leiden clustering explained10 marca 2023
where nc is the number of nodes in community c. The interpretation of the resolution parameter is quite straightforward. There are many different approaches and algorithms to perform clustering tasks. Phys. The Leiden algorithm guarantees all communities to be connected, but it may yield badly connected communities. That is, one part of such an internally disconnected community can reach another part only through a path going outside the community. Publishers note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. 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. The refined partition \({{\mathscr{P}}}_{{\rm{refined}}}\) is obtained as follows. Clustering the neighborhood graph As with Seurat and many other frameworks, we recommend the Leiden graph-clustering method (community detection based on optimizing modularity) by Traag *et al. Starting from the second iteration, Leiden outperformed Louvain in terms of the percentage of badly connected communities. This should be the first preference when choosing an algorithm. It means that there are no individual nodes that can be moved to a different community. https://doi.org/10.1038/s41598-019-41695-z, DOI: https://doi.org/10.1038/s41598-019-41695-z. 2008. V. A. Traag. 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. Nevertheless, depending on the relative strengths of the different connections, these nodes may still be optimally assigned to their current community. Rev. Table2 provides an overview of the six networks. These are the same networks that were also studied in an earlier paper introducing the smart local move algorithm15. The property of -separation is also guaranteed by the Louvain algorithm. J. You will not need much Python to use it. 7, whereas Louvain becomes much slower for more difficult partitions, Leiden is much less affected by the difficulty of the partition. 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. Note that Leiden clustering directly clusters the neighborhood graph of cells, which we already computed in the previous section. Importantly, the first iteration of the Leiden algorithm is the most computationally intensive one, and subsequent iterations are faster. 4, in the first iteration of the Louvain algorithm, the percentage of badly connected communities can be quite high. Article Communities in \({\mathscr{P}}\) may be split into multiple subcommunities in \({{\mathscr{P}}}_{{\rm{refined}}}\). E Stat. A structure that is more informative than the unstructured set of clusters returned by flat clustering. Because the percentage of disconnected communities in the first iteration of the Louvain algorithm usually seems to be relatively low, the problem may have escaped attention from users of the algorithm. E 70, 066111, https://doi.org/10.1103/PhysRevE.70.066111 (2004). This continues until the queue is empty. 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. In particular, it yields communities that are guaranteed to be connected. Nodes 13 should form a community and nodes 46 should form another community. After a stable iteration of the Leiden algorithm, it is guaranteed that: All nodes are locally optimally assigned. The algorithm is run iteratively, using the partition identified in one iteration as starting point for the next iteration. Finally, we compare the performance of the algorithms on the empirical networks. Leiden keeps finding better partitions for empirical networks also after the first 10 iterations of the algorithm. V.A.T. As shown in Fig. The 'devtools' package will be used to install 'leiden' and the dependancies (igraph and reticulate). The value of the resolution parameter was determined based on the so-called mixing parameter 13. In the initial stage of Louvain (when all nodes belong to their own community), nearly any move will result in a modularity gain, and it doesnt matter too much which move is chosen. One of the most popular algorithms to optimise modularity is the so-called Louvain algorithm10, named after the location of its authors. 2013. B 86, 471, https://doi.org/10.1140/epjb/e2013-40829-0 (2013). E 69, 026113, https://doi.org/10.1103/PhysRevE.69.026113 (2004). Leiden consists of the following steps: The refinement step allows badly connected communities to be split before creating the aggregate network. The nodes that are more interconnected have been partitioned into separate clusters. Neurosci. Acad. 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. Each of these can be used as an objective function for graph-based community detection methods, with our goal being to maximize this value. Eur. CPM has the advantage that it is not subject to the resolution limit. We also suggested that the Leiden algorithm is faster than the Louvain algorithm, because of the fast local move approach. It partitions the data space and identifies the sub-spaces using the Apriori principle. 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. An iteration of the Leiden algorithm in which the partition does not change is called a stable iteration. Traag, V. A., Van Dooren, P. & Nesterov, Y. Finding community structure in networks using the eigenvectors of matrices. In fact, by implementing the refinement phase in the right way, several attractive guarantees can be given for partitions produced by the Leiden algorithm. It is a directed graph if the adjacency matrix is not symmetric. J. The Leiden algorithm starts from a singleton partition (a). They identified an inefficiency in the Louvain algorithm: computes modularity gain for all neighbouring nodes per loop in local moving phase, even though many of these nodes will not have moved. Leiden algorithm. 1 and summarised in pseudo-code in AlgorithmA.1 in SectionA of the Supplementary Information. Graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. Clustering algorithms look for similarities or dissimilarities among data points so that similar ones can be grouped together. Finding and Evaluating Community Structure in Networks. Phys. Nevertheless, when CPM is used as the quality function, the Louvain algorithm may still find arbitrarily badly connected communities. To ensure readability of the paper to the broadest possible audience, we have chosen to relegate all technical details to the Supplementary Information. This step will involve reducing the dimensionality of our data into two dimensions using uniform manifold approximation (UMAP), allowing us to visualize our cell populations as they are binned into discrete populations using Leiden clustering. This contrasts with the Leiden algorithm. Louvain community detection algorithm was originally proposed in 2008 as a fast community unfolding method for large networks. Conversely, if Leiden does not find subcommunities, there is no guarantee that modularity cannot be increased by splitting up the community. We here introduce the Leiden algorithm, which guarantees that communities are well connected. Newman, M E J, and M Girvan. sign in 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. I tracked the number of clusters post-clustering at each step. Waltman, L. & van Eck, N. J. Use Git or checkout with SVN using the web URL. Speed of the first iteration of the Louvain and the Leiden algorithm for benchmark networks with increasingly difficult partitions (n=107). An alternative quality function is the Constant Potts Model (CPM)13, which overcomes some limitations of modularity. When the Leiden algorithm found that a community could be split into multiple subcommunities, we counted the community as badly connected. There was a problem preparing your codespace, please try again. Eng. Clearly, it would be better to split up the community. Phys. & Bornholdt, S. Statistical mechanics of community detection. The PyPI package leiden-clustering receives a total of 15 downloads a week. 8 (3): 207. https://pdfs.semanticscholar.org/4ea9/74f0fadb57a0b1ec35cbc5b3eb28e9b966d8.pdf. This will compute the Leiden clusters and add them to the Seurat Object Class. 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 ). Even though clustering can be applied to networks, it is a broader field in unsupervised machine learning which deals with multiple attribute types. 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. Requirements Developed using: scanpy v1.7.2 sklearn v0.23.2 umap v0.4.6 numpy v1.19.2 leidenalg Installation pip pip install leiden_clustering local 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. Communities may even be disconnected. Disconnected community. In our experimental analysis, we observe that up to 25% of the communities are badly connected and up to 16% are disconnected. 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. We conclude that the Leiden algorithm is strongly preferable to the Louvain algorithm. Community detection can then be performed using this graph. Community detection in complex networks using extremal optimization. Modularity optimization. We used the CPM quality function. In this way, the constant acts as a resolution parameter, and setting the constant higher will result in fewer communities. Rev. Presumably, many of the badly connected communities in the first iteration of Louvain become disconnected in the second iteration. Technol. A score of -1 means that there are no edges connecting nodes within the community, and they instead all connect nodes outside the community. 4. Based on project statistics from the GitHub repository for the PyPI package leiden-clustering, we found that it has been starred 1 times. 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. This amounts to a clustering problem, where we aim to learn an optimal set of groups (communities) from the observed data. 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. 20, 172188, https://doi.org/10.1109/TKDE.2007.190689 (2008). However, it is also possible to start the algorithm from a different partition15. Note that this code is . E 74, 036104, https://doi.org/10.1103/PhysRevE.74.036104 (2006). Technol. Natl. Phys. Source Code (2018). We first applied the Scanpy pipeline, including its clustering method (Leiden clustering), on the PBMC dataset. It is good at identifying small clusters. Clauset, A., Newman, M. E. J. Higher resolutions lead to more communities and lower resolutions lead to fewer communities, similarly to the resolution parameter for modularity. Later iterations of the Louvain algorithm only aggravate the problem of disconnected communities, even though the quality function (i.e. Nodes 16 have connections only within this community, whereas node 0 also has many external connections. This contrasts to benchmark networks, for which Leiden often converges after a few iterations. In doing so, Louvain keeps visiting nodes that cannot be moved to a different community. Class wrapper based on scanpy to use the Leiden algorithm to directly cluster your data matrix with a scikit-learn flavor. For all networks, Leiden identifies substantially better partitions than Louvain. Newman, M. E. J. The resolution limit describes a limitation where there is a minimum community size able to be resolved by optimizing modularity (or other related functions). In this case, refinement does not change the partition (f). 8, the Leiden algorithm is significantly faster than the Louvain algorithm also in empirical networks. Performance of modularity maximization in practical contexts. Excluding node mergers that decrease the quality function makes the refinement phase more efficient. Louvain algorithm. This contrasts with optimisation algorithms such as simulated annealing, which do allow the quality function to decrease4,8. Initially, \({{\mathscr{P}}}_{{\rm{refined}}}\) is set to a singleton partition, in which each node is in its own community. 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. Additionally, we implemented a Python package, available from https://github.com/vtraag/leidenalg and deposited at Zenodo24). One may expect that other nodes in the old community will then also be moved to other communities. The algorithm is described in pseudo-code in AlgorithmA.2 in SectionA of the Supplementary Information. We provide the full definitions of the properties as well as the mathematical proofs in SectionD of the Supplementary Information. . See the documentation for these functions. In fact, if we keep iterating the Leiden algorithm, it will converge to a partition without any badly connected communities, as discussed earlier. 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. The solution provided by Leiden is based on the smart local moving algorithm. modularity) increases. To install the development version: The current release on CRAN can be installed with: First set up a compatible adjacency matrix: An adjacency matrix is any binary matrix representing links between nodes (column and row names). A new methodology for constructing a publication-level classification system of science. Here we can see partitions in the plotted results. You signed in with another tab or window. Leiden is both faster than Louvain and finds better partitions. If nothing happens, download GitHub Desktop and try again. Node optimality is also guaranteed after a stable iteration of the Louvain algorithm. Sign up for the Nature Briefing newsletter what matters in science, free to your inbox daily. Runtime versus quality for empirical networks. By moving these nodes, Louvain creates badly connected communities. PubMed It maximizes a modularity score for each community, where the modularity quantifies the quality of an assignment of nodes to communities. & Clauset, A. That is, no subset can be moved to a different community. For each community in a partition that was uncovered by the Louvain algorithm, we determined whether it is internally connected or not. Nonlin. Finding communities in large networks is far from trivial: algorithms need to be fast, but they also need to provide high-quality results. J. Each point corresponds to a certain iteration of an algorithm, with results averaged over 10 experiments. In the first iteration, Leiden is roughly 220 times faster than Louvain. The algorithm may yield arbitrarily badly connected communities, over and above the well-known issue of the resolution limit14. The Web of Science network is the most difficult one. Nonlin. The quality improvement realised by the Leiden algorithm relative to the Louvain algorithm is larger for empirical networks than for benchmark networks. In all experiments reported here, we used a value of 0.01 for the parameter that determines the degree of randomness in the refinement phase of the Leiden 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. In this way, Leiden implements the local moving phase more efficiently than Louvain. The DBLP network is somewhat more challenging, requiring almost 80 iterations on average to reach a stable iteration. 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. http://dx.doi.org/10.1073/pnas.0605965104. The fast local move procedure can be summarised as follows. Basically, there are two types of hierarchical cluster analysis strategies - 1. Similarly, in citation networks, such as the Web of Science network, nodes in a community are usually considered to share a common topic26,27. 2007. Nonetheless, some networks still show large differences. As can be seen in Fig. Later iterations of the Louvain algorithm are very fast, but this is only because the partition remains the same. http://iopscience.iop.org/article/10.1088/1742-5468/2008/10/P10008/meta, http://dx.doi.org/10.1073/pnas.0605965104, http://dx.doi.org/10.1103/PhysRevE.69.026113, https://pdfs.semanticscholar.org/4ea9/74f0fadb57a0b1ec35cbc5b3eb28e9b966d8.pdf, http://dx.doi.org/10.1103/PhysRevE.81.046114, http://dx.doi.org/10.1103/PhysRevE.92.032801, https://doi.org/10.1140/epjb/e2013-40829-0, Assign each node to a different community. This can be a shared nearest neighbours matrix derived from a graph object. Modularity is used most commonly, but is subject to the resolution limit. Networks with high modularity have dense connections between the nodes within modules but sparse connections between nodes in different modules. Therefore, clustering algorithms look for similarities or dissimilarities among data points. Data Eng. To find an optimal grouping of cells into communities, we need some way of evaluating different partitions in the graph. J. In the meantime, to ensure continued support, we are displaying the site without styles Sci. The property of -connectivity is a slightly stronger variant of ordinary connectivity. (We ensured that modularity optimisation for the subnetwork was fully consistent with modularity optimisation for the whole network13) The Leiden algorithm was run until a stable iteration was obtained. 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. The horizontal axis indicates the cumulative time taken to obtain the quality indicated on the vertical axis. This is not the case when nodes are greedily merged with the community that yields the largest increase in the quality function. Unsupervised clustering of cells is a common step in many single-cell expression workflows.