750 iterations on average to reach a stable iteration. Once aggregation is complete we restart the local moving phase, and continue to iterate until everything converges down to one node. Google Scholar. Rev. Randomness in the selection of a community allows the partition space to be explored more broadly. The above results shows that the problem of disconnected and badly connected communities is quite pervasive in practice. For each network, Table2 reports the maximal modularity obtained using the Louvain and the Leiden algorithm. Besides the relative flexibility of the implementation, it also scales well, and can be run on graphs of millions of nodes (as long as they can fit in memory). Rev. These steps are repeated until no further improvements can be made. Good, B. H., De Montjoye, Y. Resolution Limit in Community Detection. Proc. 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. However, modularity suffers from a difficult problem known as the resolution limit (Fortunato and Barthlemy 2007). A Smart Local Moving Algorithm for Large-Scale Modularity-Based Community Detection. Eur. Zenodo, https://doi.org/10.5281/zenodo.1469357 https://github.com/vtraag/leidenalg. Technol. In the Louvain algorithm, an aggregate network is created based on the partition \({\mathscr{P}}\) resulting from the local moving phase. 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). Sci. Starting from the second iteration, Leiden outperformed Louvain in terms of the percentage of badly connected communities. Community detection is an important task in the analysis of complex networks. The Leiden algorithm is typically iterated: the output of one iteration is used as the input for the next iteration. Clustering algorithms look for similarities or dissimilarities among data points so that similar ones can be grouped together. The nodes are added to the queue in a random order. In this section, we analyse and compare the performance of the two algorithms in practice. This continues until the queue is empty. Louvain pruning keeps track of a list of nodes that have the potential to change communities, and only revisits nodes in this list, which is much smaller than the total number of nodes. This is the crux of the Leiden paper, and the authors show that this exact problem happens frequently in practice. Based on this partition, an aggregate network is created (c). 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. Note that communities found by the Leiden algorithm are guaranteed to be connected. This package implements the Leiden algorithm in C++ and exposes it to python.It relies on (python-)igraph for it to function. When a sufficient number of neighbours of node 0 have formed a community in the rest of the network, it may be optimal to move node 0 to this community, thus creating the situation depicted in Fig. 104 (1): 3641. Class wrapper based on scanpy to use the Leiden algorithm to directly cluster your data matrix with a scikit-learn flavor. All experiments were run on a computer with 64 Intel Xeon E5-4667v3 2GHz CPUs and 1TB internal memory. Ayan Sinha, David F. Gleich & Karthik Ramani, Marinka Zitnik, Rok Sosi & Jure Leskovec, Zhenqi Lu, Johan Wahlstrm & Arye Nehorai, Natalie Stanley, Roland Kwitt, Peter J. Mucha, Scientific Reports ADS Not. 10, 186198, https://doi.org/10.1038/nrn2575 (2009). 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. Other networks show an almost tenfold increase in the percentage of disconnected communities. For the Amazon, DBLP and Web UK networks, Louvain yields on average respectively 23%, 16% and 14% badly connected communities. S3. 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. In this post, I will cover one of the common approaches which is hierarchical clustering. Yang, Z., Algesheimer, R. & Tessone, C. J. Speed of the first iteration of the Louvain and the Leiden algorithm for six empirical networks. Phys. Sci. Acad. Traag, V A. V. A. Traag. In this case, refinement does not change the partition (f). E 69, 026113, https://doi.org/10.1103/PhysRevE.69.026113 (2004). We used modularity with a resolution parameter of =1 for the experiments. to use Codespaces. After a stable iteration of the Leiden algorithm, the algorithm may still be able to make further improvements in later iterations. The Leiden algorithm is considerably more complex than the Louvain algorithm. The algorithm then moves individual nodes in the aggregate network (d). The Louvain algorithm10 is very simple and elegant. MathSciNet wrote the manuscript. 4, in the first iteration of the Louvain algorithm, the percentage of badly connected communities can be quite high. MATH Please Besides being pervasive, the problem is also sizeable. Phys. Phys. B 86, 471, https://doi.org/10.1140/epjb/e2013-40829-0 (2013). In the Louvain algorithm, a node may be moved to a different community while it may have acted as a bridge between different components of its old community. This should be the first preference when choosing an algorithm. Nodes 16 have connections only within this community, whereas node 0 also has many external connections. 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. A structure that is more informative than the unstructured set of clusters returned by flat clustering. performed the experimental analysis. Rev. On Modularity Clustering. 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. We show that this algorithm has a major defect that largely went unnoticed until now: the Louvain algorithm may yield arbitrarily badly connected communities. 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. partition_type : Optional [ Type [ MutableVertexPartition ]] (default: None) Type of partition to use. CAS For each network, we repeated the experiment 10 times. Therefore, by selecting a community based by choosing randomly from the neighbors, we choose the community to evaluate with probability proportional to the composition of the neighbors communities. Finally, we compare the performance of the algorithms on the empirical networks. The property of -separation is also guaranteed by the Louvain algorithm. However, as increases, the Leiden algorithm starts to outperform the Louvain algorithm. We start by initialising a queue with all nodes in the network. The Leiden algorithm provides several guarantees. Article We find that the Leiden algorithm is faster than the Louvain algorithm and uncovers better partitions, in addition to providing explicit guarantees. Nat. It implies uniform -density and all the other above-mentioned properties. Article In this case we know the answer is exactly 10. An overview of the various guarantees is presented in Table1. On the other hand, Leiden keeps finding better partitions, especially for higher values of , for which it is more difficult to identify good partitions. 9, the Leiden algorithm also performs better than the Louvain algorithm in terms of the quality of the partitions that are obtained. Newman, M. E. J. By creating the aggregate network based on \({{\mathscr{P}}}_{{\rm{refined}}}\) rather than P, the Leiden algorithm has more room for identifying high-quality partitions. Hence, in general, Louvain may find arbitrarily badly connected communities. Basically, there are two types of hierarchical cluster analysis strategies - 1. This contrasts with optimisation algorithms such as simulated annealing, which do allow the quality function to decrease4,8. Rev. volume9, Articlenumber:5233 (2019) Waltman, L. & van Eck, N. J. In this way, the constant acts as a resolution parameter, and setting the constant higher will result in fewer communities. Rev. When iterating Louvain, the quality of the partitions will keep increasing until the algorithm is unable to make any further improvements. From Louvain to Leiden: Guaranteeing Well-Connected Communities, October. In the first iteration, Leiden is roughly 220 times faster than Louvain. Klavans, R. & Boyack, K. W. Which Type of Citation Analysis Generates the Most Accurate Taxonomy of Scientific and Technical Knowledge? Random moving can result in some huge speedups, since Louvain spends about 95% of its time computing the modularity gain from moving nodes. We also suggested that the Leiden algorithm is faster than the Louvain algorithm, because of the fast local move approach. Another important difference between the Leiden algorithm and the Louvain algorithm is the implementation of the local moving phase. 92 (3): 032801. http://dx.doi.org/10.1103/PhysRevE.92.032801. Importantly, mergers are performed only within each community of the partition \({\mathscr{P}}\). The DBLP network is somewhat more challenging, requiring almost 80 iterations on average to reach a stable iteration. This contrasts to benchmark networks, for which Leiden often converges after a few iterations. 2013. This is not too difficult to explain. Table2 provides an overview of the six networks. You signed in with another tab or window. Clustering is a machine learning technique in which similar data points are grouped into the same cluster based on their attributes. Nodes 13 should form a community and nodes 46 should form another community. All authors conceived the algorithm and contributed to the source code. Phys. There is an entire Leiden package in R-cran here The horizontal axis indicates the cumulative time taken to obtain the quality indicated on the vertical axis. The property of -connectivity is a slightly stronger variant of ordinary connectivity. 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. Article By moving these nodes, Louvain creates badly connected communities. In short, the problem of badly connected communities has important practical consequences. The steps for agglomerative clustering are as follows: USA 104, 36, https://doi.org/10.1073/pnas.0605965104 (2007). Fast Unfolding of Communities in Large Networks. Journal of Statistical , January. SPATA2 currently offers the functions findSeuratClusters (), findMonocleClusters () and findNearestNeighbourClusters () which are wrapper around widely used clustering algorithms. Random moving is a very simple adjustment to Louvain local moving proposed in 2015 (Traag 2015). We use six empirical networks in our analysis. Figure3 provides an illustration of the algorithm. Rev. Then the Leiden algorithm can be run on the adjacency matrix. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate. Are you sure you want to create this branch? Here is some small debugging code I wrote to find this. We here introduce the Leiden algorithm, which guarantees that communities are well connected. This may have serious consequences for analyses based on the resulting partitions. J. 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. Weights for edges an also be passed to the leiden algorithm either as a separate vector or weights or a weighted adjacency matrix. Both conda and PyPI have leiden clustering in Python which operates via iGraph. This is very similar to what the smart local moving algorithm does. Number of iterations until stability. Additionally, we implemented a Python package, available from https://github.com/vtraag/leidenalg and deposited at Zenodo24). Mech. Google Scholar. Speed and quality for the first 10 iterations of the Louvain and the Leiden algorithm for six empirical networks. 2(b). In practical applications, the Leiden algorithm convincingly outperforms the Louvain algorithm, both in terms of speed and in terms of quality of the results, as shown by the experimental analysis presented in this paper. Google Scholar. J. Stat. Phys. Directed Undirected Homogeneous Heterogeneous Weighted 1. Phys. As the use of clustering is highly depending on the biological question it makes sense to use several approaches and algorithms. Traag, V. 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. Article You are using a browser version with limited support for CSS. 7, whereas Louvain becomes much slower for more difficult partitions, Leiden is much less affected by the difficulty of the partition. Excluding node mergers that decrease the quality function makes the refinement phase more efficient. 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. Nonetheless, some networks still show large differences. 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. 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. Graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. That is, one part of such an internally disconnected community can reach another part only through a path going outside the community. That is, no subset can be moved to a different community. 10008, 6, https://doi.org/10.1088/1742-5468/2008/10/P10008 (2008). In particular, benchmark networks have a rather simple structure. To study the scaling of the Louvain and the Leiden algorithm, we rely on a variant of a well-known approach for constructing benchmark networks28. This contrasts with the Leiden algorithm. Fortunato, S. Community detection in graphs. Use Git or checkout with SVN using the web URL. For example, after four iterations, the Web UK network has 8% disconnected communities, but twice as many badly connected communities. Value. Rev. 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. 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 thick edges in Fig. Each point corresponds to a certain iteration of an algorithm, with results averaged over 10 experiments. Bae, S., Halperin, D., West, J. D., Rosvall, M. & Howe, B. Scalable and Efficient Flow-Based Community Detection for Large-Scale Graph Analysis. However, as shown in this paper, the Louvain algorithm has a major shortcoming: the algorithm yields communities that may be arbitrarily badly connected. 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. ADS The Louvain algorithm starts from a singleton partition in which each node is in its own community (a). 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. https://doi.org/10.1038/s41598-019-41695-z. 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 . where nc is the number of nodes in community c. The interpretation of the resolution parameter is quite straightforward. Some of these nodes may very well act as bridges, similarly to node 0 in the above example. The corresponding results are presented in the Supplementary Fig. Leiden keeps finding better partitions for empirical networks also after the first 10 iterations of the algorithm. We applied the Louvain and the Leiden algorithm to exactly the same networks, using the same seed for the random number generator. Sign up for the Nature Briefing newsletter what matters in science, free to your inbox daily. It only implies that individual nodes are well connected to their community. 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. In addition, we prove that the algorithm converges to an asymptotically stable partition in which all subsets of all communities are locally optimally assigned. Although originally defined for modularity, the Louvain algorithm can also be used to optimise other quality functions. Narrow scope for resolution-limit-free community detection. These are the same networks that were also studied in an earlier paper introducing the smart local move algorithm15. Moreover, when the algorithm is applied iteratively, it converges to a partition in which all subsets of all communities are guaranteed to be locally optimally assigned. Such algorithms are rather slow, making them ineffective for large networks. In the aggregation phase, an aggregate network is created based on the partition obtained in the local moving phase. 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. Cluster your data matrix with the Leiden algorithm. To ensure readability of the paper to the broadest possible audience, we have chosen to relegate all technical details to the Supplementary Information. Moreover, Louvain has no mechanism for fixing these communities. Duch, J. The solution provided by Leiden is based on the smart local moving algorithm. 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 Once no further increase in modularity is possible by moving any node to its neighboring community, we move to the second phase of the algorithm: aggregation. The difference in computational time is especially pronounced for larger networks, with Leiden being up to 20 times faster than Louvain in empirical networks. 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). The quality improvement realised by the Leiden algorithm relative to the Louvain algorithm is larger for empirical networks than for benchmark networks. 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. First iteration runtime for empirical networks. The leidenalg package facilitates community detection of networks and builds on the package igraph. As the problem of modularity optimization is NP-hard, we need heuristic methods to optimize modularity (or CPM). CAS In fact, if we keep iterating the Leiden algorithm, it will converge to a partition without any badly connected communities, as discussed earlier. 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.
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