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 Detecting communities in a network is therefore an important problem. A community size of 50 nodes was used for the results presented below, but larger community sizes yielded qualitatively similar results. Requirements Developed using: scanpy v1.7.2 sklearn v0.23.2 umap v0.4.6 numpy v1.19.2 leidenalg Installation pip pip install leiden_clustering local Nodes 16 have connections only within this community, whereas node 0 also has many external connections. Centre for Science and Technology Studies, Leiden University, Leiden, The Netherlands, You can also search for this author in Another important difference between the Leiden algorithm and the Louvain algorithm is the implementation of the local moving phase. We first applied the Scanpy pipeline, including its clustering method (Leiden clustering), on the PBMC dataset. The numerical details of the example can be found in SectionB of the Supplementary Information. Nevertheless, depending on the relative strengths of the different connections, these nodes may still be optimally assigned to their current community. 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. It identifies the clusters by calculating the densities of the cells. A new methodology for constructing a publication-level classification system of science. Proc. Phys. We typically reduce the dimensionality of the data first by running PCA, then construct a neighbor graph in the reduced space. contrastive-sc works best on datasets with fewer clusters when using the KMeans clustering and conversely for Leiden. 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, the problem of Louvain outlined above is independent from the issue of the resolution limit. Google Scholar. This is similar to what we have seen for benchmark networks. In this case we know the answer is exactly 10. Finding communities in large networks is far from trivial: algorithms need to be fast, but they also need to provide high-quality results. This will compute the Leiden clusters and add them to the Seurat Object Class. This phenomenon can be explained by the documented tendency KMeans has to identify equal-sized , combined with the significant class imbalance associated with the datasets having more than 8 clusters (Table 1). As can be seen in the figure, Louvain quickly reaches a state in which it is unable to find better partitions. Class wrapper based on scanpy to use the Leiden algorithm to directly cluster your data matrix with a scikit-learn flavor. E 76, 036106, https://doi.org/10.1103/PhysRevE.76.036106 (2007). Rev. 10, for the IMDB and Amazon networks, Leiden reaches a stable iteration relatively quickly, presumably because these networks have a fairly simple community structure. Unlike the Louvain algorithm, the Leiden algorithm uses a fast local move procedure in this phase. Subpartition -density does not imply that individual nodes are locally optimally assigned. 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. Hence, for lower values of , the difference in quality is negligible. Importantly, the output of the local moving stage will depend on the order that the nodes are considered in. The Louvain algorithm is a simple and popular method for community detection (Blondel, Guillaume, and Lambiotte 2008). Note that this code is . Rep. 6, 30750, https://doi.org/10.1038/srep30750 (2016). For each network, Table2 reports the maximal modularity obtained using the Louvain and the Leiden algorithm. Nodes 06 are in the same community. We thank Lovro Subelj for his comments on an earlier version of this paper. 2013. 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. As can be seen in Fig. Many Git commands accept both tag and branch names, so creating this branch may cause unexpected behavior. To obtain Additionally, we implemented a Python package, available from https://github.com/vtraag/leidenalg and deposited at Zenodo24). ISSN 2045-2322 (online). In the worst case, almost a quarter of the communities are badly connected. Traag, V. A., Van Dooren, P. & Nesterov, Y. Acad. It partitions the data space and identifies the sub-spaces using the Apriori principle. Nonlin. Therefore, clustering algorithms look for similarities or dissimilarities among data points. Such a modular structure is usually not known beforehand. 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. For the results reported below, the average degree was set to \(\langle k\rangle =10\). 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. In the aggregation phase, an aggregate network is created based on the partition obtained in the local moving phase. This is the crux of the Leiden paper, and the authors show that this exact problem happens frequently in practice. Besides being pervasive, the problem is also sizeable. Zenodo, https://doi.org/10.5281/zenodo.1466831 https://github.com/CWTSLeiden/networkanalysis. In that case, nodes 16 are all locally optimally assigned, despite the fact that their community has become disconnected. If nothing happens, download GitHub Desktop and try again. Communities may even be disconnected. Speed and quality for the first 10 iterations of the Louvain and the Leiden algorithm for six empirical networks. We consider these ideas to represent the most promising directions in which the Louvain algorithm can be improved, even though we recognise that other improvements have been suggested as well22. Package 'leiden' October 13, 2022 Type Package Title R Implementation of Leiden Clustering Algorithm Version 0.4.3 Date 2022-09-10 Description Implements the 'Python leidenalg' module to be called in R. Enables clustering using the leiden algorithm for partition a graph into communities. Article 2018. The percentage of disconnected communities even jumps to 16% for the DBLP network. Networks with high modularity have dense connections between the nodes within modules but sparse connections between nodes in different modules. Phys. Eng. When a disconnected community has become a node in an aggregate network, there are no more possibilities to split up the community. We now show that the Louvain algorithm may find arbitrarily badly connected communities. This way of defining the expected number of edges is based on the so-called configuration model. However, in the case of the Web of Science network, more than 5% of the communities are disconnected in the first iteration. E 92, 032801, https://doi.org/10.1103/PhysRevE.92.032801 (2015). Each point corresponds to a certain iteration of an algorithm, with results averaged over 10 experiments. Ronhovde, Peter, and Zohar Nussinov. Number of iterations until stability. 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. 8, 207218, https://doi.org/10.17706/IJCEE.2016.8.3.207-218 (2016). Rev. E Stat. In the Louvain algorithm, a node may be moved to a different community while it may have acted as a bridge between different components of its old community. J. 8, the Leiden algorithm is significantly faster than the Louvain algorithm also in empirical networks. Sci. 1 and summarised in pseudo-code in AlgorithmA.1 in SectionA of the Supplementary Information. Acad. Subpartition -density is not guaranteed by the Louvain algorithm. Positive values above 2 define the total number of iterations to perform, -1 has the algorithm run until it reaches its optimal clustering. Ph.D. thesis, (University of Oxford, 2016). To address this problem, we introduce the Leiden algorithm. If we move the node to a different community, we add to the rear of the queue all neighbours of the node that do not belong to the nodes new community and that are not yet in the queue. Mech. Removing such a node from its old community disconnects the old community. The Leiden algorithm guarantees all communities to be connected, but it may yield badly connected communities. Sci. The steps for agglomerative clustering are as follows: We generated benchmark networks in the following way. Rev. 6 show that Leiden outperforms Louvain in terms of both computational time and quality of the partitions. How many iterations of the Leiden clustering algorithm to perform. Scientific Reports (Sci Rep) 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. As such, we scored leiden-clustering popularity level to be Limited. In general, Leiden is both faster than Louvain and finds better partitions. Contrary to what might be expected, iterating the Louvain algorithm aggravates the problem of badly connected communities, as we will also see in our experimental analysis. In this stage we essentially collapse communities down into a single representative node, creating a new simplified graph. The nodes are added to the queue in a random order. Value. N.J.v.E. Blondel, V. D., Guillaume, J.-L., Lambiotte, R. & Lefebvre, E. Fast unfolding of communities in large networks. The Leiden algorithm is considerably more complex than the Louvain algorithm. In particular, it yields communities that are guaranteed to be connected. Speed and quality of the Louvain and the Leiden algorithm for benchmark networks of increasing size (two iterations). As can be seen in Fig. Based on this partition, an aggregate network is created (c). To ensure readability of the paper to the broadest possible audience, we have chosen to relegate all technical details to the Supplementary Information. We then created a certain number of edges such that a specified average degree \(\langle k\rangle \) was obtained. For the Amazon, DBLP and Web UK networks, Louvain yields on average respectively 23%, 16% and 14% badly connected communities. The classic Louvain algorithm should be avoided due to the known problem with disconnected communities. Note that if Leiden finds subcommunities, splitting up the community is guaranteed to increase modularity. We demonstrate the performance of the Leiden algorithm for several benchmark and real-world networks. Hence, in general, Louvain may find arbitrarily badly connected communities. Rev. Clustering algorithms look for similarities or dissimilarities among data points so that similar ones can be grouped together. Directed Undirected Homogeneous Heterogeneous Weighted 1. Rotta, R. & Noack, A. Multilevel local search algorithms for modularity clustering. Graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. Once aggregation is complete we restart the local moving phase, and continue to iterate until everything converges down to one node. We now compare how the Leiden and the Louvain algorithm perform for the six empirical networks listed in Table2. Even worse, the Amazon network has 5% disconnected communities, but 25% badly connected communities. CAS Lancichinetti, A., Fortunato, S. & Radicchi, F. Benchmark graphs for testing community detection algorithms. In short, the problem of badly connected communities has important practical consequences. the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Scaling of benchmark results for network size. The algorithm moves individual nodes from one community to another to find a partition (b), which is then refined (c). This enables us to find cases where its beneficial to split a community. 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. The algorithm may yield arbitrarily badly connected communities, over and above the well-known issue of the resolution limit14. Google Scholar. Fortunato, S. & Barthlemy, M. Resolution Limit in Community Detection. Initially, \({{\mathscr{P}}}_{{\rm{refined}}}\) is set to a singleton partition, in which each node is in its own community. 20, 172188, https://doi.org/10.1109/TKDE.2007.190689 (2008). When node 0 is moved to a different community, the red community becomes internally disconnected, as shown in (b). However, this is not necessarily the case, as the other nodes may still be sufficiently strongly connected to their community, despite the fact that the community has become disconnected. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate. After a stable iteration of the Leiden algorithm, the algorithm may still be able to make further improvements in later iterations. Waltman, Ludo, and Nees Jan van Eck. In the worst case, communities may even be disconnected, especially when running the algorithm iteratively. 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. Any sub-networks that are found are treated as different communities in the next aggregation step. In this paper, we show that the Louvain algorithm has a major problem, for both modularity and CPM. The constant Potts model might give better communities in some cases, as it is not subject to the resolution limit. and JavaScript. We prove that the new algorithm is guaranteed to produce partitions in which all communities are internally connected. The quality of such an asymptotically stable partition provides an upper bound on the quality of an optimal partition. Louvain keeps visiting all nodes in a network until there are no more node movements that increase the quality function. You are using a browser version with limited support for CSS. Nonlin. Below we offer an intuitive explanation of these properties. 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. Due to the resolution limit, modularity may cause smaller communities to be clustered into larger communities. Besides the relative flexibility of the implementation, it also scales well, and can be run on graphs of millions of nodes (as long as they can fit in memory). As the use of clustering is highly depending on the biological question it makes sense to use several approaches and algorithms. On the other hand, Leiden keeps finding better partitions, especially for higher values of , for which it is more difficult to identify good partitions. Note that this code is designed for Seurat version 2 releases. Blondel, V D, J L Guillaume, and R Lambiotte. Furthermore, by relying on a fast local move approach, the Leiden algorithm runs faster than the Louvain algorithm. Rev. Technol. Phys. E 78, 046110, https://doi.org/10.1103/PhysRevE.78.046110 (2008). b, The elephant graph (in a) is clustered using the Leiden clustering algorithm 51 (resolution r = 0.5). For each set of parameters, we repeated the experiment 10 times. CAS There was a problem preparing your codespace, please try again. http://iopscience.iop.org/article/10.1088/1742-5468/2008/10/P10008/meta, http://dx.doi.org/10.1073/pnas.0605965104, http://dx.doi.org/10.1103/PhysRevE.69.026113, https://pdfs.semanticscholar.org/4ea9/74f0fadb57a0b1ec35cbc5b3eb28e9b966d8.pdf, http://dx.doi.org/10.1103/PhysRevE.81.046114, http://dx.doi.org/10.1103/PhysRevE.92.032801, https://doi.org/10.1140/epjb/e2013-40829-0, Assign each node to a different community. Leiden is faster than Louvain especially for larger networks. MATH http://iopscience.iop.org/article/10.1088/1742-5468/2008/10/P10008/meta. We start by initialising a queue with all nodes in the network. As can be seen in Fig. Subset optimality is the strongest guarantee that is provided by the Leiden algorithm. In particular, we show that Louvain may identify communities that are internally disconnected. By submitting a comment you agree to abide by our Terms and Community Guidelines. J. Exp. We use six empirical networks in our analysis. Nonlin. One of the best-known methods for community detection is called modularity3. As can be seen in Fig. These nodes can be approximately identified based on whether neighbouring nodes have changed communities. The Leiden algorithm starts from a singleton partition (a). In this way, Leiden implements the local moving phase more efficiently than Louvain. Rev. 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. Importantly, mergers are performed only within each community of the partition \({\mathscr{P}}\). Rev. 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. Raghavan, U., Albert, R. & Kumara, S. Near linear time algorithm to detect community structures in large-scale networks. This method tries to maximise the difference between the actual number of edges in a community and the expected number of such edges. 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. Similarly, in citation networks, such as the Web of Science network, nodes in a community are usually considered to share a common topic26,27. Rev. Sci. Disconnected community. 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. and L.W. Scaling of benchmark results for difficulty of the partition. Modularity optimization. The R implementation of Leiden can be run directly on the snn igraph object in Seurat. If nothing happens, download Xcode and try again. The inspiration for this method of community detection is the optimization of modularity as the algorithm progresses.
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