leiden clustering explained
As can be seen in Fig. In fact, if we keep iterating the Leiden algorithm, it will converge to a partition without any badly connected communities, as discussed earlier. We prove that the Leiden algorithm yields communities that are guaranteed to be connected. Below, the quality of a partition is reported as \(\frac{ {\mathcal H} }{2m}\), where H is defined in Eq. PDF leiden: R Implementation of Leiden Clustering Algorithm 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). Nonlin. Wolf, F. A. et al. To address this important shortcoming, we introduce a new algorithm that is faster, finds better partitions and provides explicit guarantees and bounds. GitHub on Feb 15, 2020 Do you think the performance improvements will also be implemented in leidenalg? Cluster your data matrix with the Leiden algorithm. The differences are not very large, which is probably because both algorithms find partitions for which the quality is close to optimal, related to the issue of the degeneracy of quality functions29. Phys. 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. We therefore require a more principled solution, which we will introduce in the next section. The refined partition \({{\mathscr{P}}}_{{\rm{refined}}}\) is obtained as follows. In this case, refinement does not change the partition (f). volume9, Articlenumber:5233 (2019) CAS The constant Potts model (CPM), so called due to the use of a constant value in the Potts model, is an alternative objective function for community detection. Based on project statistics from the GitHub repository for the PyPI package leiden-clustering, we found that it has been starred 1 times. and L.W. Therefore, clustering algorithms look for similarities or dissimilarities among data points. The solution provided by Leiden is based on the smart local moving algorithm. However, focussing only on disconnected communities masks the more fundamental issue: Louvain finds arbitrarily badly connected communities. MATH N.J.v.E. Higher resolutions lead to more communities and lower resolutions lead to fewer communities, similarly to the resolution parameter for modularity. Table2 provides an overview of the six networks. o CLIQUE (Clustering in Quest): - CLIQUE is a combination of density-based and grid-based clustering algorithm. leiden function - RDocumentation Performance of modularity maximization in practical contexts. 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. Thank you for visiting nature.com. 2. Brandes, U. et al. In other words, communities are guaranteed to be well separated. MathSciNet ML | Hierarchical clustering (Agglomerative and Divisive clustering Waltman, L. & van Eck, N. J. 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). 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. The Leiden algorithm starts from a singleton partition (a). Introduction leidenalg 0.9.2.dev0+gb530332.d20221214 documentation Klavans, R. & Boyack, K. W. Which Type of Citation Analysis Generates the Most Accurate Taxonomy of Scientific and Technical Knowledge? Here is some small debugging code I wrote to find this. This will compute the Leiden clusters and add them to the Seurat Object Class. Number of iterations until stability. The Leiden algorithm guarantees all communities to be connected, but it may yield badly connected communities. Google Scholar. Rev. This amounts to a clustering problem, where we aim to learn an optimal set of groups (communities) from the observed data. Louvain has two phases: local moving and aggregation. 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Int. However, for higher values of , Leiden becomes orders of magnitude faster than Louvain, reaching 10100 times faster runtimes for the largest networks. Ozaki, N., Tezuka, H. & Inaba, M. A Simple Acceleration Method for the Louvain Algorithm. Badly connected communities. Traag, V. A., Van Dooren, P. & Nesterov, Y. In the most difficult case (=0.9), Louvain requires almost 2.5 days, while Leiden needs fewer than 10 minutes. First, we created a specified number of nodes and we assigned each node to a community. This package implements the Leiden algorithm in C++ and exposes it to python.It relies on (python-)igraph for it to function. Importantly, mergers are performed only within each community of the partition \({\mathscr{P}}\). We use six empirical networks in our analysis. 10X10Xleiden - Additionally, we implemented a Python package, available from https://github.com/vtraag/leidenalg and deposited at Zenodo24). Four popular community detection algorithms are explained . Local Resolution-Limit-Free Potts Model for Community Detection. Phys. 2.3. IEEE Trans. Community detection is often used to understand the structure of large and complex networks. In the aggregation phase, an aggregate network is created based on the partition obtained in the local moving phase. With one exception (=0.2 and n=107), all results in Fig. Raghavan, U., Albert, R. & Kumara, S. Near linear time algorithm to detect community structures in large-scale networks. Google Scholar. Am. It is a directed graph if the adjacency matrix is not symmetric. It was originally developed for modularity optimization, although the same method can be applied to optimize CPM. Communities in \({\mathscr{P}}\) may be split into multiple subcommunities in \({{\mathscr{P}}}_{{\rm{refined}}}\). The aggregate network is created based on the partition \({{\mathscr{P}}}_{{\rm{refined}}}\). Rev. We abbreviate the leidenalg package as la and the igraph package as ig in all Python code throughout this documentation. Importantly, the first iteration of the Leiden algorithm is the most computationally intensive one, and subsequent iterations are faster. From Louvain to Leiden: guaranteeing well-connected communities - Nature Data Eng. In this stage we essentially collapse communities down into a single representative node, creating a new simplified graph. The R implementation of Leiden can be run directly on the snn igraph object in Seurat. The authors act as bibliometric consultants to CWTS B.V., which makes use of community detection algorithms in commercial products and services. 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. Nat. Subset optimality is the strongest guarantee that is provided by the Leiden algorithm. Eng. Rev. That is, one part of such an internally disconnected community can reach another part only through a path going outside the community. Any sub-networks that are found are treated as different communities in the next aggregation step. Two ways of doing this are graph modularity (Newman and Girvan 2004) and the constant Potts model (Ronhovde and Nussinov 2010). Please 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. 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. 2010. Basically, there are two types of hierarchical cluster analysis strategies - 1. bioRxiv, https://doi.org/10.1101/208819 (2018). MathSciNet Sci Rep 9, 5233 (2019). We now show that the Louvain algorithm may find arbitrarily badly connected communities. Rep. 486, 75174, https://doi.org/10.1016/j.physrep.2009.11.002 (2010). leiden: Run Leiden clustering algorithm in leiden: R Implementation of & Clauset, A. First calculate k-nearest neighbors and construct the SNN graph. To use Leiden with the Seurat pipeline for a Seurat Object object that has an SNN computed (for example with Seurat::FindClusters with save.SNN = TRUE). Usually, the Louvain algorithm starts from a singleton partition, in which each node is in its own community. The 'devtools' package will be used to install 'leiden' and the dependancies (igraph and reticulate). Community detection in complex networks using extremal optimization. Duch, J. A community size of 50 nodes was used for the results presented below, but larger community sizes yielded qualitatively similar results. This is not too difficult to explain. Faster Unfolding of Communities: Speeding up the Louvain Algorithm. Phys. The algorithm then locally merges nodes in \({{\mathscr{P}}}_{{\rm{refined}}}\): nodes that are on their own in a community in \({{\mathscr{P}}}_{{\rm{refined}}}\) can be merged with a different community. The Louvain algorithm guarantees that modularity cannot be increased by merging communities (it finds a locally optimal solution). Using the fast local move procedure, the first visit to all nodes in a network in the Leiden algorithm is the same as in the Louvain algorithm. b, The elephant graph (in a) is clustered using the Leiden clustering algorithm 51 (resolution r = 0.5). This is the crux of the Leiden paper, and the authors show that this exact problem happens frequently in practice. While current approaches are successful in reducing the number of sequence alignments performed, the generated clusters are . Modularity optimization. 1 I am using the leiden algorithm implementation in iGraph, and noticed that when I repeat clustering using the same resolution parameter, I get different results. 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. In short, the problem of badly connected communities has important practical consequences. Then optimize the modularity function to determine clusters. 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 is good at identifying small clusters. ADS The Leiden algorithm is considerably more complex than the Louvain algorithm. 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. The algorithm is run iteratively, using the partition identified in one iteration as starting point for the next iteration. Runtime versus quality for benchmark networks. 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). As the problem of modularity optimization is NP-hard, we need heuristic methods to optimize modularity (or CPM). If nothing happens, download Xcode and try again. 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. Provided by the Springer Nature SharedIt content-sharing initiative. 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. The current state of the art when it comes to graph-based community detection is Leiden, which incorporates about 10 years of algorithmic improvements to the original Louvain method. More subtle problems may occur as well, causing Louvain to find communities that are connected, but only in a very weak sense. We gratefully acknowledge computational facilities provided by the LIACS Data Science Lab Computing Facilities through Frank Takes. Neurosci. Hence, in general, Louvain may find arbitrarily badly connected communities. Finally, we demonstrate the excellent performance of the algorithm for several benchmark and real-world 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. Google Scholar. The Leiden community detection algorithm outperforms other clustering methods. As we prove in SectionC1 of the Supplementary Information, even when node mergers that decrease the quality function are excluded, the optimal partition of a set of nodes can still be uncovered. In later stages, most neighbors will belong to the same community, and its very likely that the best move for the node is to the community that most of its neighbors already belong to. Article As shown in Fig. However, modularity suffers from a difficult problem known as the resolution limit (Fortunato and Barthlemy 2007). This way of defining the expected number of edges is based on the so-called configuration model. The main ideas of our algorithm are explained in an intuitive way in the main text of the paper. https://doi.org/10.1038/s41598-019-41695-z. 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. the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Directed Undirected Homogeneous Heterogeneous Weighted 1. 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. 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. Google Scholar. Nevertheless, depending on the relative strengths of the different connections, these nodes may still be optimally assigned to their current community. This commit does not belong to any branch on this repository, and may belong to a fork outside of the repository. The classic Louvain algorithm should be avoided due to the known problem with disconnected communities. When the Leiden algorithm found that a community could be split into multiple subcommunities, we counted the community as badly connected. After a stable iteration of the Leiden algorithm, the algorithm may still be able to make further improvements in later iterations. 69 (2 Pt 2): 026113. http://dx.doi.org/10.1103/PhysRevE.69.026113. A. E 69, 026113, https://doi.org/10.1103/PhysRevE.69.026113 (2004). The speed difference is especially large for larger networks. In the fast local move procedure in the Leiden algorithm, only nodes whose neighbourhood has changed are visited. However, if communities are badly connected, this may lead to incorrect attributions of shared functionality. Agglomerative Clustering: Also known as bottom-up approach or hierarchical agglomerative clustering (HAC). 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 74, 016110, https://doi.org/10.1103/PhysRevE.74.016110 (2006). 4. The percentage of disconnected communities even jumps to 16% for the DBLP network. 2015. https://doi.org/10.1038/s41598-019-41695-z, DOI: https://doi.org/10.1038/s41598-019-41695-z. This enables us to find cases where its beneficial to split a community. 6 show that Leiden outperforms Louvain in terms of both computational time and quality of the partitions. We generated benchmark networks in the following way. Clustering biological sequences with dynamic sequence similarity 7, whereas Louvain becomes much slower for more difficult partitions, Leiden is much less affected by the difficulty of the partition. 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. 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 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. & Bornholdt, S. Statistical mechanics of community detection. Google Scholar. It identifies the clusters by calculating the densities of the cells. Bullmore, E. & Sporns, O. For all networks, Leiden identifies substantially better partitions than Louvain. 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. Cite this article. Ronhovde, Peter, and Zohar Nussinov. Leiden is both faster than Louvain and finds better partitions. Sci. Phys. In the first iteration, Leiden is roughly 220 times faster than Louvain. This is similar to ideas proposed recently as pruning16 and in a slightly different form as prioritisation17. In fact, by implementing the refinement phase in the right way, several attractive guarantees can be given for partitions produced by the Leiden algorithm. 2 represent stronger connections, while the other edges represent weaker connections. We conclude that the Leiden algorithm is strongly preferable to the Louvain algorithm. Uniform -density means that no matter how a community is partitioned into two parts, the two parts will always be well connected to each other. 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. (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. 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. Networks with high modularity have dense connections between the nodes within modules but sparse connections between nodes in different modules. 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. 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 \({\mathscr{P}}\). Lancichinetti, A. CPM is defined as. PubMedGoogle Scholar. Scanpy Tutorial - 65k PBMCs - Parse Biosciences Due to the resolution limit, modularity may cause smaller communities to be clustered into larger communities. This contrasts to benchmark networks, for which Leiden often converges after a few iterations. The problem of disconnected communities has been observed before19,20, also in the context of the label propagation algorithm21. 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. In the Louvain algorithm, an aggregate network is created based on the partition \({\mathscr{P}}\) resulting from the local moving phase. However, the initial partition for the aggregate network is based on P, just like in the Louvain algorithm. Rev. An iteration of the Leiden algorithm in which the partition does not change is called a stable iteration. 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. Leiden is the most recent major development in this space, and highlighted a flaw in the original Louvain algorithm (Traag, Waltman, and Eck 2018). The second iteration of Louvain shows a large increase in the percentage of disconnected communities. 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. leidenalg. The Leiden algorithm provides several guarantees. Electr. scanpy_04_clustering - GitHub Pages The algorithm moves individual nodes from one community to another to find a partition (b), which is then refined (c). First, we show that the Louvain algorithm finds disconnected communities, and more generally, badly connected communities in the empirical networks. A Simple Acceleration Method for the Louvain Algorithm. Int. 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 . In this section, we analyse and compare the performance of the two algorithms in practice. Cluster cells using Louvain/Leiden community detection Description. 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. V.A.T. To use Leiden with the Seurat pipeline for a Seurat Object object that has an SNN computed (for example with Seurat::FindClusters with save.SNN = TRUE ). 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. PubMed Central We will use sklearns K-Means implementation looking for 10 clusters in the original 784 dimensional data. However, as increases, the Leiden algorithm starts to outperform the Louvain 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. It maximizes a modularity score for each community, where the modularity quantifies the quality of an assignment of nodes to communities. The phase one loop can be greatly accelerated by finding the nodes that have the potential to change community and only revisit those nodes. The algorithm continues to move nodes in the rest of the network. Phys. This will compute the Leiden clusters and add them to the Seurat Object Class. In the worst case, almost a quarter of the communities are badly connected. This is similar to what we have seen for benchmark networks. In the first step of the next iteration, Louvain will again move individual nodes in the network. Crucially, however, the percentage of badly connected communities decreases with each iteration of the Leiden algorithm. & Girvan, M. Finding and evaluating community structure in networks. Leiden consists of the following steps: The refinement step allows badly connected communities to be split before creating the aggregate network. Speed of the first iteration of the Louvain and the Leiden algorithm for six empirical networks. Using UMAP for Clustering umap 0.5 documentation - Read the Docs and JavaScript. leiden-clustering - Python Package Health Analysis | Snyk The solution proposed in smart local moving is to alter how the local moving step in Louvain works. The nodes are added to the queue in a random order. Blondel, V D, J L Guillaume, and R Lambiotte. Rev. ADS CAS Resolution Limit in Community Detection. Proc. E 81, 046106, https://doi.org/10.1103/PhysRevE.81.046106 (2010). CAS Below we offer an intuitive explanation of these properties. We then created a certain number of edges such that a specified average degree \(\langle k\rangle \) was obtained. This contrasts with the Leiden algorithm. This represents the following graph structure. Traag, Vincent, Ludo Waltman, and Nees Jan van Eck. Node optimality is also guaranteed after a stable iteration of the Louvain algorithm. Finding communities in large networks is far from trivial: algorithms need to be fast, but they also need to provide high-quality results. E 74, 036104, https://doi.org/10.1103/PhysRevE.74.036104 (2006). The percentage of badly connected communities is less affected by the number of iterations of the Louvain algorithm.
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