Faster Unfolding of Communities: Speeding up the Louvain Algorithm. Phys. Rev. contrastive-sc works best on datasets with fewer clusters when using the KMeans clustering and conversely for Leiden. The main ideas of our algorithm are explained in an intuitive way in the main text of the paper. Cluster your data matrix with the Leiden algorithm. As discussed earlier, the Louvain algorithm does not guarantee connectivity. 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 leidenalg package facilitates community detection of networks and builds on the package igraph. Hence, no further improvements can be made after a stable iteration of the Louvain algorithm. 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. Traag, V. A. To obtain Louvain algorithm. Publishers note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. The corresponding results are presented in the Supplementary Fig. We show that this algorithm has a major defect that largely went unnoticed until now: the Louvain algorithm may yield arbitrarily badly connected communities. To do this we just sum all the edge weights between nodes of the corresponding communities to get a single weighted edge between them, and collapse each community down to a single new node. J. In particular, we show that Louvain may identify communities that are internally disconnected. partition_type : Optional [ Type [ MutableVertexPartition ]] (default: None) Type of partition to use. 2010. For each network, we repeated the experiment 10 times. Fast Unfolding of Communities in Large Networks. Journal of Statistical , January. Hence, the community remains disconnected, unless it is merged with another community that happens to act as a bridge. The smart local moving algorithm (Waltman and Eck 2013) identified another limitation in the original Louvain method: it isnt able to split communities once theyre merged, even when it may be very beneficial to do so. Clustering with the Leiden Algorithm in R Finding community structure in networks using the eigenvectors of matrices. Preprocessing and clustering 3k PBMCs Scanpy documentation 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. As such, we scored leiden-clustering popularity level to be Limited. A number of iterations of the Leiden algorithm can be performed before the Louvain algorithm has finished its first iteration. In this paper, we show that the Louvain algorithm has a major problem, for both modularity and CPM. leiden-clustering - Python Package Health Analysis | Snyk 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. At each iteration all clusters are guaranteed to be connected and well-separated. However, as shown in this paper, the Louvain algorithm has a major shortcoming: the algorithm yields communities that may be arbitrarily badly connected. We also suggested that the Leiden algorithm is faster than the Louvain algorithm, because of the fast local move approach. Use Git or checkout with SVN using the web URL. In the refinement phase, nodes are not necessarily greedily merged with the community that yields the largest increase in the quality function. I tracked the number of clusters post-clustering at each step. This can be a shared nearest neighbours matrix derived from a graph object. In that case, some optimal partitions cannot be found, as we show in SectionC2 of the Supplementary Information. Importantly, the first iteration of the Leiden algorithm is the most computationally intensive one, and subsequent iterations are faster. Elect. E 80, 056117, https://doi.org/10.1103/PhysRevE.80.056117 (2009). Clustering with the Leiden Algorithm in R Rev. to use Codespaces. We can guarantee a number of properties of the partitions found by the Leiden algorithm at various stages of the iterative process. Figure6 presents total runtime versus quality for all iterations of the Louvain and the Leiden algorithm. * (2018). The Leiden algorithm is considerably more complex than the Louvain algorithm. A Comparative Analysis of Community Detection Algorithms on Artificial Networks. 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. It is good at identifying small clusters. It implies uniform -density and all the other above-mentioned properties. For the Amazon, DBLP and Web UK networks, Louvain yields on average respectively 23%, 16% and 14% badly connected communities. 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. This step will involve reducing the dimensionality of our data into two dimensions using uniform manifold approximation (UMAP), allowing us to visualize our cell populations as they are binned into discrete populations using Leiden clustering. Subpartition -density is not guaranteed by the Louvain algorithm. 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 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. Google Scholar. 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. MATH For larger networks and higher values of , Louvain is much slower than Leiden. Analyses based on benchmark networks have only a limited value because these networks are not representative of empirical real-world networks. Instead, a node may be merged with any community for which the quality function increases. Powered by DataCamp DataCamp This is very similar to what the smart local moving algorithm does. 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. A Simple Acceleration Method for the Louvain Algorithm. Int. This function takes a cell_data_set as input, clusters the cells using . Phys. Article Scaling of benchmark results for network size. J. o CLIQUE (Clustering in Quest): - CLIQUE is a combination of density-based and grid-based clustering algorithm. To overcome the problem of arbitrarily badly connected communities, we introduced a new algorithm, which we refer to as the Leiden algorithm. In the worst case, almost a quarter of the communities are badly connected. The algorithm is described in pseudo-code in AlgorithmA.2 in SectionA of the Supplementary Information. Leiden consists of the following steps: The refinement step allows badly connected communities to be split before creating the aggregate network. For each set of parameters, we repeated the experiment 10 times. We start by initialising a queue with all nodes in the network. 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. 8, the Leiden algorithm is significantly faster than the Louvain algorithm also in empirical networks. 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. As we will demonstrate in our experimental analysis, the problem occurs frequently in practice when using the Louvain algorithm. The algorithm may yield arbitrarily badly connected communities, over and above the well-known issue of the resolution limit14. As the problem of modularity optimization is NP-hard, we need heuristic methods to optimize modularity (or CPM). Note that if Leiden finds subcommunities, splitting up the community is guaranteed to increase modularity. It is a directed graph if the adjacency matrix is not symmetric. The triumphs and limitations of computational methods for - Nature Guimer, R. & Nunes Amaral, L. A. Functional cartography of complex metabolic networks. Note that this code is designed for Seurat version 2 releases. Therefore, clustering algorithms look for similarities or dissimilarities among data points. (We implemented both algorithms in Java, available from https://github.com/CWTSLeiden/networkanalysis and deposited at Zenodo23. Natl. The constant Potts model might give better communities in some cases, as it is not subject to the resolution limit. Nevertheless, depending on the relative strengths of the different connections, these nodes may still be optimally assigned to their current community. In practice, this means that small clusters can hide inside larger clusters, making their identification difficult. 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. 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. Value. Nonlin. These steps are repeated until the quality cannot be increased further. The Leiden algorithm is considerably more complex than the Louvain algorithm. E 81, 046106, https://doi.org/10.1103/PhysRevE.81.046106 (2010). U. S. A. We prove that the new algorithm is guaranteed to produce partitions in which all communities are internally connected. Finding communities in large networks is far from trivial: algorithms need to be fast, but they also need to provide high-quality results. Finding and Evaluating Community Structure in Networks. Phys. MathSciNet Modularity is a measure of the structure of networks or graphs which measures the strength of division of a network into modules (also called groups, clusters or communities). 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. E 70, 066111, https://doi.org/10.1103/PhysRevE.70.066111 (2004). Runtime versus quality for benchmark networks. Lancichinetti, A. wrote the manuscript. The random component also makes the algorithm more explorative, which might help to find better community structures. The degree of randomness in the selection of a community is determined by a parameter >0. Soft Matter Phys. The Louvain method for community detection is a popular way to discover communities from single-cell data. When node 0 is moved to a different community, the red community becomes internally disconnected, as shown in (b). In this way, the constant acts as a resolution parameter, and setting the constant higher will result in fewer communities. https://doi.org/10.1038/s41598-019-41695-z. Louvain - Neo4j Graph Data Science Narrow scope for resolution-limit-free community detection. Hence, in general, Louvain may find arbitrarily badly connected communities. For this network, Leiden requires over 750 iterations on average to reach a stable iteration. DBSCAN Clustering Explained. Detailed theorotical explanation and Computer Syst. Ph.D. thesis, (University of Oxford, 2016). 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. Discovering cell types using manifold learning and enhanced After a stable iteration of the Leiden algorithm, it is guaranteed that: All nodes are locally optimally assigned. reviewed the manuscript. To find an optimal grouping of cells into communities, we need some way of evaluating different partitions in the graph. Are you sure you want to create this branch? GitHub - vtraag/leidenalg: Implementation of the Leiden algorithm for 2015. In fact, if we keep iterating the Leiden algorithm, it will converge to a partition without any badly connected communities, as discussed earlier. 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 ). 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. 2004. Rotta, R. & Noack, A. Multilevel local search algorithms for modularity clustering. PDF leiden: R Implementation of Leiden Clustering Algorithm From Louvain to Leiden: Guaranteeing Well-Connected Communities, October. We provide the full definitions of the properties as well as the mathematical proofs in SectionD of the Supplementary Information. Faster unfolding of communities: Speeding up the Louvain algorithm. Community Detection Algorithms - Towards Data Science Consider the partition shown in (a). 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. Starting from the second iteration, Leiden outperformed Louvain in terms of the percentage of badly connected communities. The minimum resolvable community size depends on the total size of the network and the degree of interconnectedness of the modules. & Bornholdt, S. Statistical mechanics of community detection. Obviously, this is a worst case example, showing that disconnected communities may be identified by the Louvain algorithm. In short, the problem of badly connected communities has important practical consequences. However, focussing only on disconnected communities masks the more fundamental issue: Louvain finds arbitrarily badly connected communities. Fortunato, S. & Barthlemy, M. Resolution Limit in Community Detection. To elucidate the problem, we consider the example illustrated in Fig. Eng. This may have serious consequences for analyses based on the resulting partitions. 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. The Leiden community detection algorithm outperforms other clustering methods. Rev. USA 104, 36, https://doi.org/10.1073/pnas.0605965104 (2007). V. A. Traag. When a disconnected community has become a node in an aggregate network, there are no more possibilities to split up the community. Such a modular structure is usually not known beforehand. The Louvain algorithm starts from a singleton partition in which each node is in its own community (a). The solution provided by Leiden is based on the smart local moving algorithm. Technol. 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). We now compare how the Leiden and the Louvain algorithm perform for the six empirical networks listed in Table2. 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. cluster_cells: Cluster cells using Louvain/Leiden community detection leiden_clustering Description Class wrapper based on scanpy to use the Leiden algorithm to directly cluster your data matrix with a scikit-learn flavor. Community detection is often used to understand the structure of large and complex networks. Clustering algorithms look for similarities or dissimilarities among data points so that similar ones can be grouped together. 92 (3): 032801. http://dx.doi.org/10.1103/PhysRevE.92.032801. Scientific Reports (Sci Rep) Article When iterating Louvain, the quality of the partitions will keep increasing until the algorithm is unable to make any further improvements. 4. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate. Due to the resolution limit, modularity may cause smaller communities to be clustered into larger communities. import leidenalg as la import igraph as ig Example output. J. Assoc. We applied the Louvain and the Leiden algorithm to exactly the same networks, using the same seed for the random number generator. 8 (3): 207. https://pdfs.semanticscholar.org/4ea9/74f0fadb57a0b1ec35cbc5b3eb28e9b966d8.pdf. Another important difference between the Leiden algorithm and the Louvain algorithm is the implementation of the local moving phase. 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). This is because Louvain only moves individual nodes at a time. 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. Nat. 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. Class wrapper based on scanpy to use the Leiden algorithm to directly cluster your data matrix with a scikit-learn flavor. PubMed Leiden algorithm. The Leiden algorithm starts from a singleton 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 algorithm moves individual nodes from one community to another to find a partition (b), which is then refined (c). In this new situation, nodes 2, 3, 5 and 6 have only internal connections. From Louvain to Leiden: guaranteeing well-connected communities - Nature 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. It states that there are no communities that can be merged. 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 . Higher resolutions lead to more communities, while lower resolutions lead to fewer communities. The steps for agglomerative clustering are as follows: leiden function - RDocumentation In the meantime, to ensure continued support, we are displaying the site without styles PubMed Based on this partition, an aggregate network is created (c). Fortunato, S. Community detection in graphs. Sci. We abbreviate the leidenalg package as la and the igraph package as ig in all Python code throughout this documentation. We used modularity with a resolution parameter of =1 for the experiments. performed the experimental analysis. Community detection - Tim Stuart First iteration runtime for empirical networks. Not. ADS Traag, V A. 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. Importantly, the problem of disconnected communities is not just a theoretical curiosity. Phys. Zenodo, https://doi.org/10.5281/zenodo.1469357 https://github.com/vtraag/leidenalg. Inf. 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. Traag, V. A., Waltman, L. & van Eck, N. J. networkanalysis. Each point corresponds to a certain iteration of an algorithm, with results averaged over 10 experiments. 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. 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. 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. Rather than evaluating the modularity gain for moving a node to each neighboring communities, we choose a neighboring node at random and evaluate whether there is a gain in modularity if we were to move the node to that neighbors community. Please Speed of the first iteration of the Louvain and the Leiden algorithm for benchmark networks with increasingly difficult partitions (n=107). Usually, the Louvain algorithm starts from a singleton partition, in which each node is in its own community. 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 phase one loop can be greatly accelerated by finding the nodes that have the potential to change community and only revisit those nodes. Networks with high modularity have dense connections between the nodes within modules but sparse connections between nodes in different modules. Yang, Z., Algesheimer, R. & Tessone, C. J. The Leiden algorithm starts from a singleton partition (a). Slider with three articles shown per slide. In addition, we prove that the algorithm converges to an asymptotically stable partition in which all subsets of all communities are locally optimally assigned. ISSN 2045-2322 (online). Modularity is used most commonly, but is subject to the resolution limit. The docs are here. The quality improvement realised by the Leiden algorithm relative to the Louvain algorithm is larger for empirical networks than for benchmark networks. That is, no subset can be moved to a different community.
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