dataesr/scientific-paragraphs-categorization huggingface dataset:
eea. europa. eu ). In this version of the dataset, species distributions were only recorded for two time periods: 1851-1950 and 1951-2010. The update to EuroDiad 3. 2 addressed gaps in spatial coverage, adding diadromous species distributions for 63 small-sized catchments located in Russia, Norway, France, Greece, Spain, Italy, Sicily, Sardinia, and Morocco. Temporal coverage of the dataset was also improved by updating the historic distribution of each species within the 63 newly entered catchments to also include 1751-1850. This was not done for all catchments within the database, however. For the 196 catchments originally entered into the database, the time period of 1751-1850 was only added in version 3. 2 for four emblematic species: Alosa alosa, Acipenser sturio, Anguilla anguilla and Salmo salar.
For the 2019-2020 update resulting in the most recent version of this dataset, EuroDiad 4. 0, effort was focused on catchments located in the Atlantic Area of Europe. This was primarily for use in several ongoing projects focusing on species distributions in this particular geographic location. The EuroDiad 4. 0 update validated the existing data for the Atlantic Area and improved the spatial extent of the dataset by adding several more small-sized catchments, increasing the total number of recorded catchments to 350. While this is a large improvement over EuroDiad 1. 0, the precision of available information for each country still varies ( Table  13  ) and the proportion of European catchments included in the dataset could still be improved ( Table  14  ). The 2019-2020 update also improved the temporal extent of the dataset to include all three time periods for all catchments where this information was available.
Last external validation process Morphological and distribution data associated with catchments in the Atlantic Area were validated in 2019-2020 by DiadES project partners. Data was divided by country, and validation was performed for catchments in Ireland, the UK, Spain, Portugal, and France, by national organisations involved in fisheries and environmental management ( Table  12  ). In the U. K. , local experts were available to validate data in all regions except Scotland. For the validation process, species experts were identified regionally using partners for the DiadES project and their local affiliations. Participants were asked to validate morphological information for the catchment (location of the outlet, surface area of the drainage basin, length of the main watercourse, elevation at the headwaters), as well as the presence/absence information and population functionality categories for all species already present in EuroDiad for their country.
If possible, verification was done for each of the three time periods. Participants were also asked to provide data for any other catchments for which they had access to information on diadromous species population status. Several questions were raised and addressed over the course of the validation process to ensure that each participant had the same interpretation of data categories. This was especially instead of deleting the record so that uncertainty about a species within a particular catchment could be recorded with comments and references in the event of future discussions or updates. This approach also ensured that these records with no reliable information could be excluded from queries. The second question involved the temporal extend of the dataset. For some species and catchments, there was a mismatch between the rate of population change and this 100-year time periods, meaning that there was a change in population functionality category within a time period instead of between time periods.
The last question involved the four population functionality categories. These categories were designated during the development of the original versions of EuroDiad as "Missing", "Rare", "Common", and "Abundant". However, as these descriptive words can have different definitions depending on the context and a researcher's background, it was decided for the 2019-2020 dataset update to use a numeric code instead of a character code ( Table  15  ) for these four categories in order to alleviate any confusion. The definitions of these categories was not changed between EuroDiad 2. 0 and EuroDiad 4. 0, only the way they were presented in the data tables within the dataset. The focus of these categories was on functional versus non-functional populations, as this is an important designation when using habitat suitability to predict future fish distributions.
Motivation: High-throughput single-cell molecular profiling is revolutionizing biology and medicine by unveiling the diversity of cell types and states contributing to development and disease. The identification and characterization of cellular heterogeneity are typically achieved through unsupervised clustering, which crucially relies on a similarity metric. Results: We here propose the use of Optimal Transport (OT) as a cell-cell similarity metric for single-cell omics data. OT defines distances to compare high-dimensional data represented as probability distributions. To speed up computations and cope with the high dimensionality of single-cell data, we consider the entropic regularization of the classical OT distance. We then extensively benchmark OT against state-of-the-art metrics over 13 independent datasets, including simulated, scRNA-seq, scATAC-seq and single-cell DNA methylation data.
Indeed, most of the existing biological studies use single-cell data to discover and characterize the cell populations/types present in a biological sample, a task that is intrinsically unsupervised. We finally recently developed a joint metric learning method simultaneously computing OT distances between both genes and cells, but not providing relevant improvements over existing single-cell approaches  (Huizing et al. , 2021). Here, we propose the use of OT as a cell-cell similarity metric for single-cell data. In particular, we use OT with entropic regularization  (Cuturi, 2013) , expected to control the systematic noise due to the stochasticity of gene expression at single-cell level and to the presence of dropouts. In addition, using OT with entropic regularization we could efficiently analyze datasets with large numbers of cells using a Graphics Processing Unit (GPU).
We further extensively benchmark OT against state-of-the-art metrics. We apply the different metrics to single-cell data with known groups (e. g. cell types, cell lines of origin) and we evaluate their ability to detect the similarity between cells belonging to the same group. We then apply different unsupervised clustering algorithms to the computed distance matrices and test the quality of the resulting clusters. Of note, all the tests are performed in three conditions: (i) simulated scRNA-seq data, where the effect of the number of cells and of the size and overlap of the clusters can be tested in-depth; (ii) real scRNA-seq data, profiled from cell lines and colorectal tissue and (iii) other omics data, including scATAC-seq and single-cell DNA methylation. All the performed analyses are reproducible using the OT-scOmics Jupyter notebook provided on GitHub (https://github.
scRNA-seq data simulation scRNA-seq data with 5000 genes and three underlying clusters have been simulated using the R Bioconductor package Splatter  (Zappia et al. , 2017). Splatter simulates scRNA-seq data using the Splat model, built around a Gamma-Poisson distribution. Different parameters can be tuned in the Splatter simulation. Details on the parameters used to run Splatter are available in Supplementary Text S1. Using simulated scRNA-seq data, we can assess in-depth the influence of different factors on the quality of the inferred cell-cell similarities. We simulated five scRNA-seq datasets (Table  1 ) obtained by varying three main factors: 1. The number of cells constituting the scRNA-seq dataset (batchCells parameter in Splatter). Datasets with 500, 1000 and 10 000 cells are simulated.
Single-cell omics data acquisition and preprocessing Several publicly available single-cell omics datasets have been employed (Table  1 ). Only public datasets providing ground-truth labels for all the profiled cells were considered. The labels are intended to associate each cell to a specific group (e. g. cell type, cell line of origin). Of note, labels are only used to evaluate the quality of our results, as all the performed benchmarking is unsupervised. For scRNA-seq data four datasets have been considered. First, the scRNA-seq data (called 'Liu scRNA') present in the scCAT-seq joint profiling of  (Liu et al. , 2019)  containing 206 cells profiled from three cancer cell lines (HCT116, HeLa-S3, K562). Next, a bigger dataset composed of 561 cells profiled from seven cell lines (A549, GM12878, H1437, HCT116, IMR90, H1, K562) from  Li et al.
(2017)  (called 'Li cell lines'). Finally, two colorectal cancer (CRC) datasets, corresponding to primary CRC tumors and matched normal mucosa have been also taken into account. The first (called 'Li Tumor') contains 364 cells clustered into seven cell types: B cells, endothelial cells, epithelial cells, fibroblasts, macrophages, mast cells and T cells. The second (called 'Li NM') is composed of 266 cells clustered according to the same seven cell types. Other single-cell omics are also included in our analysis: methylation and scATAC-seq data. For scATAC-seq data we considered: (i) the dataset included into the scCAT-seq joint profiling of  Liu et al. (2019)  (called 'Liu scATAC-seq') composed of 206 cells extracted from three cancer cell lines (HCT116, HeLa-S3, K562); (ii) the leukemia scATACseq data from  Corces et al.
(2016)  (called 'Leukemia scATAC'), containing 391 cells and composed of monocytes and lymphoid-primed multipotent progenitors (LMPP) isolated from a healthy human donor, together with leukemia stem cells (SU070_LSC, SU353_LSC) and blast cells (SU070_Leuk, SU353_Blast), isolated from two patients with acute myeloid leukemia. To represent single-cell DNA methylation, we considered two neuronal snmC-seq datasets from  Luo et al. (2017). The first (called 'scMethylation mouse') is composed of 3377 cells extracted from mouse frontal cortical neurons clustered into 16 neuronal subtypes. The second (called 'scMethylation human') is composed of 2740 cells, extracted from human frontal cortical neurons and clustered into 21 neuronal subtypes. A summary of the considered datasets is available in Table  1.
The downloaded datasets had already undergone standard preliminary preprocessing and, following standard practices  (Luecken and Theis, 2019) , we log-transformed the scRNA-seq counts and selected the 10 000 most varying features. Alternative preprocessing strategies for scRNA-seq  (Hafemeister and Satija, 2019; Lun et al. , 2016; Yip et al. , 2017)  have also been tested using the code provided in  Chen et al. (2021) , with no impact on the results (Supplementary Fig. S1  and Tables  S1  and S2 ).
Baseline metrics We consider a single-cell omics dataset as a matrix X, whose columns correspond to cells, and whose rows correspond to features (e. g. peaks, genes). Given two cells indexed by l and m as columns of X, different metrics are classically used to infer the similarity between their omic profiles x ¼ X½Á; l ¼ ðx 1. x n Þ and y ¼ X½Á; m ¼ ðy 1. y n Þ. We here focus on four state-of-the-art metrics, henceforth called baseline metrics, and defined as 1. Euclidean distance (L2): jjx À yjj 2 :¼ ð P n i¼1 ðx i À y i Þ 2 Þ 1=2 2. Manhattan distance (L1): jjx À yjj 1 :¼ P n i¼1 jx i À y i j 3. Cosine similarity: cos x; y ð Þ :¼ xÁy jjxjjÂjjyjj ; where jj Á jj is the Euclidean norm 4. Pearson correlation: corrðx; yÞ :¼ cosðx À x; y À yÞ, where x and y are the mean of the values of x and y, respectively.
For cosine similarity and Pearson correlation, we used the distance-like formulation 1 À cosðx; yÞ and 1 À corrðx; yÞ. Of note, these are not strictly speaking distances, in particular, they do not respect the triangular inequality. The baseline metrics have been computed using functions from the Python package SciPy (scipy. spatial. distance): euclidean, cityblock, cosine, correlation. Baseline metrics have been computed on the input data, after the data preprocessing detailed in the section above. Optional per-cell normalization and feature scaling have been also considered (Fig. 1 ), but they resulted to be less performant (Supplementary Table  S1 ).
Hence, C should be chosen in such a way that similar bins i and j have a low cost C ij. We propose the use of the OT distance to capture cell-cell similarity in different single-cell omics data. For simplicity, let us consider a scRNA-seq dataset ðXÞ; the same concepts apply to other single-cell omics. Given a pair of cells l and m, as done for baseline metrics, we consider their expression profiles, corresponding to the vectors  1 ) is defined only for discrete probability distributions, we transform x and y into two discrete probability distributions a ¼ x x j j j j 1 and b ¼ y y j j j j 1. In the following, we refer to such a transformation as per-cell normalization. After transformation, we can apply Equation (1) and compute the OT distance W C ða; bÞ, between a and b; which corresponds to evaluating the minimal cost required to transform the gene expression discrete probability distribution (a) of the first cell into the gene expression discrete probability distribution (b) of the second cell.
The choice of the ground cost plays a central role in the final performances of OT and, in our case, there is no straightforward choice. Also ground costs based on prior information (e. g. pathways) could be employed. However, dataset/tissue specific ground costs are expected to be able to be more performant. It is for this reason that for all couples of genes i and j in the single-cell matrix X, we define Note: In the first part of the table ('Data description'), for each dataset, we specify the name with which we denote it in the paper, the reference to its original publication, the type of data, the number of cells, the number of features after preprocessing and the ground-truth number of clusters (e. g. cell types, cell lines) present in the data. In the second part of the table ('Clustering results'), we report the number of clusters obtained by maximizing the silhouette score, with hierarchical clustering (for Pearson correlation and OT distance) and for a typical single-cell clustering workflow based on Leiden clustering (for the Euclidean distance on PCA components and for the OT distance).
At the same time, the entropic regularization allows a faster execution of the algorithm thus opening to the possibility of analyzing single-cell datasets bigger than those that can be analyzed with the classical OT (Supplementary Table  S3  and Text S3 ). Finally, the entropic regularization, encouraging exchanges of mass in between features, allows OT to give more importance to the relationships between features (e. g. genes), which further motivates its application to complex data like single-cell data. The parameter e thus plays a central role in the final performances of Sinkhorn divergence and should be carefully chosen. The advantage of the formulation at Equation (  3 ) is that W C; e can be efficiently computed on a GPU, thereby coping with the high dimensionality of single-cell data.
For every dataset, we performed a grid search varying e among 1000; 5; 1; 0:5; 0:1; 0:05; 0:01 and the ground cost among Euclidean, Manhattan, Cosine and Pearson correlation. As shown in Supplementary Table  S2 , the best performances on average across datasets and ground costs were obtained for the regularization parameter e set at 0. 5. We thus suggest 0. 5 as default e for future users. In contrast, the best performing ground cost C varied depending on the analyzed data. In scRNA-seq simulated data and in single-cell DNA methylation data, Pearson correlation achieved the best performances, while on scRNA-seq and scATAC-seq data, cosine similarity performed the best. The performances presented in Section 3 thus correspond to this choice of e and C. The computation of the OT distance has been implemented using the Python package PyTorch and run on a GPU.
Performance evaluation For all single-cell datasets, simulated and real, ground-truth labels are available. For the real single-cell omics, the ground-truth labels correspond to cell types, defined through clustering in the original publication, or to the cell lines from which the cells have been extracted. We first use the C-index and Silhouette score to evaluate to which extent the various metrics detect the similarity between cells associated with the same label, as well as the difference between cells with different labels (Fig. 1 ). The C-index  (Hubert and Schultz, 1976 ) is an internal clustering evaluation index. Given a cell-to-cell distance matrix, the C-index measures if the closest pairwise distances correspond to cells belonging to the same cluster. It is defined as C ¼ S À S min S max À S min ; where n is the number of intracluster pairwise distances, S min is the sum of the n smallest distances if all pairs of cells are considered, S max is the sum of the n largest distances out of all pairs and S is the sum of distances over all pairs of cells form the same cluster.
We used the Silhouette score implementation of the Python package scikit-learn (sklearn;  Pedregosa et al. , 2011). To further test the quality of the inferred cell-to-cell distance matrices, we used them as inputs for a clustering algorithm and assessed the agreement between the inferred clusters and the ground-truth labels (Fig. 1 ). We considered clustering algorithms for which applications to single-cell data have been already proposed and directly applicable to the cell-to-cell distance matrices. We thus selected hierarchical clustering, with complete linkage, and spectral clustering  (Von Luxburg, 2007; Zheng et al. , 2019) , both implemented in scikit-learn. Regarding hierarchical clustering, we chose complete linkage in place of average linkage, used in other singlecell clustering works  (Guo et al.
Second, four real scRNA-seq data, profiled from CRC and cell lines, are considered. Finally, we further challenged the distance measures on other single-cell omics: scATAC-seq and single-cell DNA methylation. See Section 2 and Table  1  for details concerning the data. In all three contexts, ground-truth labels were available for all cells. In simulated scRNA-seq data, the ground-truth labels have been imposed during the data simulation (see Section 2). In real single-cell omics, the ground-truth labels are extracted from the original publications. For the four profilings of cell lines (Liu scRNA, Li cell lines, Liu scATAC and Leukemia scATAC), labels correspond to the cell line of origin and thus reflect strong transcriptional/epigenetic differences. In contrast, in the case of the neuronal single-cell DNA methylation (scMethylation mouse and scMethylation human) and scRNA-seq from CRC samples  (Li Tumor and Li NM) , the ground-truth labels reflect clusters previously identified in the data, based on the activity of predefined markers.
These results also suggest that OT is scalable to highdimensional datasets, a crucial feature for the analysis of single-cell data. Finally, OT achieves superior performance with highly unbalanced clusters, which is more realistic as biological samples are often composed of a mixture of rare and common populations of cells, and also with overlapping clusters, which reflects the scenario of subpopulations of cells sharing similar transcriptional patterns, as cell populations tracked over different developmental phases. We then considered four scRNA-seq datasets: two of them correspond to cancer cell lines  (Li et al. , 2017; Liu et al. , 2019) , while the remaining two correspond to colorectal tumor tissue and matched normal mucosa  (Li et al. , 2017). All metrics tend to perform better in cancer cell lines than CRC samples.
This result is most probably the consequence of the stronger transcriptional difference existing between cell lines. Overall, in all the four scRNAseq datasets, OT outperformed baseline metrics (Fig. 2B ). The improvement provided by OT in cell lines is important, especially according to Silhouette score (þ0. 6 Silhouette score). To show to which extent C-index and Silhouette score reflect a clear clustering structure in the cell-to-cell distance matrices, we focused on the smallest dataset, Liu scRNA  (Liu et al. , 2019). Figure  2C  reports the cell-to-cell distance matrices obtained for this dataset with OT distance, Pearson correlation and Euclidean distance. Cells in the matrices are sorted based on their cell line of origin. OT powerfully detected the similarity between cells belonging to the same cancer cell line, showing three clear blocks of cells at distance close to zero.
In contrast, the blocks corresponding to the three cell lines are less marked with Pearson correlation. Finally, with Euclidean distance, the values outside the three blocks tend to be less close to one, indicating a less clear separation between cells belonging to different cell lines. Finally, we challenged the various metrics on other single-cell omics data (Fig. 2D ). Also in this case, OT shows better performance than Pearson correlation. Overall, OT performed better than existing metrics in the detection of cell-cell similarities in all considered datasets. See Supplementary Table  S1  for the performances of other state-of-the-art baseline metrics.
Comparing OT against baseline metrics based on hierarchical clustering Hierarchical clustering was applied to the cell-to-cell distance matrices computed with OT and Pearson correlation. In all datasets, the number of clusters was optimized based on the Silhouette score (Section 2). Table  1  summarizes the number of clusters obtained across all datasets and compares them with those defined in the original publications. The resulting clusters were then compared with the ground-truth labels based on ARI and NMI (Fig. 3 ). In simulated data, all the five datasets contain three underlying clusters. As described in Table  1 , in four out of five cases, both OT and Pearson correlation identified the correct number of clusters. The only exception is represented by the dataset composed of 10 000 cells, where OT correctly detects the presence of three clusters, while Pearson correlation overclustered the data, by subdividing the three groups into five clusters.
According to ARI and NMI, both Pearson correlation and OT give rise to perfect results (Fig. 3A ). Pearson correlation also led to optimal ARI and NMI scores in the dataset of 10 000 cells, as overclustering is not captured by these scores. Turning to real scRNA-seq data, in Liu scRNA data, both Pearson correlation and OT detected the correct number of clusters (Table  1 ). Concerning the two CRC datasets, for Li Tumor, containing seven cell types, OT only detected three clusters while Pearson predicted the presence of six clusters, thus missing only the rare population of mast cells, represented by one cell. In contrast, for Li NM, Pearson correlation dramatically overclustered the data and inferred 23 clusters, while OT suggested the presence of nine clusters. Finally, for Li cell lines, composed of seven cell lines, OT suggested the presence of eight clusters, while Pearson identified 10.