leiden clustering explained

2.3. The new algorithm integrates several earlier improvements, incorporating a combination of smart local move15, fast local move16,17 and random neighbour move18. leiden_clustering Description Class wrapper based on scanpy to use the Leiden algorithm to directly cluster your data matrix with a scikit-learn flavor. Directed Undirected Homogeneous Heterogeneous Weighted 1. For the results reported below, the average degree was set to \(\langle k\rangle =10\). Two ways of doing this are graph modularity (Newman and Girvan 2004) and the constant Potts model (Ronhovde and Nussinov 2010). Our analysis is based on modularity with resolution parameter =1. Importantly, the first iteration of the Leiden algorithm is the most computationally intensive one, and subsequent iterations are faster. https://doi.org/10.1038/s41598-019-41695-z, DOI: https://doi.org/10.1038/s41598-019-41695-z. In particular, benchmark networks have a rather simple structure. Speed of the first iteration of the Louvain and the Leiden algorithm for benchmark networks with increasingly difficult partitions (n=107). 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. Furthermore, by relying on a fast local move approach, the Leiden algorithm runs faster than the Louvain algorithm. Rather than evaluating the modularity gain for moving a node to each neighboring communities, we choose a neighboring node at random and evaluate whether there is a gain in modularity if we were to move the node to that neighbors community. 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. Faster unfolding of communities: Speeding up the Louvain algorithm. MathSciNet E 78, 046110, https://doi.org/10.1103/PhysRevE.78.046110 (2008). Luecken, M. D. Application of multi-resolution partitioning of interaction networks to the study of complex disease. Communities were all of equal size. Basically, there are two types of hierarchical cluster analysis strategies - 1. More subtle problems may occur as well, causing Louvain to find communities that are connected, but only in a very weak sense. Newman, M. E. J. Klavans, R. & Boyack, K. W. Which Type of Citation Analysis Generates the Most Accurate Taxonomy of Scientific and Technical Knowledge? Soft Matter Phys. Google Scholar. As discussed earlier, the Louvain algorithm does not guarantee connectivity. In addition, a node is merged with a community in \({{\mathscr{P}}}_{{\rm{refined}}}\) only if both are sufficiently well connected to their community in \({\mathscr{P}}\). 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 It is a directed graph if the adjacency matrix is not symmetric. Traag, V A. All experiments were run on a computer with 64 Intel Xeon E5-4667v3 2GHz CPUs and 1TB internal memory. By submitting a comment you agree to abide by our Terms and Community Guidelines. 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. ADS 92 (3): 032801. http://dx.doi.org/10.1103/PhysRevE.92.032801. The corresponding results are presented in the Supplementary Fig. 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). Inf. In the local moving phase, individual nodes are moved to the community that yields the largest increase in the quality function. In our experimental analysis, we observe that up to 25% of the communities are badly connected and up to 16% are disconnected. E 74, 036104, https://doi.org/10.1103/PhysRevE.74.036104 (2006). We generated networks with n=103 to n=107 nodes. Neurosci. As can be seen in Fig. Phys. These nodes can be approximately identified based on whether neighbouring nodes have changed communities. J. For all networks, Leiden identifies substantially better partitions than Louvain. For each community, modularity measures the number of edges within the community and the number of edges going outside the community, and gives a value between -1 and +1. Article Yang, Z., Algesheimer, R. & Tessone, C. J. ADS Default behaviour is calling cluster_leiden in igraph with Modularity (for undirected graphs) and CPM cost functions. Excluding node mergers that decrease the quality function makes the refinement phase more efficient. The algorithm moves individual nodes from one community to another to find a partition (b), which is then refined (c). Lancichinetti, A., Fortunato, S. & Radicchi, F. Benchmark graphs for testing community detection algorithms. Google Scholar. Figure3 provides an illustration of the algorithm. The resolution limit describes a limitation where there is a minimum community size able to be resolved by optimizing modularity (or other related functions). reviewed the manuscript. Work fast with our official CLI. 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. Ph.D. thesis, (University of Oxford, 2016). Crucially, however, the percentage of badly connected communities decreases with each iteration of the Leiden algorithm. Table2 provides an overview of the six networks. In the refinement phase, nodes are not necessarily greedily merged with the community that yields the largest increase in the quality function. Thank you for visiting nature.com. E Stat. Duch, J. The Leiden algorithm is considerably more complex than the Louvain algorithm. Note that this code is . Presumably, many of the badly connected communities in the first iteration of Louvain become disconnected in the second iteration. Rev. Soc. In the case of the Louvain algorithm, after a stable iteration, all subsequent iterations will be stable as well. where nc is the number of nodes in community c. The interpretation of the resolution parameter is quite straightforward. A smart local moving algorithm for large-scale modularity-based community detection. Nonlin. Lancichinetti, A. 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). The algorithm then locally merges nodes in \({{\mathscr{P}}}_{{\rm{refined}}}\): nodes that are on their own in a community in \({{\mathscr{P}}}_{{\rm{refined}}}\) can be merged with a different community. This package implements the Leiden algorithm in C++ and exposes it to python.It relies on (python-)igraph for it to function. Article Knowl. The main ideas of our algorithm are explained in an intuitive way in the main text of the paper. E 69, 026113, https://doi.org/10.1103/PhysRevE.69.026113 (2004). Sci. This function takes a cell_data_set as input, clusters the cells using . 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. Number of iterations until stability. For both algorithms, 10 iterations were performed. wrote the manuscript. In the case of modularity, communities may have significant substructure both because of the resolution limit and because of the shortcomings of Louvain. 104 (1): 3641. Other networks show an almost tenfold increase in the percentage of disconnected communities. 69 (2 Pt 2): 026113. http://dx.doi.org/10.1103/PhysRevE.69.026113. This aspect of the Louvain algorithm can be used to give information about the hierarchical relationships between communities by tracking at which stage the nodes in the communities were aggregated. Cluster cells using Louvain/Leiden community detection Description. How many iterations of the Leiden clustering algorithm to perform. A Smart Local Moving Algorithm for Large-Scale Modularity-Based Community Detection. Eur. Phys. Slider with three articles shown per slide. Conversely, if Leiden does not find subcommunities, there is no guarantee that modularity cannot be increased by splitting up the community. We name our algorithm the Leiden algorithm, after the location of its authors. Sci. & Moore, C. Finding community structure in very large networks. conda install -c conda-forge leidenalg pip install leiden-clustering Used via. The images or other third party material in this article are included in the articles Creative Commons license, unless indicated otherwise in a credit line to the material. Traag, V.A., Waltman, L. & van Eck, N.J. From Louvain to Leiden: guaranteeing well-connected communities. N.J.v.E. After a stable iteration of the Leiden algorithm, it is guaranteed that: All nodes are locally optimally assigned. Scientific Reports (Sci Rep) The algorithm moves individual nodes from one community to another to find a partition (b). As the use of clustering is highly depending on the biological question it makes sense to use several approaches and algorithms. Communities may even be internally disconnected. https://leidenalg.readthedocs.io/en/latest/reference.html. At each iteration all clusters are guaranteed to be connected and well-separated. http://iopscience.iop.org/article/10.1088/1742-5468/2008/10/P10008/meta. 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. 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. Higher resolutions lead to more communities, while lower resolutions lead to fewer communities. Value. b, The elephant graph (in a) is clustered using the Leiden clustering algorithm 51 (resolution r = 0.5). 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. Speed and quality for the first 10 iterations of the Louvain and the Leiden algorithm for benchmark networks (n=106 and n=107). Therefore, by selecting a community based by choosing randomly from the neighbors, we choose the community to evaluate with probability proportional to the composition of the neighbors communities. Louvain can also be quite slow, as it spends a lot of time revisiting nodes that may not have changed neighborhoods. 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. Additionally, we implemented a Python package, available from https://github.com/vtraag/leidenalg and deposited at Zenodo24). In particular, we show that Louvain may identify communities that are internally disconnected. This is the crux of the Leiden paper, and the authors show that this exact problem happens frequently in practice. Brandes, U. et al. Google Scholar. SPATA2 currently offers the functions findSeuratClusters (), findMonocleClusters () and findNearestNeighbourClusters () which are wrapper around widely used clustering algorithms. Porter, M. A., Onnela, J.-P. & Mucha, P. J. 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). Nodes 13 should form a community and nodes 46 should form another community. 20, 172188, https://doi.org/10.1109/TKDE.2007.190689 (2008). V. A. Traag. If you cant use Leiden, choosing Smart Local Moving will likely give very similar results, but might be a bit slower as it doesnt include some of the simple speedups to Louvain like random moving and Louvain pruning. Waltman, L. & van Eck, N. J. Eng. Raghavan, U., Albert, R. & Kumara, S. Near linear time algorithm to detect community structures in large-scale networks. Article leidenalg. Subset optimality is the strongest guarantee that is provided by the Leiden algorithm. In this stage we essentially collapse communities down into a single representative node, creating a new simplified graph. Sci. Bae, S., Halperin, D., West, J. D., Rosvall, M. & Howe, B. Scalable and Efficient Flow-Based Community Detection for Large-Scale Graph Analysis. This is because Louvain only moves individual nodes at a time. Each point corresponds to a certain iteration of an algorithm, with results averaged over 10 experiments. Runtime versus quality for benchmark networks. The quality of such an asymptotically stable partition provides an upper bound on the quality of an optimal partition. Mech. The idea of the refinement phase in the Leiden algorithm is to identify a partition \({{\mathscr{P}}}_{{\rm{refined}}}\) that is a refinement of \({\mathscr{P}}\). In the worst case, communities may even be disconnected, especially when running the algorithm iteratively. The Web of Science network is the most difficult one. In other words, communities are guaranteed to be well separated. Newman, M. E. J. 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 Weights for edges an also be passed to the leiden algorithm either as a separate vector or weights or a weighted adjacency matrix. Louvain quickly converges to a partition and is then unable to make further improvements. Note that Leiden clustering directly clusters the neighborhood graph of cells, which we already computed in the previous section. Below we offer an intuitive explanation of these properties. Rev. Data Eng. Are you sure you want to create this branch? Communities in Networks. ADS 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. Article J. (We implemented both algorithms in Java, available from https://github.com/CWTSLeiden/networkanalysis and deposited at Zenodo23. This method tries to maximise the difference between the actual number of edges in a community and the expected number of such edges. Nonlin. 10, for the IMDB and Amazon networks, Leiden reaches a stable iteration relatively quickly, presumably because these networks have a fairly simple community structure. Usually, the Louvain algorithm starts from a singleton partition, in which each node is in its own community. In the local move procedure in the Leiden algorithm, only nodes whose neighborhood . As can be seen in Fig. 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. Nevertheless, depending on the relative strengths of the different connections, these nodes may still be optimally assigned to their current community. It does not guarantee that modularity cant be increased by moving nodes between communities. Phys. Finally, we demonstrate the excellent performance of the algorithm for several benchmark and real-world networks. In short, the problem of badly connected communities has important practical consequences. (We ensured that modularity optimisation for the subnetwork was fully consistent with modularity optimisation for the whole network13) The Leiden algorithm was run until a stable iteration was obtained. Analyses based on benchmark networks have only a limited value because these networks are not representative of empirical real-world networks. J. Stat. In particular, it yields communities that are guaranteed to be connected. Electr. Int. 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. In the most difficult case (=0.9), Louvain requires almost 2.5 days, while Leiden needs fewer than 10 minutes. Louvain pruning keeps track of a list of nodes that have the potential to change communities, and only revisits nodes in this list, which is much smaller than the total number of nodes. PubMed The R implementation of Leiden can be run directly on the snn igraph object in Seurat. 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. Hence, for lower values of , the difference in quality is negligible. It implies uniform -density and all the other above-mentioned properties. 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 fact, by implementing the refinement phase in the right way, several attractive guarantees can be given for partitions produced by the Leiden algorithm. Later iterations of the Louvain algorithm are very fast, but this is only because the partition remains the same. The Louvain algorithm10 is very simple and elegant. 9 shows that more than 10 iterations of the Leiden algorithm can be performed before the Louvain algorithm has finished its first iteration. You are using a browser version with limited support for CSS. The DBLP network is somewhat more challenging, requiring almost 80 iterations on average to reach a stable iteration. Higher resolutions lead to more communities and lower resolutions lead to fewer communities, similarly to the resolution parameter for modularity. The algorithm is described in pseudo-code in AlgorithmA.2 in SectionA of the Supplementary Information. To address this important shortcoming, we introduce a new algorithm that is faster, finds better partitions and provides explicit guarantees and bounds. The Louvain algorithm starts from a singleton partition in which each node is in its own community (a). partition_type : Optional [ Type [ MutableVertexPartition ]] (default: None) Type of partition to use. Is modularity with a resolution parameter equivalent to leidenalg.RBConfigurationVertexPartition? Phys. Powered by DataCamp DataCamp The thick edges in Fig. Scaling of benchmark results for difficulty of the partition. Node optimality is also guaranteed after a stable iteration of the Louvain algorithm. Technol. Instead, a node may be merged with any community for which the quality function increases. In this case we know the answer is exactly 10. AMS 56, 10821097 (2009). That is, one part of such an internally disconnected community can reach another part only through a path going outside the community. Leiden keeps finding better partitions for empirical networks also after the first 10 iterations of the algorithm. 2004. Each point corresponds to a certain iteration of an algorithm, with results averaged over 10 experiments. They show that the original Louvain algorithm that can result in badly connected communities (even communities that are completely disconnected internally) and propose an alternative method, Leiden, that guarantees that communities are well connected. It partitions the data space and identifies the sub-spaces using the Apriori principle.