leiden clustering explained leiden clustering explained

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 other words, communities are guaranteed to be well separated. 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 This may have serious consequences for analyses based on the resulting partitions. Bae, S., Halperin, D., West, J. D., Rosvall, M. & Howe, B. Scalable and Efficient Flow-Based Community Detection for Large-Scale Graph Analysis. Porter, M. A., Onnela, J.-P. & Mucha, P. J. Sci. If nothing happens, download GitHub Desktop and try again. 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. Segmentation & Clustering SPATA2 - GitHub Pages When node 0 is moved to a different community, the red community becomes internally disconnected, as shown in (b). Fortunato, Santo, and Marc Barthlemy. However, modularity suffers from a difficult problem known as the resolution limit (Fortunato and Barthlemy 2007). Cluster Determination Source: R/generics.R, R/clustering.R Identify clusters of cells by a shared nearest neighbor (SNN) modularity optimization based clustering algorithm. Number of iterations before the Leiden algorithm has reached a stable iteration for six empirical networks. E 81, 046106, https://doi.org/10.1103/PhysRevE.81.046106 (2010). Preprocessing and clustering 3k PBMCs Scanpy documentation & Bornholdt, S. Statistical mechanics of community detection. A major goal of single-cell analysis is to study the cell-state heterogeneity within a sample by discovering groups within the population of cells. There is an entire Leiden package in R-cran here Nodes 13 should form a community and nodes 46 should form another community. Phys. Zenodo, https://doi.org/10.5281/zenodo.1469357 https://github.com/vtraag/leidenalg. This is similar to ideas proposed recently as pruning16 and in a slightly different form as prioritisation17. 2013. Sci Rep 9, 5233 (2019). You will not need much Python to use it. We used the CPM quality function. One of the best-known methods for community detection is called modularity3. Article Removing such a node from its old community disconnects the old community. igraph R manual pages 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. Importantly, mergers are performed only within each community of the partition \({\mathscr{P}}\). That is, one part of such an internally disconnected community can reach another part only through a path going outside the community. 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. Sci. Table2 provides an overview of the six networks. Four popular community detection algorithms are explained . 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. 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. ML | Hierarchical clustering (Agglomerative and Divisive clustering We start by initialising a queue with all nodes in the network. Phys. The algorithm optimises a quality function such as modularity or CPM in two elementary phases: (1) local moving of nodes; and (2) aggregation of the network. 20, 172188, https://doi.org/10.1109/TKDE.2007.190689 (2008). Both conda and PyPI have leiden clustering in Python which operates via iGraph. https://leidenalg.readthedocs.io/en/latest/reference.html. Eur. Lancichinetti, A. and JavaScript. 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. The PyPI package leiden-clustering receives a total of 15 downloads a week. Am. Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. To address this important shortcoming, we introduce a new algorithm that is faster, finds better partitions and provides explicit guarantees and bounds. . We name our algorithm the Leiden algorithm, after the location of its authors. From Louvain to Leiden: guaranteeing well-connected communities - Nature For larger networks and higher values of , Louvain is much slower than Leiden. 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. In contrast, Leiden keeps finding better partitions in each iteration. 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. All authors conceived the algorithm and contributed to the source code. We first applied the Scanpy pipeline, including its clustering method (Leiden clustering), on the PBMC dataset. Rep. 486, 75174, https://doi.org/10.1016/j.physrep.2009.11.002 (2010). One may expect that other nodes in the old community will then also be moved to other communities. V.A.T. The resolution limit describes a limitation where there is a minimum community size able to be resolved by optimizing modularity (or other related functions). Community detection can then be performed using this graph. Runtime versus quality for empirical networks. Leiden algorithm. We provide the full definitions of the properties as well as the mathematical proofs in SectionD of the Supplementary Information. After a stable iteration of the Leiden algorithm, it is guaranteed that: All nodes are locally optimally assigned. 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. In this paper, we show that the Louvain algorithm has a major problem, for both modularity and CPM. We typically reduce the dimensionality of the data first by running PCA, then construct a neighbor graph in the reduced space. We show that this algorithm has a major defect that largely went unnoticed until now: the Louvain algorithm may yield arbitrarily badly connected communities. Leiden is both faster than Louvain and finds better partitions. One of the most popular algorithms for uncovering community structure is the so-called Louvain algorithm. It therefore does not guarantee -connectivity either. 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. 4. We find that the Leiden algorithm is faster than the Louvain algorithm and uncovers better partitions, in addition to providing explicit guarantees. In a stable iteration, the partition is guaranteed to be node optimal and subpartition -dense. Later iterations of the Louvain algorithm are very fast, but this is only because the partition remains the same. Higher resolutions lead to more communities and lower resolutions lead to fewer communities, similarly to the resolution parameter for modularity. In this post, I will cover one of the common approaches which is hierarchical clustering. 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 this case we know the answer is exactly 10. In particular, it yields communities that are guaranteed to be connected. The leidenalg package facilitates community detection of networks and builds on the package igraph. Speed of the first iteration of the Louvain and the Leiden algorithm for six empirical networks. Scaling of benchmark results for difficulty of the partition. The R implementation of Leiden can be run directly on the snn igraph object in Seurat. These are the same networks that were also studied in an earlier paper introducing the smart local move algorithm15. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate. However, as shown in this paper, the Louvain algorithm has a major shortcoming: the algorithm yields communities that may be arbitrarily badly connected. The resulting clusters are shown as colors on the 3D model (top) and t -SNE embedding . E 80, 056117, https://doi.org/10.1103/PhysRevE.80.056117 (2009). CAS Below we offer an intuitive explanation of these properties. Leiden is faster than Louvain especially for larger networks. Consider the partition shown in (a). The inspiration for this method of community detection is the optimization of modularity as the algorithm progresses. Newman, M. E. J. Correspondence to leiden: Run Leiden clustering algorithm in leiden: R Implementation of In this iterative scheme, Louvain provides two guarantees: (1) no communities can be merged and (2) no nodes can be moved. Modularity is a popular objective function used with the Louvain method for community detection. Louvain can also be quite slow, as it spends a lot of time revisiting nodes that may not have changed neighborhoods. However, focussing only on disconnected communities masks the more fundamental issue: Louvain finds arbitrarily badly connected communities. Nodes 16 have connections only within this community, whereas node 0 also has many external connections. In this case, refinement does not change the partition (f). Clustering algorithms look for similarities or dissimilarities among data points so that similar ones can be grouped together. Here we can see partitions in the plotted results. Based on project statistics from the GitHub repository for the PyPI package leiden-clustering, we found that it has been starred 1 times. Nonlin. Using UMAP for Clustering umap 0.5 documentation - Read the Docs Google Scholar. Google Scholar. Figure3 provides an illustration of the algorithm. Clauset, A., Newman, M. E. J. MathSciNet In this case we can solve one of the hard problems for K-Means clustering - choosing the right k value, giving the number of clusters we are looking for. The refined partition \({{\mathscr{P}}}_{{\rm{refined}}}\) is obtained as follows. Waltman, Ludo, and Nees Jan van Eck. J. Comput. Note that communities found by the Leiden algorithm are guaranteed to be connected. Louvain pruning is another improvement to Louvain proposed in 2016, and can reduce the computational time by as much as 90% while finding communities that are almost as good as Louvain (Ozaki, Tezuka, and Inaba 2016). Learn more. where >0 is a resolution parameter4. At each iteration all clusters are guaranteed to be connected and well-separated. leiden clustering explained Louvain method - Wikipedia 92 (3): 032801. http://dx.doi.org/10.1103/PhysRevE.92.032801. Moreover, when no more nodes can be moved, the algorithm will aggregate the network. 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. Analyses based on benchmark networks have only a limited value because these networks are not representative of empirical real-world networks. Article J. Assoc. However, the initial partition for the aggregate network is based on P, just like in the Louvain algorithm. The percentage of disconnected communities even jumps to 16% for the DBLP network. Natl. http://dx.doi.org/10.1073/pnas.0605965104. As discussed earlier, the Louvain algorithm does not guarantee connectivity. It was found to be one of the fastest and best performing algorithms in comparative analyses11,12, and it is one of the most-cited works in the community detection literature. DBSCAN Clustering Explained. Detailed theorotical explanation and 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. Hierarchical Clustering: Agglomerative + Divisive Explained | Built In Please CPM has the advantage that it is not subject to the resolution limit. 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. Blondel, V D, J L Guillaume, and R Lambiotte. More subtle problems may occur as well, causing Louvain to find communities that are connected, but only in a very weak sense. Communities in \({\mathscr{P}}\) may be split into multiple subcommunities in \({{\mathscr{P}}}_{{\rm{refined}}}\). Louvain algorithm. Clustering the neighborhood graph As with Seurat and many other frameworks, we recommend the Leiden graph-clustering method (community detection based on optimizing modularity) by Traag *et al. This package implements the Leiden algorithm in C++ and exposes it to python.It relies on (python-)igraph for it to function. The algorithm is run iteratively, using the partition identified in one iteration as starting point for the next iteration. It maximizes a modularity score for each community, where the modularity quantifies the quality of an assignment of nodes to communities. Article 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. & Girvan, M. Finding and evaluating community structure in networks. For example, after four iterations, the Web UK network has 8% disconnected communities, but twice as many badly connected communities. Other networks show an almost tenfold increase in the percentage of disconnected communities. Soft Matter Phys. cluster_cells: Cluster cells using Louvain/Leiden community detection In fact, although it may seem that the Louvain algorithm does a good job at finding high quality partitions, in its standard form the algorithm provides only one guarantee: the algorithm yields partitions for which it is guaranteed that no communities can be merged. Traag, V A. This will compute the Leiden clusters and add them to the Seurat Object Class. Provided by the Springer Nature SharedIt content-sharing initiative. All communities are subpartition -dense. N.J.v.E. Centre for Science and Technology Studies, Leiden University, Leiden, The Netherlands, You can also search for this author in Phys. The new algorithm integrates several earlier improvements, incorporating a combination of smart local move15, fast local move16,17 and random neighbour move18. Is modularity with a resolution parameter equivalent to leidenalg.RBConfigurationVertexPartition? In this way, the constant acts as a resolution parameter, and setting the constant higher will result in fewer communities. By creating the aggregate network based on \({{\mathscr{P}}}_{{\rm{refined}}}\) rather than P, the Leiden algorithm has more room for identifying high-quality partitions. 10, for the IMDB and Amazon networks, Leiden reaches a stable iteration relatively quickly, presumably because these networks have a fairly simple community structure. An overview of the various guarantees is presented in Table1. This is because Louvain only moves individual nodes at a time. In other words, modularity may hide smaller communities and may yield communities containing significant substructure. In fact, if we keep iterating the Leiden algorithm, it will converge to a partition without any badly connected communities, as discussed earlier. In the worst case, almost a quarter of the communities are badly connected. Lancichinetti, A., Fortunato, S. & Radicchi, F. Benchmark graphs for testing community detection algorithms. However, nodes 16 are still locally optimally assigned, and therefore these nodes will stay in the red community. Leiden algorithm. The Leiden algorithm starts from a singleton Default behaviour is calling cluster_leiden in igraph with Modularity (for undirected graphs) and CPM cost functions. In general, Leiden is both faster than Louvain and finds better partitions. Then the Leiden algorithm can be run on the adjacency matrix. Technol. Empirical networks show a much richer and more complex structure. 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. This is very similar to what the smart local moving algorithm does. As can be seen in Fig. Badly connected communities. The Leiden algorithm is considerably more complex than the Louvain algorithm. Agglomerative clustering is a bottom-up approach. Clustering is the task of grouping a set of objects with similar characteristics into one bucket and differentiating them from the rest of the group. Leiden consists of the following steps: The refinement step allows badly connected communities to be split before creating the aggregate network. 2 represent stronger connections, while the other edges represent weaker connections. This amounts to a clustering problem, where we aim to learn an optimal set of groups (communities) from the observed data. Finding community structure in networks using the eigenvectors of matrices. Google Scholar. Hence, for lower values of , the difference in quality is negligible. In this section, we analyse and compare the performance of the two algorithms in practice. Rev. The random component also makes the algorithm more explorative, which might help to find better community structures. Hence, the Leiden algorithm effectively addresses the problem of badly connected communities. In fact, for the Web of Science and Web UK networks, Fig. Detecting communities in a network is therefore an important problem. ADS Agglomerative Clustering: Also known as bottom-up approach or hierarchical agglomerative clustering (HAC). While current approaches are successful in reducing the number of sequence alignments performed, the generated clusters are . Hence, in general, Louvain may find arbitrarily badly connected communities. We use six empirical networks in our analysis. Faster Unfolding of Communities: Speeding up the Louvain Algorithm. Phys. Subset optimality is the strongest guarantee that is provided by the Leiden algorithm. Rev. scanpy.tl.leiden Scanpy 1.9.3 documentation - Read the Docs Modularity optimization. However, so far this problem has never been studied for the Louvain algorithm. ADS Phys. MATH 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. 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. We gratefully acknowledge computational facilities provided by the LIACS Data Science Lab Computing Facilities through Frank Takes. If nothing happens, download Xcode and try again. A score of -1 means that there are no edges connecting nodes within the community, and they instead all connect nodes outside the community. In the case of the Louvain algorithm, after a stable iteration, all subsequent iterations will be stable as well. 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. It was originally developed for modularity optimization, although the same method can be applied to optimize CPM. Discov. B 86, 471, https://doi.org/10.1140/epjb/e2013-40829-0 (2013). 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. J. In our experimental analysis, we observe that up to 25% of the communities are badly connected and up to 16% are disconnected. volume9, Articlenumber:5233 (2019) V. A. Traag. Then optimize the modularity function to determine clusters. On the other hand, Leiden keeps finding better partitions, especially for higher values of , for which it is more difficult to identify good partitions. 2(b). 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 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. In that case, nodes 16 are all locally optimally assigned, despite the fact that their community has become disconnected. Rev. Louvain - Neo4j Graph Data Science Cite this article. Phys. USA 104, 36, https://doi.org/10.1073/pnas.0605965104 (2007). 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. Faster unfolding of communities: Speeding up the Louvain algorithm. Excluding node mergers that decrease the quality function makes the refinement phase more efficient. After a stable iteration of the Leiden algorithm, the algorithm may still be able to make further improvements in later iterations.