leiden clustering explained

Ph.D. thesis, (University of Oxford, 2016). In the case of modularity, communities may have significant substructure both because of the resolution limit and because of the shortcomings of Louvain. Blondel, V. D., Guillaume, J.-L., Lambiotte, R. & Lefebvre, E. Fast unfolding of communities in large networks. Fortunato, S. Community detection in graphs. The algorithm may yield arbitrarily badly connected communities, over and above the well-known issue of the resolution limit14. Presumably, many of the badly connected communities in the first iteration of Louvain become disconnected in the second iteration. For each network, we repeated the experiment 10 times. Newman, M. E. J. This contrasts with the Leiden algorithm. We now consider the guarantees provided by the Leiden algorithm. MATH Rev. Subpartition -density does not imply that individual nodes are locally optimally assigned. Then optimize the modularity function to determine clusters. Usually, the Louvain algorithm starts from a singleton partition, in which each node is in its own community. 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. Rev. You are using a browser version with limited support for CSS. More subtle problems may occur as well, causing Louvain to find communities that are connected, but only in a very weak sense. We conclude that the Leiden algorithm is strongly preferable to the Louvain algorithm. 2008. U. S. A. The count of badly connected communities also included disconnected communities. The above results shows that the problem of disconnected and badly connected communities is quite pervasive in practice. Even worse, the Amazon network has 5% disconnected communities, but 25% badly connected communities. According to CPM, it is better to split into two communities when the link density between the communities is lower than the constant. A new methodology for constructing a publication-level classification system of science. For larger networks and higher values of , Louvain is much slower than Leiden. Article The PyPI package leiden-clustering receives a total of 15 downloads a week. This way of defining the expected number of edges is based on the so-called configuration model. & Arenas, A. 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 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. As can be seen in Fig. An alternative quality function is the Constant Potts Model (CPM)13, which overcomes some limitations of modularity. We can guarantee a number of properties of the partitions found by the Leiden algorithm at various stages of the iterative process. Louvain community detection algorithm was originally proposed in 2008 as a fast community unfolding method for large networks. 4, in the first iteration of the Louvain algorithm, the percentage of badly connected communities can be quite high. Random moving is a very simple adjustment to Louvain local moving proposed in 2015 (Traag 2015). To overcome the problem of arbitrarily badly connected communities, we introduced a new algorithm, which we refer to as the Leiden algorithm. Please Rev. After a stable iteration of the Leiden algorithm, the algorithm may still be able to make further improvements in later iterations. ADS We study the problem of badly connected communities when using the Louvain algorithm for several empirical networks. In the previous section, we showed that the Leiden algorithm guarantees a number of properties of the partitions uncovered at different stages of the algorithm. These nodes are therefore optimally assigned to their current community. The Web of Science network is the most difficult one. Here we can see partitions in the plotted results. Perhaps surprisingly, iterating the algorithm aggravates the problem, even though it does increase the quality function. This represents the following graph structure. import leidenalg as la import igraph as ig Example output. Rev. Correspondence to Sci. Obviously, this is a worst case example, showing that disconnected communities may be identified by the Louvain algorithm. When the Leiden algorithm found that a community could be split into multiple subcommunities, we counted the community as badly connected. 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. With one exception (=0.2 and n=107), all results in Fig. volume9, Articlenumber:5233 (2019) The two phases are repeated until the quality function cannot be increased further. GitHub on Feb 15, 2020 Do you think the performance improvements will also be implemented in leidenalg? As such, we scored leiden-clustering popularity level to be Limited. Centre for Science and Technology Studies, Leiden University, Leiden, The Netherlands, You can also search for this author in The difference in computational time is especially pronounced for larger networks, with Leiden being up to 20 times faster than Louvain in empirical networks. The algorithm is described in pseudo-code in AlgorithmA.2 in SectionA of the Supplementary Information. Based on this partition, an aggregate network is created (c). 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. We demonstrate the performance of the Leiden algorithm for several benchmark and real-world networks. Here is some small debugging code I wrote to find this. Theory Exp. From Louvain to Leiden: Guaranteeing Well-Connected Communities, October. Rev. Google Scholar. Cluster cells using Louvain/Leiden community detection Description. Get the most important science stories of the day, free in your inbox. Louvain quickly converges to a partition and is then unable to make further improvements. Faster unfolding of communities: Speeding up the Louvain algorithm. Finding and Evaluating Community Structure in Networks. Phys. For the results reported below, the average degree was set to \(\langle k\rangle =10\). The value of the resolution parameter was determined based on the so-called mixing parameter 13. For example, nodes in a community in biological or neurological networks are often assumed to share similar functions or behaviour25. https://leidenalg.readthedocs.io/en/latest/reference.html. 69 (2 Pt 2): 026113. http://dx.doi.org/10.1103/PhysRevE.69.026113. Consider the partition shown in (a). ACM Trans. ADS This makes sense, because after phase one the total size of the graph should be significantly reduced. It means that there are no individual nodes that can be moved to a different community. 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. However, the Louvain algorithm does not consider this possibility, since it considers only individual node movements. 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. To use Leiden with the Seurat pipeline for a Seurat Object object that has an SNN computed (for example with Seurat::FindClusters with save.SNN = TRUE). Hence, the Leiden algorithm effectively addresses the problem of badly connected communities. Phys. 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"). For each network, Table2 reports the maximal modularity obtained using the Louvain and the Leiden algorithm. As shown in Fig. All experiments were run on a computer with 64 Intel Xeon E5-4667v3 2GHz CPUs and 1TB internal memory. modularity) increases. Sign up for the Nature Briefing newsletter what matters in science, free to your inbox daily. Removing such a node from its old community disconnects the old community. To find an optimal grouping of cells into communities, we need some way of evaluating different partitions in the graph. Work fast with our official CLI. Modularity is used most commonly, but is subject to the resolution limit. First, we show that the Louvain algorithm finds disconnected communities, and more generally, badly connected communities in the empirical networks. 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. 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 \({\mathscr{P}}\). Use Git or checkout with SVN using the web URL. 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. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/. However, focussing only on disconnected communities masks the more fundamental issue: Louvain finds arbitrarily badly connected communities. It only implies that individual nodes are well connected to their community. First calculate k-nearest neighbors and construct the SNN graph. 7, whereas Louvain becomes much slower for more difficult partitions, Leiden is much less affected by the difficulty of the partition. PubMed We name our algorithm the Leiden algorithm, after the location of its authors. We show that this algorithm has a major defect that largely went unnoticed until now: the Louvain algorithm may yield arbitrarily badly connected communities. & Bornholdt, S. Statistical mechanics of community detection. Klavans, R. & Boyack, K. W. Which Type of Citation Analysis Generates the Most Accurate Taxonomy of Scientific and Technical Knowledge? Communities may even be disconnected. Runtime versus quality for benchmark networks. In this post Ive mainly focused on the optimisation methods for community detection, rather than the different objective functions that can be used. 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. This can be a shared nearest neighbours matrix derived from a graph object. The high percentage of badly connected communities attests to this. 92 (3): 032801. http://dx.doi.org/10.1103/PhysRevE.92.032801. Speed of the first iteration of the Louvain and the Leiden algorithm for benchmark networks with increasingly difficult partitions (n=107). Source Code (2018). 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. PubMedGoogle Scholar. 10, 186198, https://doi.org/10.1038/nrn2575 (2009). All communities are subpartition -dense. Nevertheless, depending on the relative strengths of the different connections, these nodes may still be optimally assigned to their current community. The nodes are added to the queue in a random order. If nothing happens, download GitHub Desktop and try again. Phys. In fact, if we keep iterating the Leiden algorithm, it will converge to a partition without any badly connected communities, as discussed earlier. These steps are repeated until the quality cannot be increased further. In the Louvain algorithm, an aggregate network is created based on the partition \({\mathscr{P}}\) resulting from the local moving phase. 1 and summarised in pseudo-code in AlgorithmA.1 in SectionA of the Supplementary Information. Technol. The Leiden algorithm is partly based on the previously introduced smart local move algorithm15, which itself can be seen as an improvement of the Louvain algorithm. This function takes a cell_data_set as input, clusters the cells using . 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. As can be seen in Fig. 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.

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