leiden clustering explained leiden clustering explained

4. Publishers note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Cluster Determination Source: R/generics.R, R/clustering.R Identify clusters of cells by a shared nearest neighbor (SNN) modularity optimization based clustering algorithm. 69 (2 Pt 2): 026113. http://dx.doi.org/10.1103/PhysRevE.69.026113. The thick edges in Fig. Sci. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/. (We implemented both algorithms in Java, available from https://github.com/CWTSLeiden/networkanalysis and deposited at Zenodo23. SPATA2 currently offers the functions findSeuratClusters (), findMonocleClusters () and findNearestNeighbourClusters () which are wrapper around widely used clustering algorithms. Technol. Louvain has two phases: local moving and aggregation. In this section, we analyse and compare the performance of the two algorithms in practice. 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. Work fast with our official CLI. In the first step of the next iteration, Louvain will again move individual nodes in the network. Modularity is given by. That is, one part of such an internally disconnected community can reach another part only through a path going outside the community. Phys. Indeed, the percentage of disconnected communities becomes more comparable to the percentage of badly connected communities in later iterations. A new methodology for constructing a publication-level classification system of science. Ph.D. thesis, (University of Oxford, 2016). Badly connected communities. This is not too difficult to explain. 92 (3): 032801. http://dx.doi.org/10.1103/PhysRevE.92.032801. This is very similar to what the smart local moving algorithm does. Rev. Note that if Leiden finds subcommunities, splitting up the community is guaranteed to increase modularity. This commit does not belong to any branch on this repository, and may belong to a fork outside of the repository. In the local move procedure in the Leiden algorithm, only nodes whose neighborhood . We find that the Leiden algorithm commonly finds partitions of higher quality in less time. Use Git or checkout with SVN using the web URL. However, as shown in this paper, the Louvain algorithm has a major shortcoming: the algorithm yields communities that may be arbitrarily badly connected. CPM is defined as. The difference in computational time is especially pronounced for larger networks, with Leiden being up to 20 times faster than Louvain in empirical networks. Directed Undirected Homogeneous Heterogeneous Weighted 1. Powered by DataCamp DataCamp 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. Rev. A partition of clusters as a vector of integers Examples Another important difference between the Leiden algorithm and the Louvain algorithm is the implementation of the local moving phase. Here is some small debugging code I wrote to find this. We now compare how the Leiden and the Louvain algorithm perform for the six empirical networks listed in Table2. In this paper, we show that the Louvain algorithm has a major problem, for both modularity and CPM. Neurosci. Sci. The quality of such an asymptotically stable partition provides an upper bound on the quality of an optimal partition. Article Computer Syst. These are the same networks that were also studied in an earlier paper introducing the smart local move algorithm15. All experiments were run on a computer with 64 Intel Xeon E5-4667v3 2GHz CPUs and 1TB internal memory. 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. Blondel, V D, J L Guillaume, and R Lambiotte. Traag, Vincent, Ludo Waltman, and Nees Jan van Eck. We therefore require a more principled solution, which we will introduce in the next section. We now consider the guarantees provided by the Leiden algorithm. The solution provided by Leiden is based on the smart local moving algorithm. 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. Use the Previous and Next buttons to navigate the slides or the slide controller buttons at the end to navigate through each slide. Bullmore, E. & Sporns, O. We applied the Louvain and the Leiden algorithm to exactly the same networks, using the same seed for the random number generator. However, this is not necessarily the case, as the other nodes may still be sufficiently strongly connected to their community, despite the fact that the community has become disconnected. Article Nodes 16 have connections only within this community, whereas node 0 also has many external connections. Rev. Rev. This makes sense, because after phase one the total size of the graph should be significantly reduced. However, in the case of the Web of Science network, more than 5% of the communities are disconnected in the first iteration. CAS Newman, M. E. J. 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. Even worse, the Amazon network has 5% disconnected communities, but 25% badly connected communities. Rotta, R. & Noack, A. Multilevel local search algorithms for modularity clustering. & Bornholdt, S. Statistical mechanics of community detection. 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"). Zenodo, https://doi.org/10.5281/zenodo.1466831 https://github.com/CWTSLeiden/networkanalysis. After a stable iteration of the Leiden algorithm, it is guaranteed that: All nodes are locally optimally assigned. In this way, the constant acts as a resolution parameter, and setting the constant higher will result in fewer communities. The degree of randomness in the selection of a community is determined by a parameter >0. Narrow scope for resolution-limit-free community detection. partition_type : Optional [ Type [ MutableVertexPartition ]] (default: None) Type of partition to use. The Louvain algorithm starts from a singleton partition in which each node is in its own community (a). This will compute the Leiden clusters and add them to the Seurat Object Class. 9, the Leiden algorithm also performs better than the Louvain algorithm in terms of the quality of the partitions that are obtained. By moving these nodes, Louvain creates badly connected communities. 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. bioRxiv, https://doi.org/10.1101/208819 (2018). We name our algorithm the Leiden algorithm, after the location of its authors. We demonstrate the performance of the Leiden algorithm for several benchmark and real-world networks. The Louvain algorithm guarantees that modularity cannot be increased by merging communities (it finds a locally optimal solution). Sign up for the Nature Briefing newsletter what matters in science, free to your inbox daily. Phys. PubMed The phase one loop can be greatly accelerated by finding the nodes that have the potential to change community and only revisit those nodes. Leiden algorithm. The quality improvement realised by the Leiden algorithm relative to the Louvain algorithm is larger for empirical networks than for benchmark networks. For example, after four iterations, the Web UK network has 8% disconnected communities, but twice as many badly connected communities. ADS Finally, we demonstrate the excellent performance of the algorithm for several benchmark and real-world networks. Nonlin. ISSN 2045-2322 (online). As shown in Fig. Google Scholar. Traag, V. A. Algorithmics 16, 2.1, https://doi.org/10.1145/1963190.1970376 (2011). Furthermore, by relying on a fast local move approach, the Leiden algorithm runs faster than the Louvain algorithm. 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. However, it is also possible to start the algorithm from a different partition15. On the other hand, Leiden keeps finding better partitions, especially for higher values of , for which it is more difficult to identify good partitions. Scientific Reports (Sci Rep) This can be a shared nearest neighbours matrix derived from a graph object. The value of the resolution parameter was determined based on the so-called mixing parameter 13. 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. For each network, we repeated the experiment 10 times. 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 First calculate k-nearest neighbors and construct the SNN graph. This function takes a cell_data_set as input, clusters the cells using . This will compute the Leiden clusters and add them to the Seurat Object Class. From Louvain to Leiden: Guaranteeing Well-Connected Communities, October. Sci Rep 9, 5233 (2019). The above results shows that the problem of disconnected and badly connected communities is quite pervasive in practice. The Leiden algorithm guarantees all communities to be connected, but it may yield badly connected communities. Sci. You are using a browser version with limited support for CSS. Louvain community detection algorithm was originally proposed in 2008 as a fast community unfolding method for large networks. conda install -c conda-forge leidenalg pip install leiden-clustering Used via. 2015. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate. We keep removing nodes from the front of the queue, possibly moving these nodes to a different community. & Arenas, A. Agglomerative clustering is a bottom-up approach. Good, B. H., De Montjoye, Y. Soft Matter Phys. It implies uniform -density and all the other above-mentioned properties. Then the Leiden algorithm can be run on the adjacency matrix. Graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. 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. These steps are repeated until the quality cannot be increased further. The authors show that the total computational time for Louvain depends a lot on the number of phase one loops (loops during the first local moving stage). CPM has the advantage that it is not subject to the resolution limit. As can be seen in Fig. Lancichinetti, A. However, nodes 16 are still locally optimally assigned, and therefore these nodes will stay in the red community. We will use sklearns K-Means implementation looking for 10 clusters in the original 784 dimensional data. This amounts to a clustering problem, where we aim to learn an optimal set of groups (communities) from the observed data. 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. Nonlin. A. Google Scholar. We thank Lovro Subelj for his comments on an earlier version of this paper. Performance of modularity maximization in practical contexts. When the Leiden algorithm found that a community could be split into multiple subcommunities, we counted the community as badly connected. It starts clustering by treating the individual data points as a single cluster then it is merged continuously based on similarity until it forms one big cluster containing all objects. Ozaki, Naoto, Hiroshi Tezuka, and Mary Inaba. Here we can see partitions in the plotted results. Slider with three articles shown per slide. Then, in order . The smart local moving algorithm (Waltman and Eck 2013) identified another limitation in the original Louvain method: it isnt able to split communities once theyre merged, even when it may be very beneficial to do so. The current state of the art when it comes to graph-based community detection is Leiden, which incorporates about 10 years of algorithmic improvements to the original Louvain method. 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. Guimer, R. & Nunes Amaral, L. A. Functional cartography of complex metabolic networks. 6 show that Leiden outperforms Louvain in terms of both computational time and quality of the partitions. We provide the full definitions of the properties as well as the mathematical proofs in SectionD of the Supplementary Information. Subpartition -density is not guaranteed by the Louvain algorithm. In general, Leiden is both faster than Louvain and finds better partitions. 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. Table2 provides an overview of the six networks. V. A. Traag. 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. Importantly, the problem of disconnected communities is not just a theoretical curiosity. Acad. 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). Hence, the Leiden algorithm effectively addresses the problem of badly connected communities. Hence, by counting the number of communities that have been split up, we obtained a lower bound on the number of communities that are badly connected. 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. 2. MathSciNet Subset optimality is the strongest guarantee that is provided by the Leiden algorithm. E 80, 056117, https://doi.org/10.1103/PhysRevE.80.056117 (2009). contrastive-sc works best on datasets with fewer clusters when using the KMeans clustering and conversely for Leiden. 10, for the IMDB and Amazon networks, Leiden reaches a stable iteration relatively quickly, presumably because these networks have a fairly simple community structure. Finding communities in large networks is far from trivial: algorithms need to be fast, but they also need to provide high-quality results. For empirical networks, it may take quite some time before the Leiden algorithm reaches its first stable iteration. Rev. 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. 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. Blondel, V. D., Guillaume, J.-L., Lambiotte, R. & Lefebvre, E. Fast unfolding of communities in large networks. J. Stat. The steps for agglomerative clustering are as follows: 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. 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. However, so far this problem has never been studied for the Louvain algorithm. One of the best-known methods for community detection is called modularity3. MATH Random moving is a very simple adjustment to Louvain local moving proposed in 2015 (Traag 2015). As discussed earlier, the Louvain algorithm does not guarantee connectivity. Hence, in general, Louvain may find arbitrarily badly connected communities. Rep. 6, 30750, https://doi.org/10.1038/srep30750 (2016). Technol. Ozaki, N., Tezuka, H. & Inaba, M. A Simple Acceleration Method for the Louvain Algorithm. The Louvain algorithm10 is very simple and elegant. The Leiden algorithm starts from a singleton partition (a). Package 'leiden' October 13, 2022 Type Package Title R Implementation of Leiden Clustering Algorithm Version 0.4.3 Date 2022-09-10 Description Implements the 'Python leidenalg' module to be called in R. Enables clustering using the leiden algorithm for partition a graph into communities. Communities may even be internally disconnected. 10008, 6, https://doi.org/10.1088/1742-5468/2008/10/P10008 (2008). Class wrapper based on scanpy to use the Leiden algorithm to directly cluster your data matrix with a scikit-learn flavor. Note that Leiden clustering directly clusters the neighborhood graph of cells, which we already computed in the previous section. In the first iteration, Leiden is roughly 220 times faster than Louvain. Rev. the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Two ways of doing this are graph modularity (Newman and Girvan 2004) and the constant Potts model (Ronhovde and Nussinov 2010). Figure3 provides an illustration of the algorithm. The percentage of disconnected communities even jumps to 16% for the DBLP network. In other words, communities are guaranteed to be well separated. & Girvan, M. Finding and evaluating community structure in networks. Phys. A community size of 50 nodes was used for the results presented below, but larger community sizes yielded qualitatively similar results. We study the problem of badly connected communities when using the Louvain algorithm for several empirical networks. The Leiden algorithm is clearly faster than the Louvain algorithm. Ronhovde, Peter, and Zohar Nussinov. However, values of within a range of roughly [0.0005, 0.1] all provide reasonable results, thus allowing for some, but not too much randomness. The R implementation of Leiden can be run directly on the snn igraph object in Seurat. A score of -1 means that there are no edges connecting nodes within the community, and they instead all connect nodes outside the community. Source Code (2018). In that case, some optimal partitions cannot be found, as we show in SectionC2 of the Supplementary Information. The percentage of badly connected communities is less affected by the number of iterations of the Louvain algorithm. In this way, Leiden implements the local moving phase more efficiently than Louvain. Moreover, when no more nodes can be moved, the algorithm will aggregate the network. Phys. Moreover, Louvain has no mechanism for fixing these communities. Data 11, 130, https://doi.org/10.1145/2992785 (2017). 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. 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. Newman, M. E. J. 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. Modularity scores of +1 mean that all the edges in a community are connecting nodes within the community. As can be seen in Fig. 2(b). Eng. You signed in with another tab or window. Google Scholar. Such a modular structure is usually not known beforehand. Phys. In this post Ive mainly focused on the optimisation methods for community detection, rather than the different objective functions that can be used. On the other hand, after node 0 has been moved to a different community, nodes 1 and 4 have not only internal but also external connections. One may expect that other nodes in the old community will then also be moved to other communities. For each set of parameters, we repeated the experiment 10 times. 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. Note that this code is . 9 shows that more than 10 iterations of the Leiden algorithm can be performed before the Louvain algorithm has finished its first iteration. There are many different approaches and algorithms to perform clustering tasks. Phys. Default behaviour is calling cluster_leiden in igraph with Modularity (for undirected graphs) and CPM cost functions. Usually, the Louvain algorithm starts from a singleton partition, in which each node is in its own community. Elect. In short, the problem of badly connected communities has important practical consequences. Phys. Louvain algorithm. It means that there are no individual nodes that can be moved to a different community. ACM Trans. One of the most widely used algorithms is the Louvain algorithm10, which is reported to be among the fastest and best performing community detection algorithms11,12. For lower values of , the correct partition is easy to find and Leiden is only about twice as fast as Louvain. Speed and quality of the Louvain and the Leiden algorithm for benchmark networks of increasing size (two iterations). leiden_clustering Description Class wrapper based on scanpy to use the Leiden algorithm to directly cluster your data matrix with a scikit-learn flavor. This continues until the queue is empty. Cluster your data matrix with the Leiden algorithm. Leiden is both faster than Louvain and finds better partitions.