leiden clustering explained leiden clustering explained

We study the problem of badly connected communities when using the Louvain algorithm for several empirical networks. 2004. Initially, \({{\mathscr{P}}}_{{\rm{refined}}}\) is set to a singleton partition, in which each node is in its own community. We can guarantee a number of properties of the partitions found by the Leiden algorithm at various stages of the iterative process. From Louvain to Leiden: Guaranteeing Well-Connected Communities, October. In addition, to analyse whether a community is badly connected, we ran the Leiden algorithm on the subnetwork consisting of all nodes belonging to the community. Source Code (2018). DBSCAN Clustering Explained Detailed theorotical explanation and scikit-learn implementation Clustering is a way to group a set of data points in a way that similar data points are grouped together. However, the initial partition for the aggregate network is based on P, just like in the Louvain algorithm. Figure3 provides an illustration of the algorithm. Note that Leiden clustering directly clusters the neighborhood graph of cells, which we already computed in the previous section. Algorithmics 16, 2.1, https://doi.org/10.1145/1963190.1970376 (2011). 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. An aggregate. The thick edges in Fig. Importantly, the first iteration of the Leiden algorithm is the most computationally intensive one, and subsequent iterations are faster. Cluster Determination FindClusters Seurat - Satija Lab By moving these nodes, Louvain creates badly connected communities. To address this important shortcoming, we introduce a new algorithm that is faster, finds better partitions and provides explicit guarantees and bounds. We use six empirical networks in our analysis. Nevertheless, when CPM is used as the quality function, the Louvain algorithm may still find arbitrarily badly connected communities. Traag, V. A., Waltman, L. & van Eck, N. J. networkanalysis. Sci. 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. Hence, in general, Louvain may find arbitrarily badly connected communities. leiden_clustering Description Class wrapper based on scanpy to use the Leiden algorithm to directly cluster your data matrix with a scikit-learn flavor. In the refinement phase, nodes are not necessarily greedily merged with the community that yields the largest increase in the quality function. Note that this code is . In particular, it yields communities that are guaranteed to be connected. E 84, 016114, https://doi.org/10.1103/PhysRevE.84.016114 (2011). The main ideas of our algorithm are explained in an intuitive way in the main text of the paper. It identifies the clusters by calculating the densities of the cells. The Leiden algorithm is considerably more complex than the Louvain algorithm. Fortunato, Santo, and Marc Barthlemy. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate. In this paper, we show that the Louvain algorithm has a major problem, for both modularity and CPM. 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 can be a shared nearest neighbours matrix derived from a graph object. Rev. B 86, 471, https://doi.org/10.1140/epjb/e2013-40829-0 (2013). 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 81, 046106, https://doi.org/10.1103/PhysRevE.81.046106 (2010). This represents the following graph structure. Phys. Later iterations of the Louvain algorithm only aggravate the problem of disconnected communities, even though the quality function (i.e. Lancichinetti, A., Fortunato, S. & Radicchi, F. Benchmark graphs for testing community detection algorithms. E 74, 016110, https://doi.org/10.1103/PhysRevE.74.016110 (2006). 2(a). E Stat. 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. leiden clustering explained The corresponding results are presented in the Supplementary Fig. USA 104, 36, https://doi.org/10.1073/pnas.0605965104 (2007). Internet Explorer). Lancichinetti, A. The count of badly connected communities also included disconnected communities. Discovering cell types using manifold learning and enhanced Newman, M. E. J. 1 and summarised in pseudo-code in AlgorithmA.1 in SectionA of the Supplementary Information. Provided by the Springer Nature SharedIt content-sharing initiative. First iteration runtime for empirical networks. The phase one loop can be greatly accelerated by finding the nodes that have the potential to change community and only revisit those nodes. In this stage we essentially collapse communities down into a single representative node, creating a new simplified graph. GitHub - MiqG/leiden_clustering: Cluster your data matrix with the However, if communities are badly connected, this may lead to incorrect attributions of shared functionality. In particular, benchmark networks have a rather simple structure. conda install -c conda-forge leidenalg pip install leiden-clustering Used via. This commit does not belong to any branch on this repository, and may belong to a fork outside of the repository. Importantly, the problem of disconnected communities is not just a theoretical curiosity. GitHub on Feb 15, 2020 Do you think the performance improvements will also be implemented in leidenalg? E 69, 026113, https://doi.org/10.1103/PhysRevE.69.026113 (2004). Modularity is a scale value between 0.5 (non-modular clustering) and 1 (fully modular clustering) that measures the relative density of edges inside communities with respect to edges outside communities. 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. Phys. 68, 984998, https://doi.org/10.1002/asi.23734 (2017). Traag, V A. Communities may even be internally disconnected. Local Resolution-Limit-Free Potts Model for Community Detection. Phys. Neurosci. Rep. 486, 75174, https://doi.org/10.1016/j.physrep.2009.11.002 (2010). Google Scholar. In this post Ive mainly focused on the optimisation methods for community detection, rather than the different objective functions that can be used. Blondel, V. D., Guillaume, J.-L., Lambiotte, R. & Lefebvre, E. Fast unfolding of communities in large networks. In the first step of the next iteration, Louvain will again move individual nodes in the network. The docs are here. 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. We provide the full definitions of the properties as well as the mathematical proofs in SectionD 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. 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. Usually, the Louvain algorithm starts from a singleton partition, in which each node is in its own community. In this new situation, nodes 2, 3, 5 and 6 have only internal connections. Number of iterations before the Leiden algorithm has reached a stable iteration for six empirical networks. 2 represent stronger connections, while the other edges represent weaker connections. 9 shows that more than 10 iterations of the Leiden algorithm can be performed before the Louvain algorithm has finished its first iteration. Leiden is faster than Louvain especially for larger networks. Table2 provides an overview of the six networks. 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. Our analysis is based on modularity with resolution parameter =1. 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. The inspiration for this method of community detection is the optimization of modularity as the algorithm progresses. On the other hand, Leiden keeps finding better partitions, especially for higher values of , for which it is more difficult to identify good partitions. A partition of clusters as a vector of integers Examples Powered by DataCamp DataCamp If nothing happens, download Xcode and try again. The fast local move procedure can be summarised as follows. The triumphs and limitations of computational methods for - Nature The percentage of disconnected communities even jumps to 16% for the DBLP network. 2016. In the most difficult case (=0.9), Louvain requires almost 2.5 days, while Leiden needs fewer than 10 minutes. Get the most important science stories of the day, free in your inbox. As can be seen in Fig. 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. 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. Leiden keeps finding better partitions for empirical networks also after the first 10 iterations of the algorithm. Louvain algorithm. See the documentation for these functions. Louvain keeps visiting all nodes in a network until there are no more node movements that increase the quality function. In a stable iteration, the partition is guaranteed to be node optimal and subpartition -dense. In the local move procedure in the Leiden algorithm, only nodes whose neighborhood . Good, B. H., De Montjoye, Y. Reichardt, J. 2013. E 74, 036104, https://doi.org/10.1103/PhysRevE.74.036104 (2006). The high percentage of badly connected communities attests to this. 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. leiden: Run Leiden clustering algorithm in leiden: R Implementation of These nodes are therefore optimally assigned to their current community. E 80, 056117, https://doi.org/10.1103/PhysRevE.80.056117 (2009). In the Louvain algorithm, an aggregate network is created based on the partition \({\mathscr{P}}\) resulting from the local moving phase. However, for higher values of , Leiden becomes orders of magnitude faster than Louvain, reaching 10100 times faster runtimes for the largest networks. In general, Leiden is both faster than Louvain and finds better partitions. Slider with three articles shown per slide. MathSciNet The Leiden algorithm starts from a singleton partition (a). All experiments were run on a computer with 64 Intel Xeon E5-4667v3 2GHz CPUs and 1TB internal memory. You are using a browser version with limited support for CSS. Phys. The Leiden algorithm guarantees all communities to be connected, but it may yield badly connected communities. 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. CAS Waltman, L. & van Eck, N. J. Sci. ISSN 2045-2322 (online). 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. Note that nodes can be revisited several times within a single iteration of the local moving stage, as the possible increase in modularity will change as other nodes are moved to different communities. Communities in \({\mathscr{P}}\) may be split into multiple subcommunities in \({{\mathscr{P}}}_{{\rm{refined}}}\). The steps for agglomerative clustering are as follows: Each of these can be used as an objective function for graph-based community detection methods, with our goal being to maximize this value. For this network, Leiden requires over 750 iterations on average to reach a stable iteration. 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. There are many different approaches and algorithms to perform clustering tasks. A structure that is more informative than the unstructured set of clusters returned by flat clustering. Article The larger the increase in the quality function, the more likely a community is to be selected. The 'devtools' package will be used to install 'leiden' and the dependancies (igraph and reticulate). Rev. We typically reduce the dimensionality of the data first by running PCA, then construct a neighbor graph in the reduced space. The horizontal axis indicates the cumulative time taken to obtain the quality indicated on the vertical axis. In the first iteration, Leiden is roughly 220 times faster than Louvain. Am. More subtle problems may occur as well, causing Louvain to find communities that are connected, but only in a very weak sense. PDF leiden: R Implementation of Leiden Clustering Algorithm One of the most popular algorithms to optimise modularity is the so-called Louvain algorithm10, named after the location of its authors. After each iteration of the Leiden algorithm, it is guaranteed that: In these properties, refers to the resolution parameter in the quality function that is optimised, which can be either modularity or CPM. Hence, the complex structure of empirical networks creates an even stronger need for the use of the Leiden algorithm. The idea of the refinement phase in the Leiden algorithm is to identify a partition \({{\mathscr{P}}}_{{\rm{refined}}}\) that is a refinement of \({\mathscr{P}}\). Then the Leiden algorithm can be run on the adjacency matrix. At some point, node 0 is considered for moving. Due to the resolution limit, modularity may cause smaller communities to be clustered into larger communities. This continues until the queue is empty. Newman, M E J, and M Girvan. J. Assoc. It is a directed graph if the adjacency matrix is not symmetric. Complex brain networks: graph theoretical analysis of structural and functional systems. 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. Ronhovde, Peter, and Zohar Nussinov. Clauset, A., Newman, M. E. J. A score of 0 would mean that the community has half its edges connecting nodes within the same community, and half connecting nodes outside the community. 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. We now consider the guarantees provided by the Leiden algorithm. Faster Unfolding of Communities: Speeding up the Louvain Algorithm. Phys. 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. An alternative quality function is the Constant Potts Model (CPM)13, which overcomes some limitations of modularity. J. Besides being pervasive, the problem is also sizeable. Phys. In the case of the Louvain algorithm, after a stable iteration, all subsequent iterations will be stable as well. 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. Nodes 16 have connections only within this community, whereas node 0 also has many external connections. Phys. Source Code (2018). However, values of within a range of roughly [0.0005, 0.1] all provide reasonable results, thus allowing for some, but not too much randomness. The nodes that are more interconnected have been partitioned into separate clusters. Two ways of doing this are graph modularity (Newman and Girvan 2004) and the constant Potts model (Ronhovde and Nussinov 2010). & Moore, C. Finding community structure in very large networks. 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. In fact, if we keep iterating the Leiden algorithm, it will converge to a partition without any badly connected communities, as discussed earlier. Faster unfolding of communities: Speeding up the Louvain algorithm. Acad. The numerical details of the example can be found in SectionB of the Supplementary Information. However, the Louvain algorithm does not consider this possibility, since it considers only individual node movements. At some point, the Louvain algorithm may end up in the community structure shown in Fig. PubMed However, nodes 16 are still locally optimally assigned, and therefore these nodes will stay in the red community. How many iterations of the Leiden clustering algorithm to perform. Rev. performed the experimental analysis. 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). Traag, V. A., Van Dooren, P. & Nesterov, Y. What is Clustering and Different Types of Clustering Methods We applied the Louvain and the Leiden algorithm to exactly the same networks, using the same seed for the random number generator. Agglomerative clustering is a bottom-up approach. Preprocessing and clustering 3k PBMCs Scanpy documentation As shown in Fig. A Simple Acceleration Method for the Louvain Algorithm. Int. However, focussing only on disconnected communities masks the more fundamental issue: Louvain finds arbitrarily badly connected communities. CAS Traag, V. A. 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. The DBLP network is somewhat more challenging, requiring almost 80 iterations on average to reach a stable iteration. The algorithm is run iteratively, using the partition identified in one iteration as starting point for the next iteration. Waltman, L. & van Eck, N. J. However, modularity suffers from a difficult problem known as the resolution limit (Fortunato and Barthlemy 2007). Many Git commands accept both tag and branch names, so creating this branch may cause unexpected behavior. Thank you for visiting nature.com. We generated benchmark networks in the following way. A tag already exists with the provided branch name. Nature 433, 895900, https://doi.org/10.1038/nature03288 (2005). MATH Int. First, we created a specified number of nodes and we assigned each node to a community. All authors conceived the algorithm and contributed to the source code. Nonlin. Not. Speed of the first iteration of the Louvain and the Leiden algorithm for six empirical networks. We abbreviate the leidenalg package as la and the igraph package as ig in all Python code throughout this documentation. Here we can see partitions in the plotted results. We now show that the Louvain algorithm may find arbitrarily badly connected communities. Modularity is a popular objective function used with the Louvain method for community detection. We start by initialising a queue with all nodes in the network. Here is some small debugging code I wrote to find this. where >0 is a resolution parameter4. Introduction leidenalg 0.9.2.dev0+gb530332.d20221214 documentation To obtain It does not guarantee that modularity cant be increased by moving nodes between communities. 6 show that Leiden outperforms Louvain in terms of both computational time and quality of the partitions. Moreover, Louvain has no mechanism for fixing these communities. 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. If nothing happens, download GitHub Desktop and try again. 104 (1): 3641. Nonlin. Narrow scope for resolution-limit-free community detection. The property of -separation is also guaranteed by the Louvain algorithm. It partitions the data space and identifies the sub-spaces using the Apriori principle. 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. Although originally defined for modularity, the Louvain algorithm can also be used to optimise other quality functions. 10, 186198, https://doi.org/10.1038/nrn2575 (2009). AMS 56, 10821097 (2009). & Fortunato, S. Community detection algorithms: A comparative analysis. Google Scholar. 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 ). You will not need much Python to use it. The increase in the percentage of disconnected communities is relatively limited for the Live Journal and Web of Science networks. 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. This is well illustrated by figure 2 in the Leiden paper: When a community becomes disconnected like this, there is no way for Louvain to easily split it into two separate communities. DBSCAN Clustering Explained. Detailed theorotical explanation and The minimum resolvable community size depends on the total size of the network and the degree of interconnectedness of the modules. After the refinement phase is concluded, communities in \({\mathscr{P}}\) often will have been split into multiple communities in \({{\mathscr{P}}}_{{\rm{refined}}}\), but not always. Finally, we compare the performance of the algorithms on the empirical networks. Note that if Leiden finds subcommunities, splitting up the community is guaranteed to increase modularity. Google Scholar. Random moving is a very simple adjustment to Louvain local moving proposed in 2015 (Traag 2015). 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. Zenodo, https://doi.org/10.5281/zenodo.1469357 https://github.com/vtraag/leidenalg. For larger networks and higher values of , Louvain is much slower than Leiden. Based on this partition, an aggregate network is created (c). One may expect that other nodes in the old community will then also be moved to other communities. Ph.D. thesis, (University of Oxford, 2016). 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. ADS CAS Soft Matter Phys. Speed and quality for the first 10 iterations of the Louvain and the Leiden algorithm for six empirical networks. Community detection can then be performed using this graph. python - Leiden Clustering results are not always the same given the 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 The Louvain algorithm guarantees that modularity cannot be increased by merging communities (it finds a locally optimal solution). The algorithm then moves individual nodes in the aggregate network (e). Fortunato, S. Community detection in graphs. Finally, we demonstrate the excellent performance of the algorithm for several benchmark and real-world networks. Bae, S., Halperin, D., West, J. D., Rosvall, M. & Howe, B. Scalable and Efficient Flow-Based Community Detection for Large-Scale Graph Analysis. For example an SNN can be generated: For Seurat version 3 objects, the Leiden algorithm has been implemented in the Seurat version 3 package with Seurat::FindClusters and algorithm = "leiden"). There is an entire Leiden package in R-cran here Nodes 06 are in the same community. We used modularity with a resolution parameter of =1 for the experiments. The horizontal axis indicates the cumulative time taken to obtain the quality indicated on the vertical axis. E 76, 036106, https://doi.org/10.1103/PhysRevE.76.036106 (2007). Clustering with the Leiden Algorithm in R - cran.microsoft.com Knowl. E Stat. We also suggested that the Leiden algorithm is faster than the Louvain algorithm, because of the fast local move approach. Google Scholar. Luecken, M. D. Application of multi-resolution partitioning of interaction networks to the study of complex disease. Contrastive self-supervised clustering of scRNA-seq data Conversely, if Leiden does not find subcommunities, there is no guarantee that modularity cannot be increased by splitting up the community. Obviously, this is a worst case example, showing that disconnected communities may be identified by the Louvain algorithm. Scaling of benchmark results for network size. Phys. Rev. Sci. V.A.T. Soft Matter Phys. Inf. For all networks, Leiden identifies substantially better partitions than Louvain. The Leiden algorithm is considerably more complex than the Louvain algorithm. 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. Communities may even be disconnected. 9, the Leiden algorithm also performs better than the Louvain algorithm in terms of the quality of the partitions that are obtained. Hierarchical Clustering: Agglomerative + Divisive Explained | Built In In this section, we analyse and compare the performance of the two algorithms in practice. 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. Nonlin. Four popular community detection algorithms are explained . 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. Rev. Google Scholar. You signed in with another tab or window. E 78, 046110, https://doi.org/10.1103/PhysRevE.78.046110 (2008).