The Leiden algorithm guarantees all communities to be connected, but it may yield badly connected communities. From Louvain to Leiden: Guaranteeing Well-Connected Communities, October. For this network, Leiden requires over 750 iterations on average to reach a stable iteration. Data Eng. Newman, M. E. J. Rep. 486, 75174, https://doi.org/10.1016/j.physrep.2009.11.002 (2010). This function takes a cell_data_set as input, clusters the cells using . E Stat. The authors act as bibliometric consultants to CWTS B.V., which makes use of community detection algorithms in commercial products and services. Modularity is given by. Rev. 2.3. Our analysis is based on modularity with resolution parameter =1. Runtime versus quality for empirical networks. Crucially, however, the percentage of badly connected communities decreases with each iteration of the Leiden algorithm. 2010. We then created a certain number of edges such that a specified average degree \(\langle k\rangle \) was obtained. 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). We generated networks with n=103 to n=107 nodes. Basically, there are two types of hierarchical cluster analysis strategies - 1. It is good at identifying small clusters. 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. E 78, 046110, https://doi.org/10.1103/PhysRevE.78.046110 (2008). 2008. where >0 is a resolution parameter4. We first applied the Scanpy pipeline, including its clustering method (Leiden clustering), on the PBMC dataset. Phys. Source Code (2018). We now compare how the Leiden and the Louvain algorithm perform for the six empirical networks listed in Table2. It states that there are no communities that can be merged. Communities were all of equal size. A Comparative Analysis of Community Detection Algorithms on Artificial Networks. Again, if communities are badly connected, this may lead to incorrect inferences of topics, which will affect bibliometric analyses relying on the inferred topics. 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. Hence, in general, Louvain may find arbitrarily badly connected communities. Number of iterations until stability. Discov. Louvain quickly converges to a partition and is then unable to make further improvements. 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. Ozaki, N., Tezuka, H. & Inaba, M. A Simple Acceleration Method for the Louvain Algorithm. In this post, I will cover one of the common approaches which is hierarchical clustering. Waltman, L. & van Eck, N. J. 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. Anyone you share the following link with will be able to read this content: Sorry, a shareable link is not currently available for this article. Additionally, we implemented a Python package, available from https://github.com/vtraag/leidenalg and deposited at Zenodo24). python - Leiden Clustering results are not always the same given the For each network, Table2 reports the maximal modularity obtained using the Louvain and the Leiden algorithm. The nodes are added to the queue in a random order. 8, the Leiden algorithm is significantly faster than the Louvain algorithm also in empirical networks. However, the initial partition for the aggregate network is based on P, just like in the Louvain algorithm. Faster Unfolding of Communities: Speeding up the Louvain Algorithm. Phys. Soft Matter Phys. How to get started with louvain/leiden algorithm with UMAP in R 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. The Web of Science network is the most difficult one. This will compute the Leiden clusters and add them to the Seurat Object Class. First calculate k-nearest neighbors and construct the SNN graph. Nodes 06 are in the same community. E 72, 027104, https://doi.org/10.1103/PhysRevE.72.027104 (2005). 2007. Finally, we compare the performance of the algorithms on the empirical networks. At some point, the Louvain algorithm may end up in the community structure shown in Fig. A partition of clusters as a vector of integers Examples Inf. 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. 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. With one exception (=0.2 and n=107), all results in Fig. The thick edges in Fig. Speed and quality of the Louvain and the Leiden algorithm for benchmark networks of increasing size (two iterations). 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. It was originally developed for modularity optimization, although the same method can be applied to optimize CPM. 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. Furthermore, by relying on a fast local move approach, the Leiden algorithm runs faster than the Louvain algorithm. As can be seen in Fig. A score of -1 means that there are no edges connecting nodes within the community, and they instead all connect nodes outside the community. As can be seen in Fig. The horizontal axis indicates the cumulative time taken to obtain the quality indicated on the vertical axis. ADS When node 0 is moved to a different community, the red community becomes internally disconnected, as shown in (b). The Leiden algorithm starts from a singleton partition (a). These steps are repeated until no further improvements can be made. I tracked the number of clusters post-clustering at each step. 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. MATH In the fast local move procedure in the Leiden algorithm, only nodes whose neighbourhood has changed are visited. However, it is also possible to start the algorithm from a different partition15. The random component also makes the algorithm more explorative, which might help to find better community structures. Bullmore, E. & Sporns, O. This is the crux of the Leiden paper, and the authors show that this exact problem happens frequently in practice. The 'devtools' package will be used to install 'leiden' and the dependancies (igraph and reticulate). The difference in computational time is especially pronounced for larger networks, with Leiden being up to 20 times faster than Louvain in empirical networks. 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. 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. In general, Leiden is both faster than Louvain and finds better partitions. Subpartition -density does not imply that individual nodes are locally optimally assigned. A number of iterations of the Leiden algorithm can be performed before the Louvain algorithm has finished its first iteration. Source Code (2018). You will not need much Python to use it. Waltman, L. & van Eck, N. J. Provided by the Springer Nature SharedIt content-sharing initiative. In fact, if we keep iterating the Leiden algorithm, it will converge to a partition without any badly connected communities, as discussed earlier. Clustering with the Leiden Algorithm in R - cran.microsoft.com Sci. The algorithm moves individual nodes from one community to another to find a partition (b), which is then refined (c). https://doi.org/10.1038/s41598-019-41695-z. Louvain algorithm. ADS Technol. The triumphs and limitations of computational methods for - Nature Traag, V.A., Waltman, L. & van Eck, N.J. From Louvain to Leiden: guaranteeing well-connected communities. and L.W. Here is some small debugging code I wrote to find this. We denote by ec the actual number of edges in community c. The expected number of edges can be expressed as \(\frac{{K}_{c}^{2}}{2m}\), where Kc is the sum of the degrees of the nodes in community c and m is the total number of edges in the network. & Bornholdt, S. Statistical mechanics of community detection. CPM has the advantage that it is not subject to the resolution limit. We find that the Leiden algorithm commonly finds partitions of higher quality in less time. (2) and m is the number of edges. The speed difference is especially large for larger networks. The algorithm moves individual nodes from one community to another to find a partition (b), which is then refined (c). The fast local move procedure can be summarised as follows. We find that the Leiden algorithm is faster than the Louvain algorithm and uncovers better partitions, in addition to providing explicit guarantees. The nodes that are more interconnected have been partitioned into separate clusters. In this paper, we show that the Louvain algorithm has a major problem, for both modularity and CPM. Algorithmics 16, 2.1, https://doi.org/10.1145/1963190.1970376 (2011). V.A.T. Any sub-networks that are found are treated as different communities in the next aggregation step. Nevertheless, depending on the relative strengths of the different connections, these nodes may still be optimally assigned to their current community. The new algorithm integrates several earlier improvements, incorporating a combination of smart local move15, fast local move16,17 and random neighbour move18. Class wrapper based on scanpy to use the Leiden algorithm to directly cluster your data matrix with a scikit-learn flavor. To find an optimal grouping of cells into communities, we need some way of evaluating different partitions in the graph. Run the code above in your browser using DataCamp Workspace. 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. Empirical networks show a much richer and more complex structure. The refined partition \({{\mathscr{P}}}_{{\rm{refined}}}\) is obtained as follows. . The classic Louvain algorithm should be avoided due to the known problem with disconnected communities. At some point, node 0 is considered for moving. Article After running local moving, we end up with a set of communities where we cant increase the objective function (eg, modularity) by moving any node to any neighboring 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. Instead, a node may be merged with any community for which the quality function increases. The algorithm is run iteratively, using the partition identified in one iteration as starting point for the next iteration. Duch, J. We used modularity with a resolution parameter of =1 for the experiments. cluster_leiden: Finding community structure of a graph using the Leiden 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. Sci. Phys. PubMed Central Detecting communities in a network is therefore an important problem. Leiden keeps finding better partitions for empirical networks also after the first 10 iterations of the algorithm. The Louvain method for community detection is a popular way to discover communities from single-cell data. Not. In this case, refinement does not change the partition (f). It means that there are no individual nodes that can be moved to a different community. This contrasts to benchmark networks, for which Leiden often converges after a few iterations.