Moreover, Louvain has no mechanism for fixing these communities. The Beginner's Guide to Dimensionality Reduction. 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. This is not the case when nodes are greedily merged with the community that yields the largest increase in the quality function. We conclude that the Leiden algorithm is strongly preferable to the Louvain algorithm. Hence, the problem of Louvain outlined above is independent from the issue of the resolution limit. However, the initial partition for the aggregate network is based on P, just like in the Louvain algorithm. Each point corresponds to a certain iteration of an algorithm, with results averaged over 10 experiments. Importantly, mergers are performed only within each community of the partition \({\mathscr{P}}\). Inf. Sci. Subpartition -density is not guaranteed by the Louvain algorithm. In the refinement phase, nodes are not necessarily greedily merged with the community that yields the largest increase in the quality function. Contrary to what might be expected, iterating the Louvain algorithm aggravates the problem of badly connected communities, as we will also see in our experimental analysis. 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. Besides the relative flexibility of the implementation, it also scales well, and can be run on graphs of millions of nodes (as long as they can fit in memory). The percentage of badly connected communities is less affected by the number of iterations of the Louvain algorithm. 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. 1 and summarised in pseudo-code in AlgorithmA.1 in SectionA of the Supplementary Information. Sci. 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. Google Scholar. PubMed Faster unfolding of communities: Speeding up the Louvain algorithm. Louvain keeps visiting all nodes in a network until there are no more node movements that increase the quality function. 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. When node 0 is moved to a different community, the red community becomes internally disconnected, as shown in (b). reviewed the manuscript. 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). A community size of 50 nodes was used for the results presented below, but larger community sizes yielded qualitatively similar results. Electr. Note that this code is . In addition, to analyse whether a community is badly connected, we ran the Leiden algorithm on the subnetwork consisting of all nodes belonging to the community. Table2 provides an overview of the six networks. Waltman, Ludo, and Nees Jan van Eck. Google Scholar. As we will demonstrate in our experimental analysis, the problem occurs frequently in practice when using the Louvain algorithm. Ph.D. thesis, (University of Oxford, 2016). Community detection is often used to understand the structure of large and complex networks. Then, in order . In this case, refinement does not change the partition (f). Again, if communities are badly connected, this may lead to incorrect inferences of topics, which will affect bibliometric analyses relying on the inferred topics. Correspondence to These steps are repeated until no further improvements can be made. Acad. A new methodology for constructing a publication-level classification system of science. Discov. Technol. The Web of Science network is the most difficult one. Phys. Article This method tries to maximise the difference between the actual number of edges in a community and the expected number of such edges. The Louvain algorithm10 is very simple and elegant. Phys. In that case, some optimal partitions cannot be found, as we show in SectionC2 of the Supplementary Information. 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. 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. Arguments can be passed to the leidenalg implementation in Python: In particular, the resolution parameter can fine-tune the number of clusters to be detected. In particular, we show that Louvain may identify communities that are internally disconnected. Leiden is both faster than Louvain and finds better partitions. Then optimize the modularity function to determine clusters. Google Scholar. Initially, \({{\mathscr{P}}}_{{\rm{refined}}}\) is set to a singleton partition, in which each node is in its own community. 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. This is very similar to what the smart local moving algorithm does. The Leiden algorithm provides several guarantees. One may expect that other nodes in the old community will then also be moved to other communities. 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). http://iopscience.iop.org/article/10.1088/1742-5468/2008/10/P10008/meta. For example: If you do not have root access, you can use pip install --user or pip install --prefix to install these in your user directory (which you have write permissions for) and ensure that this directory is in your PATH so that Python can find it. The Louvain algorithm is illustrated in Fig. Data 11, 130, https://doi.org/10.1145/2992785 (2017). We prove that the new algorithm is guaranteed to produce partitions in which all communities are internally connected. 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 ). Google Scholar. Even though clustering can be applied to networks, it is a broader field in unsupervised machine learning which deals with multiple attribute types. We provide the full definitions of the properties as well as the mathematical proofs in SectionD of the Supplementary Information. This should be the first preference when choosing an algorithm. From Louvain to Leiden: Guaranteeing Well-Connected Communities, October. Phys. Additionally, we implemented a Python package, available from https://github.com/vtraag/leidenalg and deposited at Zenodo24). CPM is defined as. Rev. To overcome the problem of arbitrarily badly connected communities, we introduced a new algorithm, which we refer to as the Leiden algorithm. 2(a). There are many different approaches and algorithms to perform clustering tasks. This way of defining the expected number of edges is based on the so-called configuration model. In doing so, Louvain keeps visiting nodes that cannot be moved to a different community. To address this important shortcoming, we introduce a new algorithm that is faster, finds better partitions and provides explicit guarantees and bounds. Rev. This commit does not belong to any branch on this repository, and may belong to a fork outside of the repository. As shown in Fig. To ensure readability of the paper to the broadest possible audience, we have chosen to relegate all technical details to the Supplementary Information. Is modularity with a resolution parameter equivalent to leidenalg.RBConfigurationVertexPartition? 68, 984998, https://doi.org/10.1002/asi.23734 (2017). In the Louvain algorithm, an aggregate network is created based on the partition \({\mathscr{P}}\) resulting from the local moving phase. The high percentage of badly connected communities attests to this. By submitting a comment you agree to abide by our Terms and Community Guidelines. For lower values of , the correct partition is easy to find and Leiden is only about twice as fast as Louvain. Positive values above 2 define the total number of iterations to perform, -1 has the algorithm run until it reaches its optimal clustering. Note that Leiden clustering directly clusters the neighborhood graph of cells, which we already computed in the previous section. In this paper, we show that the Louvain algorithm has a major problem, for both modularity and CPM. Reichardt, J. We demonstrate the performance of the Leiden algorithm for several benchmark and real-world networks. Please Modularity is used most commonly, but is subject to the resolution limit. Below we offer an intuitive explanation of these properties. & Moore, C. Finding community structure in very large networks. Unlike the Louvain algorithm, the Leiden algorithm uses a fast local move procedure in this phase. conda install -c conda-forge leidenalg pip install leiden-clustering Used via. The 'devtools' package will be used to install 'leiden' and the dependancies (igraph and reticulate). 2 represent stronger connections, while the other edges represent weaker connections. 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. We applied the Louvain and the Leiden algorithm to exactly the same networks, using the same seed for the random number generator. J. To find an optimal grouping of cells into communities, we need some way of evaluating different partitions in the graph. Clustering with the Leiden Algorithm in R 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 https://github.com/vtraag/leidenalg Install 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. Newman, M. E. J. leidenalg. The percentage of disconnected communities even jumps to 16% for the DBLP network. Graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. We then remove the first node from the front of the queue and we determine whether the quality function can be increased by moving this node from its current community to a different one. It is a directed graph if the adjacency matrix is not symmetric. The difference in computational time is especially pronounced for larger networks, with Leiden being up to 20 times faster than Louvain in empirical networks. Rev. 8, the Leiden algorithm is significantly faster than the Louvain algorithm also in empirical networks. Runtime versus quality for empirical networks. The PyPI package leiden-clustering receives a total of 15 downloads a week. While smart local moving and multilevel refinement can improve the communities found, the next two improvements on Louvain that Ill discuss focus on the speed/efficiency of the algorithm. E 69, 026113, https://doi.org/10.1103/PhysRevE.69.026113 (2004). 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. In particular, in an attempt to find better partitions, multiple consecutive iterations of the algorithm can be performed, using the partition identified in one iteration as starting point for the next iteration. As the problem of modularity optimization is NP-hard, we need heuristic methods to optimize modularity (or CPM). A Comparative Analysis of Community Detection Algorithms on Artificial Networks. As can be seen in the figure, Louvain quickly reaches a state in which it is unable to find better partitions. For this network, Leiden requires over 750 iterations on average to reach a stable iteration. However, so far this problem has never been studied for the Louvain algorithm. This makes sense, because after phase one the total size of the graph should be significantly reduced. The community with which a node is merged is selected randomly18. Wolf, F. A. et al. Scaling of benchmark results for difficulty of the partition. Communities may even be disconnected. However, if communities are badly connected, this may lead to incorrect attributions of shared functionality. Blondel, V D, J L Guillaume, and R Lambiotte. At some point, the Louvain algorithm may end up in the community structure shown in Fig. See the documentation for these functions. Am. We prove that the Leiden algorithm yields communities that are guaranteed to be connected. This is similar to what we have seen for benchmark networks. However, modularity suffers from a difficult problem known as the resolution limit (Fortunato and Barthlemy 2007). Later iterations of the Louvain algorithm are very fast, but this is only because the partition remains the same. volume9, Articlenumber:5233 (2019) 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. J. Consider the partition shown in (a). CAS This will compute the Leiden clusters and add them to the Seurat Object Class. Ozaki, Naoto, Hiroshi Tezuka, and Mary Inaba. ADS Modularity is given by. Rotta, R. & Noack, A. Multilevel local search algorithms for modularity clustering. A Simple Acceleration Method for the Louvain Algorithm. Int. Trying to fix the problem by simply considering the connected components of communities19,20,21 is unsatisfactory because it addresses only the most extreme case and does not resolve the more fundamental problem. where >0 is a resolution parameter4. Proc. 6 show that Leiden outperforms Louvain in terms of both computational time and quality of the partitions. However, it is also possible to start the algorithm from a different partition15. The Louvain local moving phase consists of the following steps: This process is repeated for every node in the network until no further improvement in modularity is possible. The algorithm continues to move nodes in the rest of the network. E 76, 036106, https://doi.org/10.1103/PhysRevE.76.036106 (2007). The Louvain algorithm guarantees that modularity cannot be increased by merging communities (it finds a locally optimal solution). 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. https://doi.org/10.1038/s41598-019-41695-z, DOI: https://doi.org/10.1038/s41598-019-41695-z. The property of -separation is also guaranteed by the Louvain algorithm. This contrasts with the Leiden algorithm. The Leiden algorithm starts from a singleton partition (a). 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. 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. Community detection is an important task in the analysis of complex networks. Rev. Therefore, clustering algorithms look for similarities or dissimilarities among data points. ADS Note that communities found by the Leiden algorithm are guaranteed to be connected. Traag, V. A. leidenalg 0.7.0. This contrasts to benchmark networks, for which Leiden often converges after a few iterations. The Leiden algorithm is considerably more complex than the Louvain algorithm. See the documentation on the leidenalg Python module for more information: https://leidenalg.readthedocs.io/en/latest/reference.html. The Leiden algorithm is clearly faster than the Louvain algorithm. Agglomerative Clustering: Also known as bottom-up approach or hierarchical agglomerative clustering (HAC). Any sub-networks that are found are treated as different communities in the next aggregation step. After a stable iteration of the Leiden algorithm, the algorithm may still be able to make further improvements in later iterations. When a sufficient number of neighbours of node 0 have formed a community in the rest of the network, it may be optimal to move node 0 to this community, thus creating the situation depicted in Fig. Soft Matter Phys. E 84, 016114, https://doi.org/10.1103/PhysRevE.84.016114 (2011). Cluster cells using Louvain/Leiden community detection Description. On the other hand, Leiden keeps finding better partitions, especially for higher values of , for which it is more difficult to identify good partitions. 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. On Modularity Clustering. Phys. Weights for edges an also be passed to the leiden algorithm either as a separate vector or weights or a weighted adjacency matrix. If we move the node to a different community, we add to the rear of the queue all neighbours of the node that do not belong to the nodes new community and that are not yet in the queue. Traag, V. A., Van Dooren, P. & Nesterov, Y. to use Codespaces. The degree of randomness in the selection of a community is determined by a parameter >0. Google Scholar. Finding communities in large networks is far from trivial: algorithms need to be fast, but they also need to provide high-quality results.