2010. Speed and quality of the Louvain and the Leiden algorithm for benchmark networks of increasing size (two iterations). First iteration runtime for empirical networks. Perhaps surprisingly, iterating the algorithm aggravates the problem, even though it does increase the quality function. E 92, 032801, https://doi.org/10.1103/PhysRevE.92.032801 (2015). Mech. 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. Furthermore, if all communities in a partition are uniformly -dense, the quality of the partition is not too far from optimal, as shown in SectionE of the Supplementary Information. Nonlin. Subpartition -density does not imply that individual nodes are locally optimally assigned. Rev. Leiden algorithm. E 74, 036104, https://doi.org/10.1103/PhysRevE.74.036104 (2006). For empirical networks, it may take quite some time before the Leiden algorithm reaches its first stable iteration. Basically, there are two types of hierarchical cluster analysis strategies - 1. Run the code above in your browser using DataCamp Workspace. E 74, 016110, https://doi.org/10.1103/PhysRevE.74.016110 (2006). Later iterations of the Louvain algorithm are very fast, but this is only because the partition remains the same. Moreover, when no more nodes can be moved, the algorithm will aggregate the network. Rev. Finding and Evaluating Community Structure in Networks. Phys. The horizontal axis indicates the cumulative time taken to obtain the quality indicated on the vertical axis. Subpartition -density is not guaranteed by the Louvain algorithm. Duch, J. Hence, no further improvements can be made after a stable iteration of the Louvain algorithm. As such, we scored leiden-clustering popularity level to be Limited. 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. Besides being pervasive, the problem is also sizeable. Communities in Networks. We show that this algorithm has a major defect that largely went unnoticed until now: the Louvain algorithm may yield arbitrarily 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. 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. The Beginner's Guide to Dimensionality Reduction. 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). CAS If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate. We prove that the Leiden algorithm yields communities that are guaranteed to be connected. This problem is different from the well-known issue of the resolution limit of modularity14. 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. 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. conda install -c conda-forge leidenalg pip install leiden-clustering Used via. In contrast, Leiden keeps finding better partitions in each iteration. Rev. When a disconnected community has become a node in an aggregate network, there are no more possibilities to split up the community. Nodes 13 should form a community and nodes 46 should form another community. Good, B. H., De Montjoye, Y. Phys. Google Scholar. This contrasts with the Leiden algorithm. One of the most popular algorithms to optimise modularity is the so-called Louvain algorithm10, named after the location of its authors. Second, to study the scaling of the Louvain and the Leiden algorithm, we use benchmark networks, allowing us to compare the algorithms in terms of both computational time and quality of the partitions. E 69, 026113, https://doi.org/10.1103/PhysRevE.69.026113 (2004). bioRxiv, https://doi.org/10.1101/208819 (2018). The Louvain algorithm guarantees that modularity cannot be increased by merging communities (it finds a locally optimal solution). Each point corresponds to a certain iteration of an algorithm, with results averaged over 10 experiments. Google Scholar. http://iopscience.iop.org/article/10.1088/1742-5468/2008/10/P10008/meta. Disconnected community. In the worst case, communities may even be disconnected, especially when running the algorithm iteratively. However, focussing only on disconnected communities masks the more fundamental issue: Louvain finds arbitrarily badly connected communities. Blondel, V D, J L Guillaume, and R Lambiotte. This is the crux of the Leiden paper, and the authors show that this exact problem happens frequently in practice. Communities in \({\mathscr{P}}\) may be split into multiple subcommunities in \({{\mathscr{P}}}_{{\rm{refined}}}\). Louvain can also be quite slow, as it spends a lot of time revisiting nodes that may not have changed neighborhoods. Even though clustering can be applied to networks, it is a broader field in unsupervised machine learning which deals with multiple attribute types. o CLIQUE (Clustering in Quest): - CLIQUE is a combination of density-based and grid-based clustering algorithm. 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. We find that the Leiden algorithm is faster than the Louvain algorithm and uncovers better partitions, in addition to providing explicit guarantees. For example, after four iterations, the Web UK network has 8% disconnected communities, but twice as many badly connected communities. & Clauset, A. Eur. In this paper, we show that the Louvain algorithm has a major problem, for both modularity and CPM. Agglomerative clustering is a bottom-up approach. Phys. For each set of parameters, we repeated the experiment 10 times. 2015. CPM has the advantage that it is not subject to the resolution limit. 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. Source Code (2018). ADS As shown in Fig. To address this problem, we introduce 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 \({\mathscr{P}}\). Importantly, the first iteration of the Leiden algorithm is the most computationally intensive one, and subsequent iterations are faster. Below we offer an intuitive explanation of these properties. Leiden consists of the following steps: The refinement step allows badly connected communities to be split before creating the aggregate network. 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"). Phys. 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. The numerical details of the example can be found in SectionB of the Supplementary Information. Any sub-networks that are found are treated as different communities in the next aggregation step. Each of these can be used as an objective function for graph-based community detection methods, with our goal being to maximize this value. V. A. Traag. Ph.D. thesis, (University of Oxford, 2016). 5, for lower values of the partition is well defined, and neither the Louvain nor the Leiden algorithm has a problem in determining the correct partition in only two iterations. Then optimize the modularity function to determine clusters. Louvain community detection algorithm was originally proposed in 2008 as a fast community unfolding method for large networks. CAS Article The Leiden algorithm starts from a singleton partition (a). The Louvain algorithm is a simple and popular method for community detection (Blondel, Guillaume, and Lambiotte 2008). The percentage of disconnected communities is more limited, usually around 1%. However, as increases, the Leiden algorithm starts to outperform the Louvain algorithm. Usually, the Louvain algorithm starts from a singleton partition, in which each node is in its own community. where >0 is a resolution parameter4. The Louvain method for community detection is a popular way to discover communities from single-cell data. & Moore, C. Finding community structure in very large networks. B 86, 471, https://doi.org/10.1140/epjb/e2013-40829-0 (2013). Runtime versus quality for empirical networks. Due to the resolution limit, modularity may cause smaller communities to be clustered into larger communities. To address this important shortcoming, we introduce a new algorithm that is faster, finds better partitions and provides explicit guarantees and bounds. 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 addition, we prove that the algorithm converges to an asymptotically stable partition in which all subsets of all communities are locally optimally assigned. Rev. Some of these nodes may very well act as bridges, similarly to node 0 in the above example. In this iterative scheme, Louvain provides two guarantees: (1) no communities can be merged and (2) no nodes can be moved. 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. This is similar to what we have seen for benchmark networks. Community detection is an important task in the analysis of complex networks. Excluding node mergers that decrease the quality function makes the refinement phase more efficient. Newman, M E J, and M Girvan. Rep. 6, 30750, https://doi.org/10.1038/srep30750 (2016). Although originally defined for modularity, the Louvain algorithm can also be used to optimise other quality functions. This enables us to find cases where its beneficial to split a community. import leidenalg as la import igraph as ig Example output. In our experimental analysis, we observe that up to 25% of the communities are badly connected and up to 16% are disconnected. 1 and summarised in pseudo-code in AlgorithmA.1 in SectionA of the Supplementary Information. The second iteration of Louvain shows a large increase in the percentage of disconnected communities. Computer Syst. 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. 10, for the IMDB and Amazon networks, Leiden reaches a stable iteration relatively quickly, presumably because these networks have a fairly simple community structure. The property of -separation is also guaranteed by the Louvain algorithm. ADS Article Waltman, L. & van Eck, N. J. In a stable iteration, the partition is guaranteed to be node optimal and subpartition -dense. 2 represent stronger connections, while the other edges represent weaker connections. For the results reported below, the average degree was set to \(\langle k\rangle =10\). 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. Additionally, we implemented a Python package, available from https://github.com/vtraag/leidenalg and deposited at Zenodo24). Louvain keeps visiting all nodes in a network until there are no more node movements that increase the quality function. Based on this partition, an aggregate network is created (c). 104 (1): 3641. 69 (2 Pt 2): 026113. http://dx.doi.org/10.1103/PhysRevE.69.026113. 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. Speed and quality for the first 10 iterations of the Louvain and the Leiden algorithm for six empirical networks. Introduction The Louvain method is an algorithm to detect communities in large networks. For higher values of , Leiden finds better partitions than Louvain. The Leiden algorithm has been specifically designed to address the problem of badly connected communities. However, it is also possible to start the algorithm from a different partition15. 81 (4 Pt 2): 046114. http://dx.doi.org/10.1103/PhysRevE.81.046114. 2013. In the first iteration, Leiden is roughly 220 times faster than Louvain. 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. Phys. Sci. Raghavan, U., Albert, R. & Kumara, S. Near linear time algorithm to detect community structures in large-scale networks. In the refinement phase, nodes are not necessarily greedily merged with the community that yields the largest increase in the quality function. The algorithm then moves individual nodes in the aggregate network (d). Brandes, U. et al. Use Git or checkout with SVN using the web URL. B 86 (11): 471. https://doi.org/10.1140/epjb/e2013-40829-0. Communities may even be disconnected. 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. Fortunato, S. Community detection in graphs. This can be a shared nearest neighbours matrix derived from a graph object. In other words, modularity may hide smaller communities and may yield communities containing significant substructure. Somewhat stronger guarantees can be obtained by iterating the algorithm, using the partition obtained in one iteration of the algorithm as starting point for the next iteration. Furthermore, by relying on a fast local move approach, the Leiden algorithm runs faster than the Louvain algorithm. In this section, we analyse and compare the performance of the two algorithms in practice. We find that the Leiden algorithm commonly finds partitions of higher quality in less time.
Elizabeth Shamblin Hannah Net Worth,
Red River Valley Speedway Hall Of Fame,
Articles L
