2016. The Louvain algorithm is illustrated in Fig. ADS 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. One of the most popular algorithms for uncovering community structure is the so-called Louvain algorithm. Rev. The algorithm moves individual nodes from one community to another to find a partition (b), which is then refined (c). 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. In our experimental analysis, we observe that up to 25% of the communities are badly connected and up to 16% are disconnected. In the worst case, almost a quarter of the communities are badly connected. Centre for Science and Technology Studies, Leiden University, Leiden, The Netherlands, You can also search for this author in Article The Leiden algorithm starts from a singleton partition (a). Nodes 16 have connections only within this community, whereas node 0 also has many external connections. CPM does not suffer from this issue13. Rev. Communities in \({\mathscr{P}}\) may be split into multiple subcommunities in \({{\mathscr{P}}}_{{\rm{refined}}}\). Edges were created in such a way that an edge fell between two communities with a probability and within a community with a probability 1. Traag, V. A., Van Dooren, P. & Nesterov, Y. 2. Hence, no further improvements can be made after a stable iteration of the Louvain algorithm. running Leiden clustering finished: found 16 clusters and added 'leiden_1.0', the cluster labels (adata.obs, categorical) (0:00:00) running Leiden clustering finished: found 12 clusters and added 'leiden_0.6', the cluster labels (adata.obs, categorical) (0:00:00) running Leiden clustering finished: found 9 clusters and added 'leiden_0.4', the E 84, 016114, https://doi.org/10.1103/PhysRevE.84.016114 (2011). The above results shows that the problem of disconnected and badly connected communities is quite pervasive in practice. What is Clustering and Different Types of Clustering Methods The Leiden algorithm is considerably more complex than the Louvain algorithm. By moving these nodes, Louvain creates badly connected communities. This represents the following graph structure. As we will demonstrate in our experimental analysis, the problem occurs frequently in practice when using the Louvain algorithm. Clearly, it would be better to split up the community. Importantly, the first iteration of the Leiden algorithm is the most computationally intensive one, and subsequent iterations are faster. MATH As can be seen in the figure, Louvain quickly reaches a state in which it is unable to find better partitions. Indeed, the percentage of disconnected communities becomes more comparable to the percentage of badly connected communities in later iterations. How many iterations of the Leiden clustering algorithm to perform. GitHub on Feb 15, 2020 Do you think the performance improvements will also be implemented in leidenalg? 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. For both algorithms, 10 iterations were performed. CAS Louvain community detection algorithm was originally proposed in 2008 as a fast community unfolding method for large networks. For larger networks and higher values of , Louvain is much slower than Leiden. E 70, 066111, https://doi.org/10.1103/PhysRevE.70.066111 (2004). To elucidate the problem, we consider the example illustrated in Fig. http://iopscience.iop.org/article/10.1088/1742-5468/2008/10/P10008/meta. This is similar to what we have seen for benchmark networks. Usually, the Louvain algorithm starts from a singleton partition, in which each node is in its own community. 2(a). 2007. J. We will use sklearns K-Means implementation looking for 10 clusters in the original 784 dimensional data. leiden clustering explained We applied the Louvain and the Leiden algorithm to exactly the same networks, using the same seed for the random number generator. The Leiden algorithm starts from a singleton partition (a). ADS https://doi.org/10.1038/s41598-019-41695-z, DOI: https://doi.org/10.1038/s41598-019-41695-z. contrastive-sc works best on datasets with fewer clusters when using the KMeans clustering and conversely for Leiden. The triumphs and limitations of computational methods for - Nature Google Scholar. E Stat. In a stable iteration, the partition is guaranteed to be node optimal and subpartition -dense. Another important difference between the Leiden algorithm and the Louvain algorithm is the implementation of the local moving phase. Source Code (2018). Each community in this partition becomes a node in the aggregate network. Cluster cells using Louvain/Leiden community detection Description. 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. E Stat. We also suggested that the Leiden algorithm is faster than the Louvain algorithm, because of the fast local move approach. 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. Algorithmics 16, 2.1, https://doi.org/10.1145/1963190.1970376 (2011). Perhaps surprisingly, iterating the algorithm aggravates the problem, even though it does increase the quality function. 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 Eng. Fast Unfolding of Communities in Large Networks. Journal of Statistical , January. DBSCAN Clustering Explained. Detailed theorotical explanation and Figure6 presents total runtime versus quality for all iterations of the Louvain and the Leiden algorithm. Both conda and PyPI have leiden clustering in Python which operates via iGraph. Acad. The Leiden algorithm has been specifically designed to address the problem of badly connected communities. Default behaviour is calling cluster_leiden in igraph with Modularity (for undirected graphs) and CPM cost functions. Class wrapper based on scanpy to use the Leiden algorithm to directly cluster your data matrix with a scikit-learn flavor. Yang, Z., Algesheimer, R. & Tessone, C. J. Detecting communities in a network is therefore an important problem. Preprocessing and clustering 3k PBMCs Scanpy documentation 8, 207218, https://doi.org/10.17706/IJCEE.2016.8.3.207-218 (2016). E 72, 027104, https://doi.org/10.1103/PhysRevE.72.027104 (2005). If nothing happens, download GitHub Desktop and try again. These nodes can be approximately identified based on whether neighbouring nodes have changed communities. 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. First, we created a specified number of nodes and we assigned each node to a community. Graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. Runtime versus quality for empirical networks. However, if communities are badly connected, this may lead to incorrect attributions of shared functionality. Each point corresponds to a certain iteration of an algorithm, with results averaged over 10 experiments. Phys. Am. Additionally, we implemented a Python package, available from https://github.com/vtraag/leidenalg and deposited at Zenodo24). Louvain quickly converges to a partition and is then unable to make further improvements. scanpy.tl.leiden Scanpy 1.9.3 documentation - Read the Docs The main ideas of our algorithm are explained in an intuitive way in the main text of the paper. S3. 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. http://arxiv.org/abs/1810.08473. As can be seen in Fig. Rev. Biological sequence clustering is a complicated data clustering problem owing to the high computation costs incurred for pairwise sequence distance calculations through sequence alignments, as well as difficulties in determining parameters for deriving robust clusters. Using UMAP for Clustering umap 0.5 documentation - Read the Docs Value. From Louvain to Leiden: guaranteeing well-connected communities - Nature The corresponding results are presented in the Supplementary Fig. We used modularity with a resolution parameter of =1 for the experiments. Clustering with the Leiden Algorithm in R Wolf, F. A. et al. Communities were all of equal size. First iteration runtime for empirical networks. Sci. Uniform -density means that no matter how a community is partitioned into two parts, the two parts will always be well connected to each other. This problem is different from the well-known issue of the resolution limit of modularity14. This is well illustrated by figure 2 in the Leiden paper: When a community becomes disconnected like this, there is no way for Louvain to easily split it into two separate communities. The PyPI package leiden-clustering receives a total of 15 downloads a week. For those wanting to read more, I highly recommend starting with the Leiden paper (Traag, Waltman, and Eck 2018) or the smart local moving paper (Waltman and Eck 2013). This algorithm provides a number of explicit guarantees. Node optimality is also guaranteed after a stable iteration of the Louvain algorithm. In the worst case, communities may even be disconnected, especially when running the algorithm iteratively. The inspiration for this method of community detection is the optimization of modularity as the algorithm progresses. 7, whereas Louvain becomes much slower for more difficult partitions, Leiden is much less affected by the difficulty of the partition. We keep removing nodes from the front of the queue, possibly moving these nodes to a different community. The nodes are added to the queue in a random order. Note that nodes can be revisited several times within a single iteration of the local moving stage, as the possible increase in modularity will change as other nodes are moved to different communities. 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. 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. Note that Leiden clustering directly clusters the neighborhood graph of cells, which we already computed in the previous section. 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 \({\mathscr{P}}\). to use Codespaces. Publishers note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. 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). The degree of randomness in the selection of a community is determined by a parameter >0. Phys. where nc is the number of nodes in community c. The interpretation of the resolution parameter is quite straightforward. 2.3. The Leiden algorithm is clearly faster than the Louvain algorithm. As such, we scored leiden-clustering popularity level to be Limited. Speed and quality for the first 10 iterations of the Louvain and the Leiden algorithm for six empirical networks. An alternative quality function is the Constant Potts Model (CPM)13, which overcomes some limitations of modularity. Similarly, in citation networks, such as the Web of Science network, nodes in a community are usually considered to share a common topic26,27. Traag, V. A., Waltman, L. & van Eck, N. J. networkanalysis. Article 9 shows that more than 10 iterations of the Leiden algorithm can be performed before the Louvain algorithm has finished its first iteration. We find that the Leiden algorithm commonly finds partitions of higher quality in less time. * (2018). A Simple Acceleration Method for the Louvain Algorithm. Int. modularity) increases. More subtle problems may occur as well, causing Louvain to find communities that are connected, but only in a very weak sense. The aggregate network is created based on the partition \({{\mathscr{P}}}_{{\rm{refined}}}\). The parameter functions as a sort of threshold: communities should have a density of at least , while the density between communities should be lower than . Finding and Evaluating Community Structure in Networks. Phys. The Leiden algorithm is typically iterated: the output of one iteration is used as the input for the next iteration. Starting from the second iteration, Leiden outperformed Louvain in terms of the percentage of badly connected communities. These steps are repeated until the quality cannot be increased further. Waltman, Ludo, and Nees Jan van Eck. 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. performed the experimental analysis. As far as I can tell, Leiden seems to essentially be smart local moving with the additional improvements of random moving and Louvain pruning added. Sci Rep 9, 5233 (2019). For empirical networks, it may take quite some time before the Leiden algorithm reaches its first stable iteration. We prove that the Leiden algorithm yields communities that are guaranteed to be connected. These steps are repeated until no further improvements can be made. leiden: Run Leiden clustering algorithm in leiden: R Implementation of The numerical details of the example can be found in SectionB of the Supplementary Information. Each of these can be used as an objective function for graph-based community detection methods, with our goal being to maximize this value. At this point, it is guaranteed that each individual node is optimally assigned. One of the best-known methods for community detection is called modularity3. Traag, V.A., Waltman, L. & van Eck, N.J. From Louvain to Leiden: guaranteeing well-connected communities. This is similar to ideas proposed recently as pruning16 and in a slightly different form as prioritisation17. There are many different approaches and algorithms to perform clustering tasks. Article Consider the partition shown in (a). At each iteration all clusters are guaranteed to be connected and well-separated. b, The elephant graph (in a) is clustered using the Leiden clustering algorithm 51 (resolution r = 0.5). The speed difference is especially large for larger networks. We find that the Leiden algorithm is faster than the Louvain algorithm and uncovers better partitions, in addition to providing explicit guarantees. However, in the case of the Web of Science network, more than 5% of the communities are disconnected in the first iteration. An overview of the various guarantees is presented in Table1. J. 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. MathSciNet Removing such a node from its old community disconnects the old community. The high percentage of badly connected communities attests to this. In other words, modularity may hide smaller communities and may yield communities containing significant substructure. The value of the resolution parameter was determined based on the so-called mixing parameter 13. Phys. Klavans, R. & Boyack, K. W. Which Type of Citation Analysis Generates the Most Accurate Taxonomy of Scientific and Technical Knowledge? The count of badly connected communities also included disconnected communities. scanpy_04_clustering - GitHub Pages Leiden consists of the following steps: Local moving of nodes Partition refinement Network aggregation The refinement step allows badly connected communities to be split before creating the aggregate network. In the case of modularity, communities may have significant substructure both because of the resolution limit and because of the shortcomings of Louvain. In this case we know the answer is exactly 10. In this post Ive mainly focused on the optimisation methods for community detection, rather than the different objective functions that can be used. 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. Rep. 6, 30750, https://doi.org/10.1038/srep30750 (2016). We now consider the guarantees provided by the Leiden algorithm. It identifies the clusters by calculating the densities of the cells. Phys. The new algorithm integrates several earlier improvements, incorporating a combination of smart local move15, fast local move16,17 and random neighbour move18. GitHub - vtraag/leidenalg: Implementation of the Leiden algorithm for Rev. Moreover, the deeper significance of the problem was not recognised: disconnected communities are merely the most extreme manifestation of the problem of arbitrarily badly connected communities. For each network, Table2 reports the maximal modularity obtained using the Louvain and the Leiden algorithm. the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in 9, the Leiden algorithm also performs better than the Louvain algorithm in terms of the quality of the partitions that are obtained. Below, the quality of a partition is reported as \(\frac{ {\mathcal H} }{2m}\), where H is defined in Eq. Work fast with our official CLI. The algorithm may yield arbitrarily badly connected communities, over and above the well-known issue of the resolution limit14. GitHub - MiqG/leiden_clustering: Cluster your data matrix with the 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. Modularity optimization. Weights for edges an also be passed to the leiden algorithm either as a separate vector or weights or a weighted adjacency matrix. From Louvain to Leiden: Guaranteeing Well-Connected Communities, October. For example, after four iterations, the Web UK network has 8% disconnected communities, but twice as many badly connected communities. Phys. Speed of the first iteration of the Louvain and the Leiden algorithm for six empirical networks. The authors act as bibliometric consultants to CWTS B.V., which makes use of community detection algorithms in commercial products and services. We prove that the new algorithm is guaranteed to produce partitions in which all communities are internally connected. In particular, it yields communities that are guaranteed to be connected. Below we offer an intuitive explanation of these properties. We conclude that the Leiden algorithm is strongly preferable to the Louvain algorithm. In contrast, Leiden keeps finding better partitions in each iteration. PubMed Central It is a directed graph if the adjacency matrix is not symmetric. Powered by DataCamp DataCamp sign in Rep. 486, 75174, https://doi.org/10.1016/j.physrep.2009.11.002 (2010). Besides being pervasive, the problem is also sizeable. To address this important shortcoming, we introduce a new algorithm that is faster, finds better partitions and provides explicit guarantees and bounds. 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. leidenalg. Phys. 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. It was found to be one of the fastest and best performing algorithms in comparative analyses11,12, and it is one of the most-cited works in the community detection literature. Speed and quality of the Louvain and the Leiden algorithm for benchmark networks of increasing size (two iterations). Newman, M. E. J. The resulting clusters are shown as colors on the 3D model (top) and t -SNE embedding . The solution provided by Leiden is based on the smart local moving algorithm. 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. The random component also makes the algorithm more explorative, which might help to find better community structures. We used the CPM quality function. This is not the case when nodes are greedily merged with the community that yields the largest increase in the quality function. Runtime versus quality for benchmark networks. Phys. Rev. For example, nodes in a community in biological or neurological networks are often assumed to share similar functions or behaviour25. The two phases are repeated until the quality function cannot be increased further. 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. Initially, \({{\mathscr{P}}}_{{\rm{refined}}}\) is set to a singleton partition, in which each node is in its own community. The minimum resolvable community size depends on the total size of the network and the degree of interconnectedness of the modules. Narrow scope for resolution-limit-free community detection. Rather than progress straight to the aggregation stage (as we would for the original Louvain), we next consider each community as a new sub-network and re-apply the local moving step within each 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. Reichardt, J. Random moving can result in some huge speedups, since Louvain spends about 95% of its time computing the modularity gain from moving nodes. 2013. 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. Fortunato, Santo, and Marc Barthlemy. We can guarantee a number of properties of the partitions found by the Leiden algorithm at various stages of the iterative process. However, Leiden is more than 7 times faster for the Live Journal network, more than 11 times faster for the Web of Science network and more than 20 times faster for the Web UK network. Any sub-networks that are found are treated as different communities in the next aggregation step. We generated benchmark networks in the following way. igraph R manual pages Finding communities in large networks is far from trivial: algorithms need to be fast, but they also need to provide high-quality results. 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. Higher resolutions lead to more communities, while lower resolutions lead to fewer communities. Two ways of doing this are graph modularity (Newman and Girvan 2004) and the constant Potts model (Ronhovde and Nussinov 2010). Lancichinetti, A., Fortunato, S. & Radicchi, F. Benchmark graphs for testing community detection algorithms. Traag, V A. Article 10X10Xleiden - To overcome the problem of arbitrarily badly connected communities, we introduced a new algorithm, which we refer to as the Leiden algorithm. & Arenas, A. Google Scholar. Clustering is a machine learning technique in which similar data points are grouped into the same cluster based on their attributes. The thick edges in Fig. Waltman, L. & van Eck, N. J. One of the most popular algorithms to optimise modularity is the so-called Louvain algorithm10, named after the location of its authors. To address this problem, we introduce the Leiden algorithm. Each point corresponds to a certain iteration of an algorithm, with results averaged over 10 experiments. 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. 4, in the first iteration of the Louvain algorithm, the percentage of badly connected communities can be quite high. J. Stat. 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. This amounts to a clustering problem, where we aim to learn an optimal set of groups (communities) from the observed data. Table2 provides an overview of the six networks. This package implements the Leiden algorithm in C++ and exposes it to python.It relies on (python-)igraph for it to function. J. Exp. These are the same networks that were also studied in an earlier paper introducing the smart local move algorithm15. N.J.v.E. However, as increases, the Leiden algorithm starts to outperform the Louvain algorithm. Leiden keeps finding better partitions for empirical networks also after the first 10 iterations of the algorithm. 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. However, so far this problem has never been studied for the Louvain algorithm. python - Leiden Clustering results are not always the same given the Waltman, L. & van Eck, N. J. Clauset, A., Newman, M. E. J. E 69, 026113, https://doi.org/10.1103/PhysRevE.69.026113 (2004). ISSN 2045-2322 (online). Elect. Phys. Google Scholar. Luecken, M. D. Application of multi-resolution partitioning of interaction networks to the study of complex disease. A partition of clusters as a vector of integers Examples Badly connected communities. 8, the Leiden algorithm is significantly faster than the Louvain algorithm also in empirical networks.