{"paper_id":"3481902a-e973-459c-a942-3c73e573e2b9","body_text":"Title: SpatialLeiden - Spatially-aware Leiden clustering 1 \nAuthors and affiliations  2 \nNiklas Müller-Bötticher1,2, Shashwat Sahay1,2, Roland Eils1,2,3, Naveed Ishaque1 3 \n1 Berlin Institute of Health at Charité – Universitätsmedizin Berlin, Center of Digital Health, 4 \nCharitéplatz 1, 10117, Berlin, Germany 5 \n2 Freie Universität Berlin, Department of Mathematics and Computer Science, Arnimallee 14, 6 \n14195, Berlin, Germany 7 \n3 Health Data Science Unit, Heidelberg University Hospital and BioQuant, University of 8 \nHeidelberg, Germany 9 \nCorresponding Author  10 \nCorrespondence should be sent to: naveed.ishaque@bih-charite.de  11 \n  12 \n.CC-BY 4.0 International licensemade available under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is \nThe copyright holder for this preprintthis version posted August 23, 2024. ; https://doi.org/10.1101/2024.08.23.609349doi: bioRxiv preprint \n\nAbstract 13 \nClustering can identify the natural structure that is inherent to measured data. For single-cell 14 \nomics, clustering finds cells with similar molecular phenotype after which cell types are 15 \nannotated. Leiden clustering is the algorithm of choice in the single-cell community. 16 \nHowever, in the field of spatial omics, Leiden has been considered a non-spatial clustering 17 \nmethod. Here, we show that by integrating spatial embeddings Leiden clustering is rendered 18 \ninto a computationally highly performant, spatially aware clustering method that compares 19 \nwell with state-of-the art clustering methods. 20 \nKeywords  21 \nSpatial omics, clustering, Leiden, domains, niches, spatial clustering, spatial biology, 22 \nbioinformatics 23 \nBackground 24 \nSingle-cell transcriptomics has revolutionised our understanding of cellular heterogeneity by 25 \nenabling the measurement of gene expression at the individual cell level. However, this high-26 \ndimensional data poses significant challenges in extracting meaningful biological insights. 27 \nThis can be overcome by grouping cells with similar expression profiles into distinct clusters. 28 \nBy partitioning cells based on transcriptional similarities, clustering facilitates the 29 \ncharacterization of cell-type diversity within a heterogeneous cell population. Furthermore, 30 \nclustering provides a basis for downstream analyses, such as differential expression, 31 \ntrajectory inference, and cell-cell interaction. In single-cell transcriptomics, a variety of 32 \nclustering algorithms have been used and Leiden clustering has emerged as a performant 33 \nchoice(1). Leiden clustering can be extended to consider multiomics data via the Leiden 34 \nmultiplex functionality(2). 35 \n.CC-BY 4.0 International licensemade available under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is \nThe copyright holder for this preprintthis version posted August 23, 2024. ; https://doi.org/10.1101/2024.08.23.609349doi: bioRxiv preprint \n\n 36 \nProgress in spatially resolved omics methods has empowered researchers with the ability to 37 \nmap gene expression in a spatial manner, transcending conventional cell clustering 38 \napproaches(3). With spatial omics, scientists can discern higher-order tissue structures, 39 \ntermed spatial domains, by integrating spatial information alongside gene expression data. 40 \nThe identification of spatial domains through spatial clustering has emerged as a standard 41 \npractice in constructing spatial atlases. This is instrumental in visualizing tissue anatomy, 42 \ndelineating tissue spatial continuity, pinpointing domain-specific marker genes, and 43 \nunravelling domain-dependent molecular regulatory networks. Performance of spatial 44 \ndomain identification improves when leveraging the spatial information compared to non-45 \nspatial methods(4).  46 \n 47 \nLeiden clustering has been typically categorised as a “non-spatial” clustering method. 48 \nHowever, Leiden multiplex can consider spatial embeddings during clustering, thus 49 \nrendering prior assumptions of the non-spatial nature of the Leiden algorithm untrue. The 50 \nLeiden algorithm clusters nodes in a network by optimising a quality function, in a simple 51 \ncase this can be the modularity, which maximises the differences between the actual 52 \nnumber of edges in a community and the expected number of such edges under a null 53 \nmodel. In single-cell transcriptomics, the cells (nodes) are connected to other cells based on 54 \nthe distance between cells in the gene expression space (edges), usually in a dimensionality 55 \nreduced latent space. Leiden multiplex enables the user to define an arbitrary number of 56 \nnetworks (layers) with the same set of nodes that describe different modalities of edges 57 \nbetween the nodes. So, in spatially resolved omics data, the spatial neighbourhood can be 58 \nencoded by defining a spatial connectivity (based on e.g. Euclidean distance) as the weight 59 \nof edges between nodes (cells or spots). 60 \n.CC-BY 4.0 International licensemade available under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is \nThe copyright holder for this preprintthis version posted August 23, 2024. ; https://doi.org/10.1101/2024.08.23.609349doi: bioRxiv preprint \n\nResults and Discussion 61 \nIn this study we review how Leiden clustering can utilise spatial information through selection 62 \nof spatially variable genes (SVGs) instead of highly variable genes (HVGs)(5), spatially-63 \naware dimensionality reduction through MUTLISPATI-PCA(6) (msPCA), and explicitly 64 \nmodelling the spatial embedding in the Leiden multiplex clustering (SpatialLeiden) (Figure 65 \n1a). We demonstrate their application to a 10x Visium spatial transcriptomics dataset of the 66 \nmouse dorsolateral prefrontal cortex (DLPFC), the most widely used benchmark dataset for 67 \nspatial clustering methods(7). This dataset consists of spatial gene expression data and 68 \nhistology images of 3 replicate slices from 4 donor mice, together with ground truth 69 \nannotation of anatomical domains in those tissue samples. We compare the performance of 70 \na non-spatially aware and SpatialLeiden clustering to two widely used spatially-aware 71 \ndomain detection tools, SpaGCN and BayesSpace(8,9), and evaluating performance of the 72 \ntools (Figure 1 b, c).  73 \n 74 \nWhile use of SVGs over HVGs yielded only minor improvements, we observed substantial 75 \nimprovement in performance when using spatially aware dimensionality reduction (msPCA) 76 \nand using SpatialLeiden over non-spatial Leiden, revealing a better representation of the 77 \nneocortex layering pattern (Figure 1b). We quantitatively evaluated performance of the 78 \ndifferent clustering strategies using the Adjusted Rand Index (ARI) and Normalised Mutual 79 \nInformation (NMI) score, showing significant improvements of SpatialLeiden over the non-80 \nspatial Leiden implementation, with performance that was better than SpaGCN and 81 \ncomparable to BayesSpace (Figure 1 c, Supplemental Figure 1-3, Supplemental table 1-82 \n2) at a fraction of the processing time. SpatialLeiden performed favourably when we 83 \ncompared its performance to other tools in a recent benchmark study, ranking 5th of 15 84 \ntools(4), (see Supplemental Methods for further details). 85 \n 86 \n.CC-BY 4.0 International licensemade available under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is \nThe copyright holder for this preprintthis version posted August 23, 2024. ; https://doi.org/10.1101/2024.08.23.609349doi: bioRxiv preprint \n\n 87 \nFigure 1: SpatialLeiden workflow. (a) Schematic of data processing and modelling steps 88 \nto enable spatially-aware Leiden clustering. Feature selection is performed by spatially 89 \nvariable genes (SVGs), dimensionality reduction is performed by a spatially aware 90 \nMULTISPATI-PCA (msPCA), and clustering is performed by the Leiden layer multiplex 91 \nalgorithm with both gene expression and spatial embeddings (SpatialLeiden). (b) Histology 92 \nand manually annotated neocortex layered domains for the mouse brain DLPFC (slice 93 \n151673) and spatial domains detected by Leiden, SpatialLeiden, SpaGCN and BayesSpace. 94 \n(c) Boxplot of Adjusted Rand Index (ARI) and Normalised Mutual Information (NMI) for all 12 95 \nDLPFC samples. Center line: median; box limits: upper and lower quartiles; whiskers: 1.5× 96 \n.CC-BY 4.0 International licensemade available under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is \nThe copyright holder for this preprintthis version posted August 23, 2024. ; https://doi.org/10.1101/2024.08.23.609349doi: bioRxiv preprint \n\ninterquartile range; dots: outliers; asterisks: significance (FWER, one-sided Wilcoxon signed-97 \nrank test). 98 \n 99 \nAs with other multi-modal clustering approaches, careful consideration has to be paid to a 100 \nnumber of parameters including the definition and weighting of neighbours across 101 \nmodalities, the resolution to be applied to each modality, and the weight of each modality 102 \n(Supplemental Figure 4). Furthermore, the spatial relationship between cells can be 103 \nmodelled in different ways; a regular grid pattern is suitable for Visium (isometric) and binned 104 \nStereo-seq (square), while for imaging-based spatially resolved transcriptomics methods 105 \nDelaunay triangulation or k-nearest neighbours can be used to define the topological layer.  106 \n 107 \nTo investigate the performance of SpatialLeiden across technologies, tissues and topological 108 \nmodelling we analysed a number of datasets (Stereo-Seq mouse embryo(10), BaristaSeq 109 \nmouse brain primary cortex, MERFISH mouse brain hypothalamus preoptic area(11), 110 \nosmFISH mouse brain somatosensory cortex, STARmap mouse brain medial prefrontal 111 \ncortex(12,13), STARmap1k mouse brain visual cortex) and demonstrated exceptional 112 \nimprovements over non-spatially aware Leiden clustering. SpatialLeiden ranked as the best 113 \nperforming spatial domain clustering methods for Stereo-Seq, MERFISH and osmFISH, 114 \nwhile demonstrating top tier performance for the other datasets (Figure 2). For imaging-115 \nbased spatial transcriptomics methods we found that modelling the topological 116 \nneighbourhood using the 10 k-nearest neighbours generally performed better than using 117 \nDelaunay triangulation. All non-Stereo-seq dataset were processed within 2 minutes, utilising 118 \nless than 400 MB of RAM. All Stereo-seq samples were processed within 8 minutes utilising 119 \na maximum of 3.5 GB of RAM (Supplemental Figure 5).  120 \n.CC-BY 4.0 International licensemade available under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is \nThe copyright holder for this preprintthis version posted August 23, 2024. ; https://doi.org/10.1101/2024.08.23.609349doi: bioRxiv preprint \n\n 121 \nFigure 2: Performance of SpatialLeiden across technologies and tissues: (a) Stereo-122 \nSeq of the mouse embryo at various development stages; (b) BaristaSeq of mouse primary 123 \ncortex; (c) MERFISH mouse brain hypothalamus preoptic area; (d) osmFISH of mouse 124 \nsomatosensory cortex; (e) STARmap mouse brain medial prefrontal cortex; and (f) 125 \nSTARmap* of mouse visual cortex. Performance metrics of other tools are taken from Yuan 126 \net al 2024(4). SpatialLeiden was run with 5 different random seeds and median results were 127 \nreported per sample. 128 \nConclusions 129 \nOur results show that the reference implementation of the Leiden algorithm can indeed be 130 \nused as a spatially-aware clustering algorithm. Subsequent studies that compare spatially-131 \naware clustering algorithms should clearly state that they compare to non-spatial 132 \nimplementation of Leiden, rather than misclassifying Leiden as a non-spatial algorithm. 133 \n We describe the different steps at which spatial awareness can be introduced into the 134 \nanalysis, and our implementation allows easy parameterisation of key considerations for 135 \n.CC-BY 4.0 International licensemade available under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is \nThe copyright holder for this preprintthis version posted August 23, 2024. ; https://doi.org/10.1101/2024.08.23.609349doi: bioRxiv preprint \n\nmodelling gene and spatial modalities. While many spatial domain clustering tools rely on 136 \nspatially-aware dimensionality reduction approaches this is often followed by non-spatial 137 \nclustering and we expect these methods to improve with spatially-aware clustering such as 138 \nSpatialLeiden.  139 \n 140 \nThe same way Leiden became the method of choice for clustering of single-cell data, we 141 \nbelieve that SpatialLeiden will become the method of choice for spatial data owing to its 142 \nefficiency, simplicity, and ease of integration into existing analysis workflows. 143 \nMethods 144 \nData processing 145 \nData was analysed using python (v3.10.14), Scanpy(14) (v1.10.1), and Squidpy(15) (v1.4.1). 146 \nTopological neighbourhood graph generation 147 \nThe neighbors of each cell were defined depending on the technology. For datasets with a 148 \nregular grid the neighbors were defined using squidpy.gr.spatial_neighbors with coord_type 149 \n‘grid’ and n_neighs set to 6 or 4 for Visium and Stereo-seq, respectively. For all other 150 \ndatasets the neighbors were defined either using Delaunay triangulation 151 \n(squidpy.gr.spatial_neighbors with delaunay=True) or using the 10 nearest-neighbors 152 \n(squidpy.gr.spatial_neighbors with coord_type `generic` and n_neighs set to 10). The 153 \nuntransformed neighbourhood graph ‘spatial_connectivities’ was used as is for regular grids 154 \nas all connections are equidistant. For Delaunay triangulation and kNN the 155 \n‘spatial_distances’ were transformed to ‘spatial_connectivities’ via the following formula: 156 \n1 − 𝑑\n𝑑𝑚𝑎𝑥\n 157 \n.CC-BY 4.0 International licensemade available under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is \nThe copyright holder for this preprintthis version posted August 23, 2024. ; https://doi.org/10.1101/2024.08.23.609349doi: bioRxiv preprint \n\nHVG and SVG detection 158 \nHighly variable genes (HVGs) were detected based on filtered count data 159 \n(scanpy.pp.highly_variable_genes with flavor ‘seurat_v3’). To detect spatially variable genes 160 \n(SVGs), first the neighbours were defined as described above and the Moran’s I score was 161 \ncalculated for all genes using squidpy.gr.spatial_autocorr with mode ‘moran’ and selecting 162 \nthe top 3,000 scoring genes. Gene selection was only performed for capture-based spatial 163 \ntranscriptomics technologies (Visium, Stereo-seq). 164 \nMULTISPATI-PCA 165 \nWe implemented MULTISPATI-PCA(6) in python (https://github.com/HiDiHlabs/multiSPAETI 166 \nv0.1.0) and used it to perform spatially-aware dimensionality reduction. The topological 167 \nneighbourhood graph ‘spatial_connectivities’ was used to calculate 30 components 168 \n(corresponding to the 30 largest eigenvalues) based on the 3,000 HVGs / SVGs (Visium, 169 \nStereo-seq) or all genes in the case of imaging-based technologies (STARmap, STARmap*, 170 \nMERFISH, BaristaSeq, osmFISH) as for normal PCA. 171 \nLatent neighbourhood graph generation 172 \nThe topological neighbourhood graph in the Visium grid ‘spatial_distances’ from 173 \nsquidpy.gr.spatial_neighbors (as described in SVG detection) is used as the spatial layer for 174 \nLeiden clustering. To build the neighbourhood graph in latent space of gene expression we 175 \nfirst calculated the first 30 principal components based on the top 3,000 variable genes 176 \n(scanpy.tl.pca). We identified the 15 nearest-neighbours per spot (scanpy.pp.neighbors) 177 \nbased on the PCA or MULTISPATI-PCA results from either the HVGs / SVGs (Visium, 178 \nStereo-seq) or for all genes in the case of imaging-based technologies (STARmap, 179 \nSTARmap*, MERFISH, BaristaSeq, osmFISH) and used the resulting ‘connectivities’. 180 \n.CC-BY 4.0 International licensemade available under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is \nThe copyright holder for this preprintthis version posted August 23, 2024. ; https://doi.org/10.1101/2024.08.23.609349doi: bioRxiv preprint \n\nNon-spatially aware Leiden 181 \nWe used Leiden(1) (https://github.com/vtraag/leidenalg, v0.10.2) as implemented in Scanpy 182 \nwith the default parameters and varied the resolution to achieve the correct number of 183 \nclusters for each of the DLPFC datasets following the approach of the SpaGCN.search_res 184 \nfunction (https://github.com/jianhuupenn/SpaGCN). 185 \nSpatially-aware Leiden multiplex (SpatialLeiden) 186 \nWe implemented a spatially aware version of 187 \nLeiden(https://github.com/HiDiHlabs/SpatialLeiden) by using the Layer multiplex(16). An 188 \nadditional graph encoding for the topological neighbourhood of the cells was added as 189 \nsecondary layer in addition to the layer encoding gene expression in latent space. The 190 \nadditional spatial layer was encoded as RBConfigurationVertexPartition as is the default for 191 \nthe scanpy implementation for the latent space graph. The optimal clustering was identified 192 \nby running the Optimiser.optimise_partition_multiplex from leidenalg until convergence. As 193 \nonly the ratio of the layer_weights is relevant the weight for the gene expression latent space 194 \nlayer was kept at 1 and the weight for the topological neighbourhood was set depending on 195 \ntechnology and method of neighbourhood definition. The resolution for the latent space 196 \npartition was set by running the standard Leiden clustering and identifying the resolution 197 \nwhich yields the correct number of clusters. The resolution of the topological partition was 198 \nthen varied to identify the correct number of clusters in the multiplex Leiden using the same 199 \napproach as described for the standard Leiden method.  200 \nImplementation and comparison to other spatial clustering 201 \nalgorithms 202 \nImplementation and comparison to other spatial clustering algorithms is described in the 203 \nonline methods. 204 \n.CC-BY 4.0 International licensemade available under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is \nThe copyright holder for this preprintthis version posted August 23, 2024. ; https://doi.org/10.1101/2024.08.23.609349doi: bioRxiv preprint \n\nAbbreviations 205 \nSpatially variable genes (SVGs).  206 \nHighly variable genes (HVGs). 207 \nMUTLISPATI-PCA (msPCA). 208 \nDorsolateral prefrontal cortex (DLPFC). 209 \nAdjusted Rand Index (ARI). 210 \nNormalised Mutual Information (NMI). 211 \nDeclarations 212 \nEthics approval and consent to participate 213 \nNot applicable. 214 \nConsent for publication 215 \nNot applicable. 216 \nAvailability of data and materials 217 \nThis study used publicly available spatially resolved transcriptomics data of the mouse brain 218 \nDLPFC profiled on the 10x Visium platform (http://research.libd.org/spatialLIBD/). Public 219 \nStereo-seq, STARmap, STARmap*, MERFISH, osmFISH, and BaristaSeq datasets were 220 \ndownloaded from http://sdmbench.drai.cn/. Performance metrics of other tools presented in 221 \nFigure 2 were taken from Yuan et al(4). We also provide a repository with Jupyter Notebooks 222 \nfor reproducing all results and figures of this study 223 \nhttps://github.com/HiDiHlabs/SpatialLeiden-Study.  224 \n 225 \n.CC-BY 4.0 International licensemade available under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is \nThe copyright holder for this preprintthis version posted August 23, 2024. ; https://doi.org/10.1101/2024.08.23.609349doi: bioRxiv preprint \n\nCompeting interests 226 \nThe authors declare that they have no competing interests. 227 \nFunding 228 \nThis research has received funding from the Federal Ministry of Education and Research of 229 \nGermany in the framework of SAGE (project number 031L0265). 230 \nAuthors' contributions 231 \nNI conceived and designed the study. SS implemented the spatially-aware Leiden. NMB, SS 232 \nimplemented the SpatialLeiden package. NMB implemented MULTISPATI-PCA in python. 233 \nSS performed code review. NMB performed data analysis. NI, NMB interpreted and 234 \nanalysed results. NI, NMB, SS, RE proofread and corrected the manuscript. All authors 235 \ncontributed to the article and approved the submitted version. 236 \nAcknowledgements 237 \nWe thank organisers and participants of the de.NBI BioHackathon SpaceHack 2.0 project in 238 \nBielefeld, Germany in December 2023 (Supplemental Table 3).  239 \nReferences  240 \n 1. Traag VA, Waltman L, van Eck NJ. From Louvain to Leiden: guaranteeing well-241 \nconnected communities. Sci Rep. 2019 Mar 26;9(1):5233.  242 \n2. Bredikhin D, Kats I, Stegle O. MUON: multimodal omics analysis framework. Genome 243 \nBiol. 2022 Feb 1;23(1):42.  244 \n3. Vandereyken K, Sifrim A, Thienpont B, Voet T. Methods and applications for single-cell 245 \nand spatial multi-omics. 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