leiden clustering explained

The algorithm continues to move nodes in the rest of the network. These nodes can be approximately identified based on whether neighbouring nodes have changed communities. 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. An aggregate network (d) is created based on the refined partition, using the non-refined partition to create an initial partition for the aggregate network. Wolf, F. A. et al. The property of -connectivity is a slightly stronger variant of ordinary connectivity. That is, no subset can be moved to a different 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. Rev. The Leiden algorithm provides several guarantees. 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. For empirical networks, it may take quite some time before the Leiden algorithm reaches its first stable iteration. 8, 207218, https://doi.org/10.17706/IJCEE.2016.8.3.207-218 (2016). We use six empirical networks in our analysis. All experiments were run on a computer with 64 Intel Xeon E5-4667v3 2GHz CPUs and 1TB internal memory. To find an optimal grouping of cells into communities, we need some way of evaluating different partitions in the graph. However, for higher values of , Leiden becomes orders of magnitude faster than Louvain, reaching 10100 times faster runtimes for the largest networks. The corresponding results are presented in the Supplementary Fig. Get the most important science stories of the day, free in your inbox. 2015. A structure that is more informative than the unstructured set of clusters returned by flat clustering. 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. Although originally defined for modularity, the Louvain algorithm can also be used to optimise other quality functions. Louvain has two phases: local moving and aggregation. 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. 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). B 86, 471, https://doi.org/10.1140/epjb/e2013-40829-0 (2013). To do this we just sum all the edge weights between nodes of the corresponding communities to get a single weighted edge between them, and collapse each community down to a single new node. E Stat. Google Scholar. This is because Louvain only moves individual nodes at a time. Not. As shown in Fig. A number of iterations of the Leiden algorithm can be performed before the Louvain algorithm has finished its first iteration. Number of iterations before the Leiden algorithm has reached a stable iteration for six empirical networks. E 78, 046110, https://doi.org/10.1103/PhysRevE.78.046110 (2008). (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. V.A.T. A smart local moving algorithm for large-scale modularity-based community detection. http://iopscience.iop.org/article/10.1088/1742-5468/2008/10/P10008/meta. Correspondence to Zenodo, https://doi.org/10.5281/zenodo.1466831 https://github.com/CWTSLeiden/networkanalysis. One of the most popular algorithms to optimise modularity is the so-called Louvain algorithm10, named after the location of its authors. Similarly, in citation networks, such as the Web of Science network, nodes in a community are usually considered to share a common topic26,27. The PyPI package leiden-clustering receives a total of 15 downloads a week. Ozaki, Naoto, Hiroshi Tezuka, and Mary Inaba. We can guarantee a number of properties of the partitions found by the Leiden algorithm at various stages of the iterative process. The degree of randomness in the selection of a community is determined by a parameter >0. Leiden is the most recent major development in this space, and highlighted a flaw in the original Louvain algorithm (Traag, Waltman, and Eck 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. For example, after four iterations, the Web UK network has 8% disconnected communities, but twice as many badly connected communities. Community detection is an important task in the analysis of complex networks. 8 (3): 207. https://pdfs.semanticscholar.org/4ea9/74f0fadb57a0b1ec35cbc5b3eb28e9b966d8.pdf. The two phases are repeated until the quality function cannot be increased further. These steps are repeated until the quality cannot be increased further. Google Scholar. 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. In the local moving phase, individual nodes are moved to the community that yields the largest increase in the quality function. We show that this algorithm has a major defect that largely went unnoticed until now: the Louvain algorithm may yield arbitrarily badly connected communities. Rev. It is good at identifying small clusters. Subpartition -density is not guaranteed by the Louvain algorithm. For example, nodes in a community in biological or neurological networks are often assumed to share similar functions or behaviour25. Perhaps surprisingly, iterating the algorithm aggravates the problem, even though it does increase the quality function. All communities are subpartition -dense. CAS Phys. The quality improvement realised by the Leiden algorithm relative to the Louvain algorithm is larger for empirical networks than for benchmark networks. This step will involve reducing the dimensionality of our data into two dimensions using uniform manifold approximation (UMAP), allowing us to visualize our cell populations as they are binned into discrete populations using Leiden clustering. Crucially, however, the percentage of badly connected communities decreases with each iteration of the Leiden algorithm. Guimer, R. & Nunes Amaral, L. A. Functional cartography of complex metabolic networks. This is very similar to what the smart local moving algorithm does. 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. In other words, modularity may hide smaller communities and may yield communities containing significant substructure. Sign up for the Nature Briefing newsletter what matters in science, free to your inbox daily. We now compare how the Leiden and the Louvain algorithm perform for the six empirical networks listed in Table2. Louvain community detection algorithm was originally proposed in 2008 as a fast community unfolding method for large networks. Slider with three articles shown per slide. Clustering is a machine learning technique in which similar data points are grouped into the same cluster based on their attributes. Nature 433, 895900, https://doi.org/10.1038/nature03288 (2005). The value of the resolution parameter was determined based on the so-called mixing parameter 13. The authors act as bibliometric consultants to CWTS B.V., which makes use of community detection algorithms in commercial products and services. 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. Figure6 presents total runtime versus quality for all iterations of the Louvain and the Leiden algorithm. & Arenas, A. This should be the first preference when choosing an algorithm. The differences are not very large, which is probably because both algorithms find partitions for which the quality is close to optimal, related to the issue of the degeneracy of quality functions29. The Web of Science network is the most difficult one. MATH 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. 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. This is not too difficult to explain. Internet Explorer). However, the initial partition for the aggregate network is based on P, just like in the Louvain algorithm. E 80, 056117, https://doi.org/10.1103/PhysRevE.80.056117 (2009). Leiden consists of the following steps: The refinement step allows badly connected communities to be split before creating the aggregate network. Such algorithms are rather slow, making them ineffective for large networks. N.J.v.E. Runtime versus quality for empirical networks. The community with which a node is merged is selected randomly18. Technol. Traag, V.A., Waltman, L. & van Eck, N.J. From Louvain to Leiden: guaranteeing well-connected communities. 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. conda install -c conda-forge leidenalg pip install leiden-clustering Used via. As can be seen in Fig. However, as increases, the Leiden algorithm starts to outperform the Louvain algorithm. Phys. 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. Theory Exp. Google Scholar. In practice, this means that small clusters can hide inside larger clusters, making their identification difficult. Faster unfolding of communities: Speeding up the Louvain algorithm. For the Amazon, DBLP and Web UK networks, Louvain yields on average respectively 23%, 16% and 14% badly connected communities. Provided by the Springer Nature SharedIt content-sharing initiative. Modularity is a popular objective function used with the Louvain method for community detection. In subsequent iterations, the percentage of disconnected communities remains fairly stable. The percentage of badly connected communities is less affected by the number of iterations of the Louvain algorithm. This represents the following graph structure. 4, in the first iteration of the Louvain algorithm, the percentage of badly connected communities can be quite high. To address this important shortcoming, we introduce a new algorithm that is faster, finds better partitions and provides explicit guarantees and bounds. This continues until the queue is empty. ADS Presumably, many of the badly connected communities in the first iteration of Louvain become disconnected in the second iteration. We find that the Leiden algorithm commonly finds partitions of higher quality in less time. Waltman, L. & van Eck, N. J. Inf. We typically reduce the dimensionality of the data first by running PCA, then construct a neighbor graph in the reduced space. If nothing happens, download GitHub Desktop and try again. Article * (2018). Nonlin. However, so far this problem has never been studied for the Louvain algorithm. To obtain The Leiden algorithm starts from a singleton partition (a). Later iterations of the Louvain algorithm only aggravate the problem of disconnected communities, even though the quality function (i.e. Communities may even be disconnected. Luecken, M. D. Application of multi-resolution partitioning of interaction networks to the study of complex disease. 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 For the results reported below, the average degree was set to \(\langle k\rangle =10\). (2) and m is the number of edges. As can be seen in Fig. Node mergers that cause the quality function to decrease are not considered. Then optimize the modularity function to determine clusters. Even worse, the Amazon network has 5% disconnected communities, but 25% badly connected communities. Google Scholar. 81 (4 Pt 2): 046114. http://dx.doi.org/10.1103/PhysRevE.81.046114. Note that the object for Seurat version 3 has changed. 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. 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. 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. 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. E 69, 026113, https://doi.org/10.1103/PhysRevE.69.026113 (2004). You will not need much Python to use it. Newman, M E J, and M Girvan. Based on this partition, an aggregate network is created (c). Community detection can then be performed using this graph. The 'devtools' package will be used to install 'leiden' and the dependancies (igraph and reticulate). Unlike the Louvain algorithm, the Leiden algorithm uses a fast local move procedure in this phase. In this stage we essentially collapse communities down into a single representative node, creating a new simplified graph. leiden_clsutering is distributed under a BSD 3-Clause License (see LICENSE). In fact, if we keep iterating the Leiden algorithm, it will converge to a partition without any badly connected communities, as discussed earlier. Node optimality is also guaranteed after a stable iteration of the Louvain algorithm. Leiden keeps finding better partitions for empirical networks also after the first 10 iterations of the algorithm. Speed and quality for the first 10 iterations of the Louvain and the Leiden algorithm for benchmark networks (n=106 and n=107). PubMed 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.

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