leiden clustering explained leiden clustering explained

contrastive-sc works best on datasets with fewer clusters when using the KMeans clustering and conversely for Leiden. The speed difference is especially large for larger networks. The above results shows that the problem of disconnected and badly connected communities is quite pervasive in practice. Learn more. As we will demonstrate in our experimental analysis, the problem occurs frequently in practice when using the Louvain algorithm. Node mergers that cause the quality function to decrease are not considered. Blondel, V. D., Guillaume, J.-L., Lambiotte, R. & Lefebvre, E. Fast unfolding of communities in large networks. The two phases are repeated until the quality function cannot be increased further. A new methodology for constructing a publication-level classification system of science. We applied the Louvain and the Leiden algorithm to exactly the same networks, using the same seed for the random number generator. These nodes can be approximately identified based on whether neighbouring nodes have changed communities. The algorithm moves individual nodes from one community to another to find a partition (b), which is then refined (c). In that case, some optimal partitions cannot be found, as we show in SectionC2 of the Supplementary Information. 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. leiden_clsutering is distributed under a BSD 3-Clause License (see LICENSE). We now consider the guarantees provided by the Leiden algorithm. E 80, 056117, https://doi.org/10.1103/PhysRevE.80.056117 (2009). 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. 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 quality of such an asymptotically stable partition provides an upper bound on the quality of an optimal partition. Waltman, L. & van Eck, N. J. For example, nodes in a community in biological or neurological networks are often assumed to share similar functions or behaviour25. Communities may even be disconnected. Then optimize the modularity function to determine clusters. 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. 2015. Ozaki, Naoto, Hiroshi Tezuka, and Mary Inaba. However, as shown in this paper, the Louvain algorithm has a major shortcoming: the algorithm yields communities that may be arbitrarily badly connected. Then the Leiden algorithm can be run on the adjacency matrix. In the most difficult case (=0.9), Louvain requires almost 2.5 days, while Leiden needs fewer than 10 minutes. You signed in with another tab or window. Louvain has two phases: local moving and aggregation. MathSciNet A Smart Local Moving Algorithm for Large-Scale Modularity-Based Community Detection. Eur. The algorithm then moves individual nodes in the aggregate network (e). The resolution limit describes a limitation where there is a minimum community size able to be resolved by optimizing modularity (or other related functions). As can be seen in Fig. http://dx.doi.org/10.1073/pnas.0605965104. In the worst case, almost a quarter of the communities are badly connected. In short, the problem of badly connected communities has important practical consequences. To address this important shortcoming, we introduce a new algorithm that is faster, finds better partitions and provides explicit guarantees and bounds. 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. Knowl. This way of defining the expected number of edges is based on the so-called configuration model. E 78, 046110, https://doi.org/10.1103/PhysRevE.78.046110 (2008). Edges were created in such a way that an edge fell between two communities with a probability and within a community with a probability 1. 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. PubMed Central MATH Eng. The quality improvement realised by the Leiden algorithm relative to the Louvain algorithm is larger for empirical networks than for benchmark networks. Eur. Arguments can be passed to the leidenalg implementation in Python: In particular, the resolution parameter can fine-tune the number of clusters to be detected. Narrow scope for resolution-limit-free community detection. Here is some small debugging code I wrote to find this. It partitions the data space and identifies the sub-spaces using the Apriori principle. Leiden consists of the following steps: Local moving of nodes Partition refinement Network aggregation The refinement step allows badly connected communities to be split before creating the aggregate network. 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 . Basically, there are two types of hierarchical cluster analysis strategies - 1. Community detection is an important task in the analysis of complex networks. However, nodes 16 are still locally optimally assigned, and therefore these nodes will stay in the red community. Indeed, the percentage of disconnected communities becomes more comparable to the percentage of badly connected communities in later iterations. 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. 8 (3): 207. https://pdfs.semanticscholar.org/4ea9/74f0fadb57a0b1ec35cbc5b3eb28e9b966d8.pdf. We conclude that the Leiden algorithm is strongly preferable to the Louvain algorithm. Rev. See the documentation on the leidenalg Python module for more information: https://leidenalg.readthedocs.io/en/latest/reference.html. The main ideas of our algorithm are explained in an intuitive way in the main text of the paper. where nc is the number of nodes in community c. The interpretation of the resolution parameter is quite straightforward. 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. This method tries to maximise the difference between the actual number of edges in a community and the expected number of such edges. 104 (1): 3641. Google Scholar. As can be seen in Fig. Phys. Phys. Number of iterations until stability. 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. (We implemented both algorithms in Java, available from https://github.com/CWTSLeiden/networkanalysis and deposited at Zenodo23. bioRxiv, https://doi.org/10.1101/208819 (2018). 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. 9 shows that more than 10 iterations of the Leiden algorithm can be performed before the Louvain algorithm has finished its first iteration. Starting from the second iteration, Leiden outperformed Louvain in terms of the percentage of badly connected communities. Detecting communities in a network is therefore an important problem. Soft Matter Phys. Guimer, R. & Nunes Amaral, L. A. Functional cartography of complex metabolic networks. Source Code (2018). You will not need much Python to use it. For each community in a partition that was uncovered by the Louvain algorithm, we determined whether it is internally connected or not. However, it is also possible to start the algorithm from a different partition15. The percentage of disconnected communities is more limited, usually around 1%. Phys. We prove that the new algorithm is guaranteed to produce partitions in which all communities are internally connected. and JavaScript. Finding communities in large networks is far from trivial: algorithms need to be fast, but they also need to provide high-quality results. Rev. Cite this article. Internet Explorer). Leiden is the most recent major development in this space, and highlighted a flaw in the original Louvain algorithm (Traag, Waltman, and Eck 2018). 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 This enables us to find cases where its beneficial to split a community. Phys. 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). As shown in Fig. We now compare how the Leiden and the Louvain algorithm perform for the six empirical networks listed in Table2. Initially, \({{\mathscr{P}}}_{{\rm{refined}}}\) is set to a singleton partition, in which each node is in its own community. Sci Rep 9, 5233 (2019). For example, after four iterations, the Web UK network has 8% disconnected communities, but twice as many badly connected communities. A Simple Acceleration Method for the Louvain Algorithm. Int. Eng. We use six empirical networks in our analysis. running Leiden clustering finished: found 16 clusters and added 'leiden_1.0', the cluster labels (adata.obs, categorical) (0:00:00) running Leiden clustering finished: found 12 clusters and added 'leiden_0.6', the cluster labels (adata.obs, categorical) (0:00:00) running Leiden clustering finished: found 9 clusters and added 'leiden_0.4', the 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. At each iteration all clusters are guaranteed to be connected and well-separated. 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. A partition of clusters as a vector of integers Examples The high percentage of badly connected communities attests to this. Faster Unfolding of Communities: Speeding up the Louvain Algorithm. Phys. Data 11, 130, https://doi.org/10.1145/2992785 (2017). The docs are here. Sign up for the Nature Briefing newsletter what matters in science, free to your inbox daily. Data Eng. This is the crux of the Leiden paper, and the authors show that this exact problem happens frequently in practice. Note that Leiden clustering directly clusters the neighborhood graph of cells, which we already computed in the previous section. Phys. Modularity is used most commonly, but is subject to the resolution limit. An iteration of the Leiden algorithm in which the partition does not change is called a stable iteration. 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. Electr. Positive values above 2 define the total number of iterations to perform, -1 has the algorithm run until it reaches its optimal clustering. Rev. sign in Google Scholar. Theory Exp. Powered by DataCamp DataCamp Use the Previous and Next buttons to navigate the slides or the slide controller buttons at the end to navigate through each slide. Sci. The reasoning behind this is that the best community to join will usually be the one that most of the nodes neighbors already belong to. Community detection is often used to understand the structure of large and complex networks. 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. Phys. Another important difference between the Leiden algorithm and the Louvain algorithm is the implementation of the local moving phase. 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. 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. This will compute the Leiden clusters and add them to the Seurat Object Class. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/. Waltman, L. & van Eck, N. J. It is a directed graph if the adjacency matrix is not symmetric. For those wanting to read more, I highly recommend starting with the Leiden paper (Traag, Waltman, and Eck 2018) or the smart local moving paper (Waltman and Eck 2013). As can be seen in Fig. 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. In the case of the Louvain algorithm, after a stable iteration, all subsequent iterations will be stable as well. Publishers note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Rev. USA 104, 36, https://doi.org/10.1073/pnas.0605965104 (2007). 2010. It maximizes a modularity score for each community, where the modularity quantifies the quality of an assignment of nodes to communities. After a stable iteration of the Leiden algorithm, the algorithm may still be able to make further improvements in later iterations. J. Assoc. For larger networks and higher values of , Louvain is much slower than Leiden. Rotta, R. & Noack, A. Multilevel local search algorithms for modularity clustering. 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. In many complex networks, nodes cluster and form relatively dense groupsoften called communities1,2. This is very similar to what the smart local moving algorithm does. We prove that the Leiden algorithm yields communities that are guaranteed to be connected. Such algorithms are rather slow, making them ineffective for large networks. First, we created a specified number of nodes and we assigned each node to a community. Luecken, M. D. Application of multi-resolution partitioning of interaction networks to the study of complex disease. 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. In particular, we show that Louvain may identify communities that are internally disconnected. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate. Rev. Natl. Thank you for visiting nature.com. CAS Number of iterations before the Leiden algorithm has reached a stable iteration for six empirical networks. The horizontal axis indicates the cumulative time taken to obtain the quality indicated on the vertical axis. 10, 186198, https://doi.org/10.1038/nrn2575 (2009). Article ADS However, for higher values of , Leiden becomes orders of magnitude faster than Louvain, reaching 10100 times faster runtimes for the largest networks. Clauset, A., Newman, M. E. J. This is not the case when nodes are greedily merged with the community that yields the largest increase in the quality function. Rev. 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. We then created a certain number of edges such that a specified average degree \(\langle k\rangle \) was obtained. Traag, V.A., Waltman, L. & van Eck, N.J. From Louvain to Leiden: guaranteeing well-connected communities. The aggregate network is created based on the partition \({{\mathscr{P}}}_{{\rm{refined}}}\). We show that this algorithm has a major defect that largely went unnoticed until now: the Louvain algorithm may yield arbitrarily badly connected communities. E Stat. By submitting a comment you agree to abide by our Terms and Community Guidelines. Please For the Amazon, DBLP and Web UK networks, Louvain yields on average respectively 23%, 16% and 14% badly connected communities. 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. This problem is different from the well-known issue of the resolution limit of modularity14. A number of iterations of the Leiden algorithm can be performed before the Louvain algorithm has finished its first iteration. Article You are using a browser version with limited support for CSS. U. S. A. CAS 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. Yang, Z., Algesheimer, R. & Tessone, C. J. 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). Ozaki, N., Tezuka, H. & Inaba, M. A Simple Acceleration Method for the Louvain Algorithm. We therefore require a more principled solution, which we will introduce in the next section. Subset optimality is the strongest guarantee that is provided by the Leiden algorithm. The Louvain algorithm is a simple and popular method for community detection (Blondel, Guillaume, and Lambiotte 2008). In this new situation, nodes 2, 3, 5 and 6 have only internal connections. A community is subpartition -dense if it can be partitioned into two parts such that: (1) the two parts are well connected to each other; (2) neither part can be separated from its community; and (3) each part is also subpartition -dense itself. Rev. The Web of Science network is the most difficult one. 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. This package requires the 'leidenalg' and 'igraph' modules for python (2) to be installed on your system. 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. This makes sense, because after phase one the total size of the graph should be significantly reduced. PubMed As can be seen in Fig. Local Resolution-Limit-Free Potts Model for Community Detection. Phys. The nodes that are more interconnected have been partitioned into separate clusters. On Modularity Clustering. The count of badly connected communities also included disconnected communities. performed the experimental analysis. Higher resolutions lead to more communities and lower resolutions lead to fewer communities, similarly to the resolution parameter for modularity. Nonlin. The phase one loop can be greatly accelerated by finding the nodes that have the potential to change community and only revisit those nodes. To ensure readability of the paper to the broadest possible audience, we have chosen to relegate all technical details to the Supplementary Information. Work fast with our official CLI. While current approaches are successful in reducing the number of sequence alignments performed, the generated clusters are . 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). As such, we scored leiden-clustering popularity level to be Limited. 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. We first applied the Scanpy pipeline, including its clustering method (Leiden clustering), on the PBMC dataset. Presumably, many of the badly connected communities in the first iteration of Louvain become disconnected in the second iteration. The algorithm is run iteratively, using the partition identified in one iteration as starting point for the next iteration. SPATA2 currently offers the functions findSeuratClusters (), findMonocleClusters () and findNearestNeighbourClusters () which are wrapper around widely used clustering algorithms. Rep. 486, 75174, https://doi.org/10.1016/j.physrep.2009.11.002 (2010). For example: If you do not have root access, you can use pip install --user or pip install --prefix to install these in your user directory (which you have write permissions for) and ensure that this directory is in your PATH so that Python can find it. Later iterations of the Louvain algorithm only aggravate the problem of disconnected communities, even though the quality function (i.e. import leidenalg as la import igraph as ig Example output. Zenodo, https://doi.org/10.5281/zenodo.1469357 https://github.com/vtraag/leidenalg. We provide the full definitions of the properties as well as the mathematical proofs in SectionD of the Supplementary Information. & Bornholdt, S. Statistical mechanics of community detection. Randomness in the selection of a community allows the partition space to be explored more broadly. A community is subset optimal if all subsets of the community are locally optimally assigned. E 74, 036104, https://doi.org/10.1103/PhysRevE.74.036104 (2006). MathSciNet E 76, 036106, https://doi.org/10.1103/PhysRevE.76.036106 (2007). Slider with three articles shown per slide. For the results reported below, the average degree was set to \(\langle k\rangle =10\). The Leiden algorithm is considerably more complex than the Louvain algorithm. 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. The algorithm moves individual nodes from one community to another to find a partition (b). 81 (4 Pt 2): 046114. http://dx.doi.org/10.1103/PhysRevE.81.046114. The Louvain algorithm10 is very simple and elegant. Scaling of benchmark results for network size. The Leiden community detection algorithm outperforms other clustering methods. For example, for the Web of Science network, the first iteration takes about 110120 seconds, while subsequent iterations require about 40 seconds. 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. Are you sure you want to create this branch? Phys. 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. If nothing happens, download Xcode and try again. A Comparative Analysis of Community Detection Algorithms on Artificial Networks. In this way, Leiden implements the local moving phase more efficiently than Louvain. Graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. GitHub on Feb 15, 2020 Do you think the performance improvements will also be implemented in leidenalg?