leiden clustering explained leiden clustering explained

Speed and quality of the Louvain and the Leiden algorithm for benchmark networks of increasing size (two iterations). Raghavan, U., Albert, R. & Kumara, S. Near linear time algorithm to detect community structures in large-scale networks. This makes sense, because after phase one the total size of the graph should be significantly reduced. Acad. The percentage of disconnected communities even jumps to 16% for the DBLP network. The inspiration for this method of community detection is the optimization of modularity as the algorithm progresses. 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. For larger networks and higher values of , Louvain is much slower than Leiden. If nothing happens, download Xcode and try again. Rev. There was a problem preparing your codespace, please try again. Importantly, the first iteration of the Leiden algorithm is the most computationally intensive one, and subsequent iterations are faster. Rev. A community size of 50 nodes was used for the results presented below, but larger community sizes yielded qualitatively similar results. Proc. http://dx.doi.org/10.1073/pnas.0605965104. For empirical networks, it may take quite some time before the Leiden algorithm reaches its first stable iteration. Source Code (2018). By submitting a comment you agree to abide by our Terms and Community Guidelines. The Leiden algorithm has been specifically designed to address the problem of badly connected communities. As discussed earlier, the Louvain algorithm does not guarantee connectivity. Phys. 7, whereas Louvain becomes much slower for more difficult partitions, Leiden is much less affected by the difficulty of the partition. E 92, 032801, https://doi.org/10.1103/PhysRevE.92.032801 (2015). Fortunato, S. Community detection in graphs. Learn more. Modularity is a popular objective function used with the Louvain method for community detection. Leiden is faster than Louvain especially for larger networks. Article Phys. One may expect that other nodes in the old community will then also be moved to other communities. Based on project statistics from the GitHub repository for the PyPI package leiden-clustering, we found that it has been starred 1 times. and L.W. PubMedGoogle Scholar. 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. After the refinement phase is concluded, communities in \({\mathscr{P}}\) often will have been split into multiple communities in \({{\mathscr{P}}}_{{\rm{refined}}}\), but not always. The nodes are added to the queue in a random order. Figure6 presents total runtime versus quality for all iterations of the Louvain and the Leiden algorithm. Sci. import leidenalg as la import igraph as ig Example output. Phys. Nonlin. Consider the partition shown in (a). Ozaki, Naoto, Hiroshi Tezuka, and Mary Inaba. In the case of modularity, communities may have significant substructure both because of the resolution limit and because of the shortcomings of Louvain. The Beginner's Guide to Dimensionality Reduction. A new methodology for constructing a publication-level classification system of science. 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. All authors conceived the algorithm and contributed to the source code. In this case we know the answer is exactly 10. Once aggregation is complete we restart the local moving phase, and continue to iterate until everything converges down to one node. Removing such a node from its old community disconnects the old community. We provide the full definitions of the properties as well as the mathematical proofs in SectionD of the Supplementary Information. http://iopscience.iop.org/article/10.1088/1742-5468/2008/10/P10008/meta. 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. Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. Based on this partition, an aggregate network is created (c). CPM does not suffer from this issue13. Fortunato, Santo, and Marc Barthlemy. Cluster cells using Louvain/Leiden community detection Description. Neurosci. However, modularity suffers from a difficult problem known as the resolution limit (Fortunato and Barthlemy 2007). The refined partition \({{\mathscr{P}}}_{{\rm{refined}}}\) is obtained as follows. In the local moving phase, individual nodes are moved to the community that yields the largest increase in the quality function. One of the most popular algorithms for uncovering community structure is the so-called Louvain algorithm. Computer Syst. E 74, 016110, https://doi.org/10.1103/PhysRevE.74.016110 (2006). However, in the case of the Web of Science network, more than 5% of the communities are disconnected in the first iteration. We first applied the Scanpy pipeline, including its clustering method (Leiden clustering), on the PBMC dataset. For the results reported below, the average degree was set to \(\langle k\rangle =10\). However, focussing only on disconnected communities masks the more fundamental issue: Louvain finds arbitrarily badly connected communities. Speed and quality for the first 10 iterations of the Louvain and the Leiden algorithm for benchmark networks (n=106 and n=107). 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. Local Resolution-Limit-Free Potts Model for Community Detection. Phys. The property of -separation is also guaranteed by the Louvain algorithm. This is the crux of the Leiden paper, and the authors show that this exact problem happens frequently in practice. There are many different approaches and algorithms to perform clustering tasks. AMS 56, 10821097 (2009). Then the Leiden algorithm can be run on the adjacency matrix. Modularity is a measure of the structure of networks or graphs which measures the strength of division of a network into modules (also called groups, clusters or communities). Node optimality is also guaranteed after a stable iteration of the Louvain algorithm. However, the initial partition for the aggregate network is based on P, just like in the Louvain algorithm. You are using a browser version with limited support for CSS. & Fortunato, S. Community detection algorithms: A comparative analysis. Sci. 10, 186198, https://doi.org/10.1038/nrn2575 (2009). 2(a). It partitions the data space and identifies the sub-spaces using the Apriori principle. Electr. 2004. The Louvain algorithm starts from a singleton partition in which each node is in its own community (a). Subpartition -density does not imply that individual nodes are locally optimally assigned. This is very similar to what the smart local moving algorithm does. 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. The quality improvement realised by the Leiden algorithm relative to the Louvain algorithm is larger for empirical networks than for benchmark networks. The Leiden algorithm is typically iterated: the output of one iteration is used as the input for the next iteration. J. We generated benchmark networks in the following way. You signed in with another tab or window. 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. For each network, we repeated the experiment 10 times. MathSciNet Natl. Hence, the problem of Louvain outlined above is independent from the issue of the resolution limit. Communities may even be disconnected. 10, for the IMDB and Amazon networks, Leiden reaches a stable iteration relatively quickly, presumably because these networks have a fairly simple community structure. 6 show that Leiden outperforms Louvain in terms of both computational time and quality of the partitions. If material is not included in the articles Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. This commit does not belong to any branch on this repository, and may belong to a fork outside of the repository. The quality of such an asymptotically stable partition provides an upper bound on the quality of an optimal partition. Google Scholar. (2) and m is the number of edges. This is very similar to what the smart local moving algorithm does. Hence, the community remains disconnected, unless it is merged with another community that happens to act as a bridge. 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. In this stage we essentially collapse communities down into a single representative node, creating a new simplified graph. performed the experimental analysis. Data Eng. 2015. For each community in a partition that was uncovered by the Louvain algorithm, we determined whether it is internally connected or not. 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. We used the CPM quality function. 63, 23782392, https://doi.org/10.1002/asi.22748 (2012). As the problem of modularity optimization is NP-hard, we need heuristic methods to optimize modularity (or CPM). 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. In later stages, most neighbors will belong to the same community, and its very likely that the best move for the node is to the community that most of its neighbors already belong to. ADS E Stat. Runtime versus quality for benchmark networks. Analyses based on benchmark networks have only a limited value because these networks are not representative of empirical real-world networks. Google Scholar. This is not too difficult to explain. Such algorithms are rather slow, making them ineffective for large networks. Such a modular structure is usually not known beforehand. ADS 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 this way, the constant acts as a resolution parameter, and setting the constant higher will result in fewer communities. 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. Good, B. H., De Montjoye, Y. As can be seen in the figure, Louvain quickly reaches a state in which it is unable to find better partitions. CAS Powered by DataCamp DataCamp Louvain quickly converges to a partition and is then unable to make further improvements. IEEE Trans. When iterating Louvain, the quality of the partitions will keep increasing until the algorithm is unable to make any further improvements. One of the most popular algorithms to optimise modularity is the so-called Louvain algorithm10, named after the location of its authors. Run the code above in your browser using DataCamp Workspace.