dataesr/scientific-paragraphs-categorization huggingface dataset:
DNA was extracted using a Qiagen DNeasy Blood and Tissue Kit with a lysozyme pre-treatment step, as previously described  (17) , and submitted to the University of Minnesota Genomics Center. Libraries were prepared using a NEBNext Ultra II FS DNA Library Prep Kit for Illumina and a Nextera® XT Index Kit v2 Set A. Libraries were sequenced on a NextSeq P1 flow cell (150 PE) with ~2. 1 million reads per sample (~300 reads/mutant). Mutant abundance was quantified using custom scripts as previously described  (5, 17).
Acknowledgements This work was supported by a grant from  Boehringer Ingelheim Fonds  to AL,  American Heart Association  fellowship  907592  to DB,  National Institutes of Health  grant  K99AI151080  to JLEW, and  National Institutes of Health  grant  R01AI122742  to GMD. The authors thank  Cristel Archambaud  and  Pascale Serror  for supporting the participation of AL and  Jose Lemos  for supporting the participation of DB. The authors are also grateful to  Pascale Serror  and  Jose Lemos  for helpful comments on the manuscript.
Conventional dimensionality reduction methods like Multidimensional Scaling (MDS) are sensitive to the presence of orthogonal outliers, leading to significant defects in the embedding. We introduce a robust MDS method, called DeCOr-MDS (Detection and Correction of Orthogonal outliers using MDS), based on the geometry and statistics of simplices formed by data points, that allows to detect orthogonal outliers and subsequently reduce dimensionality. We validate our methods using synthetic datasets, and further show how it can be applied to a variety of large real biological datasets, including cancer image cell data, human microbiome project data and single cell RNA sequencing data, to address the task of data cleaning and visualization.
We present here a robust MDS method, called DeCOr-MDS, Detection and Correction of Orthogonal outliers using MDS. DeCOr-MDS takes advantage of geometrical characteristics of the data to reduce the influence of orthogonal outliers, and estimate the dimension of the dataset. Our paper is organized as follows. We first describe the procedure and its implementation in detail. We then validate our method on synthetic data to confirm the accuracy and characterize the importance of different parts of our procedure. We further run the method on different experimental datasets from single cell images, microbiome sequencing data, and scRNA-seq data. Our experiments show that DeCOr-MDS can detect artefacts in cell shape data, improve the visualization of clusters in microbiome data, and be used as a step for quality control for scRNA-seq data, illustrating how it can be broadly applied to interpret and improve the performance of MDS on biological datasets.
Orthogonal outlier detection and dimensionality estimation We now consider a dataset X of size N × d, where N is the sample size and d the dimension of the data. We associate with X a matrix D of size N × N, which represents all the pairwise distances between observations of X. We also assume that the data points can be mapped into a vector space with regular observations that form a main subspace of unknown dimension d* with some small noise, and additional orthogonal outliers of relatively large orthogonal distance to the main subspace (Figure  1A ). Our proposed method aims to infer from D the dimension of the main data subspace d*, using the geometric properties of simplices with respect to their number of vertices: Consider a (n + 2)-simplex containing a data point x i and its associated height, that can be computed using Eq.
Overall procedure and implementation The overall procedure, called DeCOr-MDS, is described in Algorithm 1. The values for the parameters S and c were set by default and in our experiments to S = 100 and c = 3. We also provide an implementation in Python 3. 8. 10 available on this github repository: https://github. com/wxli0/DeCOr-MDS. The complexity of the algorithm can be briefly evaluated as follows. for n in E dim do for i in [1,N] do for j in [1,S] do Sample a (n + 2)-simplex V i,j containing x i Compute the height (using D and Eq. 1) h (j,n) i ≔ h j i (V i,j , x i ) end for h n i ≔ median(h (1,n) i , h (2,n) i ,. , h (S,n) i ) end for hn ≔ mean(h n 1 , h n 2 ,. , h n N ) σ(n) ≔ std(h n 1 , h n 2 ,. , h n N ) end for n ≔ arg max n hn-1 hn O ≔ i | h n i > h n + c × σ n p≔|O|/N n* n -( n + 1) × p (Skip if 1.
Synthetic datasets The "cross" dataset  (Spence and Lewandowsky, 1989) , which is a two-dimensional dataset representing a simple cross structure (Figure  2 ) was generated with N = 25 points, and d* = 2. We introduced orthogonal outliers by randomly sampling three points and by adding a third coordinate of random amplitude to them. Other synthetic datasets were generated by sampling Gaussian-distributed coordinates in the main subspace, and adding some small noise in the whole space with variance between 0. 0001 and 0. 0003. A fraction p of the points was considered to define the orthogonal outliers, with coordinates modified by randomly increasing the coordinate(s) orthogonal to the plane; the amount increased is drawn from a uniform distribution between -30 and 30 or -100 to 100. These datasets were generated for a main subspace of dimension 2, 10 and 40, with p = 0.
Cell shape dataset The cell shape dataset contains mouse osteosarcoma 2D imaged cells  (Alizadeh et al. , 2019) , that were processed into a 100 × 2 vector of coordinates that define the cell shape contour, used as a test dataset in the Python package Geomstats  (Miolane et al. , 2020)  (for more details, see also  (Miolane et al. , 2021)  and the associated Github link). We more specifically considered the subset of "DUNN" cells (that denotes a specific lineage) from the control group (no treatment on the cells), which yields 207 cells in total. The pairwise distance matrix of all cell shapes was obtained from the same reference  (Miolane et al. (2020; 2021) ) using the so-called Square Root Velocity metric that derives from the L 2 distance between velocities of the curves  (Srivastava et al.
HMP dataset The Human Microbiome Project (HMP)  (Turnbaugh et al. , 2007)  dataset represents the microbiome measured across thousands of human subjects. The human microbiome corresponds to the set of microorganisms associated to the human body, including the gut flora, or the skin microbiota. The data used here corresponds to the HMP1 phase of clinical production. The hypervariable region v13 of ribosomal RNA was sequenced for each sample, which allowed to identify and count each specific microorganism, called phylotype. The processing and classification were performed by the HMP using MOTHUR, and made available as low quality counts (https://www. hmpdacc. org/hmp/HMMCP/)  (Turnbaugh et al. , 2007). We downloaded this dataset, and subsequently, counts were filtered and normalized as previously described  (Legrand, 2017).
For our analysis, we also restricted our dataset to samples collected in nose and throat. Samples and phylogenies with less than 10 strictly positive counts were filtered out  (Legrand, 2017) , resulting in an n × p-matrix where n = 270 samples and p = 425 phylotypes. Next, the data distribution was identified with an exponential distribution, by fitting its rate parameter. Normalization was then achieved by replacing the abundances (counts) with the corresponding quantiles. Lastly, the matrix of pairwise distances was obtained using the Euclidean distance.
scRNA-seq dataset The scRNA-seq dataset contains single-cell transcriptomic profiles from mouse pancreatic cells (raw count data accession number: GSE84133), which were first processed using standard quality control methods from  McCarthy et al. (2017). From the gene count matrix, which originally contained 1,886 cells with 13,357 genes, we focused on the cells from Mouse 2, yielding 1,063 cells with 13,357 genes. We further lognormalized the data (Luecken and Theis, 2019) and selected highly variable genes using scanpy package  (Wolf et al. , 2018). This procedure resulted in a normalized gene count matrix of 1,603 cells with 2,601 genes. To obtain a matrix of pairwise distances, we used the Euclidean distance.
Using n-simplices for orthogonal outlier detection and dimensionality reduction We propose a robust method to reduce and infer the dimensionality of a dataset from its pairwise distance matrix, by detecting and correcting orthogonal outliers. The method, called DeCOr-MDS, can be divided into three sub-procedures detailed in Sections 2. 2-2. 4, with the overall algorithm provided in Section 2. 5. The first procedure detects orthogonal outliers and estimates the subspace dimension using the statistics of simplices that are sampled from the data, using Eqs 4, 5. The second procedure corrects for potential bias in estimated dimension when the fraction of outlier is large. The third procedure corrects the pairwise distance of the original data, by replacing the distance to orthogonal outliers by that to their estimated projection on the main subspace.
Performance on synthetic datasets We first illustrate and evaluate the performance of the method on synthetic datasets, (for a detailed description of the datasets and their generation, see the Methods Section 2. 6). On a simple dataset of points forming a 2D cross embedded in 3D (Figure  2A ), we observed that the MDS is sensitive to the presence of orthogonal outliers and distorts the cross when reducing the data in 2D (Figure  2B ). In contrast, our procedure recovers the original geometry of the uncontaminated dataset, with the outliers being correctly projected (Figure  2C ). The same results were obtained when sampling regular points from a 2D plane (Supplementary Figure  S1 ). We further tested higher dimensions, and illustrate in Figure  3A  how the distribution of heights becomes concentrated around 0, when testing for the true dimension (d* = 10), as suggested in the Methods Section 2.
2. As a result, our method allows to infer the main subspace dimension from Eq. 4, as shown in Figure  3B. In addition, the procedure accurately corrects the pairwise distances to orthogonal points with the distances to their projections on the main subspace, as shown in Figure  3C. When the dimension of the subspace and fraction of outliers get significantly large, we also illustrate the importance of the correction step (see Methods Section 2. 3), due to the sampling of simplices that contain several outliers. Upon using synthetic datasets with d* = 40 and varying the number (fraction) of outliers from 20 (2%) to 100 (10%), we observe this bias appearing before correction, with d* being overestimated by 2 or 3 dimensions (Figure  4 ). Using the debiased estimate n* from Eq. 6 successfully reduced the bias, with an error ≤ 1 for all the parameters tested.
Application to cell shape data We further show how DeCOr-MDS can be broadly applied to biological data, ranging from images to high throughput sequencing. We first studied a dataset of single cell images, from osteosarcoma cells (see Figure  5A ), which were processed to extract from their contour a 100 × 2 array of xy coordinates representing a discretization of a closed curve (see Dataset Section 2. 6). We obtained a pairwise distance matrix on this set of curves by using the so-called Square Root Velocity (SRV) metric, which defines a Euclidean distance on the space of velocities that derive from a regular parameterization of the curve  (Srivastava et al. , 2010; Miolane et al. , 2020). Using DeCOr-MDS, we found a main subspace of dimension 2 (Figure  5B ), with 14 (7%) outliers detected among the 207 cells of this dataset.
The comparison between the resulting embedding and that obtained from a simple MDS is shown in Supplementary Figure  S2 , and reveals that outliers, when uncorrected, affect the embedding coordinates, while our correction mitigates it. By examining in more details the regular and inferred outlier cells (Figure  5C , with all cell shapes shown in Supplementary Figure  S3 ), we found regular observations to approximately describe elliptic shapes, which is in agreement with the dimension found, since ellipses are defined by 2 parameters. One can also visually interpret the orthogonal outliers detected as being more irregular, with the presence of more spikes and small protusions. Interestingly, the procedure also identified as outliers some images containing errors, due to bad cropping or segmentation (with 2 cells shown instead of one), which should thus be removed of the dataset for downstream analysis.
Application to HMP data As another example of application to biological data, we next considered a dataset from the Human Microbiome Project (HMP). The Human Microbiome Project aims at describing and studying the microbial contribution to the human body. In particular, genes contributed by microbes in the gut are of primary importance in health and disease  (Turnbaugh et al. , 2007). The resulting data is an Application of DeCOr-MDS on a cell shapes dataset. (A) An example of osteocarcoma cell image obtained from fluorescence microscopy. We process and extract the cell contour in our analysis. (B) Dimensionality inference of the dataset obtained from 207 cell shapes using DeCOr-MDS. We estimate the dimension of the main subspace n* = 2. The red line shows the median of heights and the black curve shows the heights median ratios between h n-1 and h n.
(C) Examples of cell shapes, including regular cells (in black), and orthogonal outliers detected. Among these outliers, we highlight cell shapes that are likely to be invalid due to segmentation errors (in blue), with the other outliers shown in red. array which typically contains the abundance of different elements of the microbiome (typically 10 2 -10 3 ), denoted phylotypes, measured in different human subjects. To analyze such high dimensional datasets, dimensionality reduction methods including MDS (often denoted Principal Coordinates Analysis PCoA), are typically applied and used to visualize the data  (Brooks et al. , 2018; Trevelline and Kohl, 2022; Zhou et al. , 2022). To assess our method incrementally, we restricted first the analysis to a representative specific site (nose), yielding a 136 × 425 array that was further normalized to generate Euclidean pairwise distance matrices (see Material and Methods Section 2.
6 for more details). Upon running DeCOr-MDS, we estimated the main dimension to be 3, with 9 (6. 62%) orthogonal outliers detected, as shown in Figure  6A. This is also supported by another study that the estimated dimension of HMP dataset is 2 or 3  (Tomassi et al. , 2021). We also computed the average distance between these orthogonal outliers and the barycenter of regular points in the reduced subspace, and obtained a decrease from 1. 21 when using MDS to 0. 91 when using DeCOr-MDS. This decrease suggests that orthogonal outliers get corrected and projected closer to the regular points, to improve the visualization of the data in the reduced subspace, like in our experiments with the synthetic datasets (Figure  2  and Supplementary Figure  S2 ). In Figure  6B , we next aggregated data points from another site (throat) to study how the method performs in this case, yielding a 270 × 425 array that was further normalized to generate Euclidean pairwise distance matrices.
As augmenting the dataset brings a separate cluster of data points, the dimension of the main dataset was then estimated to be 2, with 13 (5%) orthogonal outliers detected, as shown in Figure  6B. The average distance between the projected outliers and the barycenter of projected regular points are approximately the same when using MDS (1. 46) as when using DeCOr-MDS (1. 45) for nose, and are also approximately the same when using MDS (1. 75) to when using DeCOr-MDS (1. 74) for throat. This decrease also suggests that orthogonal outliers get corrected and projected closer to the regular points.
Application to scRNA-seq data We further evaluated DeCOr-MDS on single cell RNA-seq (scRNA-seq) data. In general, analyzing scRNA seq data requires dimensionality reduction for visualization (including MDS-based methods  Canzar et al. (2021) ;  Senabouth et al. (2019) ), and specific quality control procedures to mitigate various technical artifacts  McCarthy et al. (2017) ;  Luecken and Theis (2019). We applied our method as a potentially relevant tool for this purpose. We applied DeCOr-MDS first on a dataset containing the expression level of 1063 cells for 2,601 genes (detailed in Methods Section 2. 6). We found the dimension of the main subspace to be 3, with 77 (7%) outliers detected. In Figures  7A, B , we compared the embeddings in 3D using MDS and DeCOr-MDS. Similarly to the previous experiments, the mean distance between the orthogonal outliers and barycenter of regular points in the reduced subspace decreases when using DeCOr-MDS (from 4.
Discussion We proposed DeCOr-MDS, a novel approach using geometric characteristics to detect dimension, and to correct orthogonal outliers in high dimensional space. That is, to the best of our knowledge, the first statistical tool that addresses the challenge of the presence of orthogonal outliers in high dimensional space. We validated the method using synthetic datasets and demonstrated its potential applications to analyze biological datasets, including cell shape data, count arrays from microbiome data and scRNA-seq data. The visualization and numerical comparison confirmed that DeCOr-MDS effectively detects dimensionalities in many instances, corrects orthogonal outliers, and demonstrates superior performance to classical dimension reduction methods. The notion of simplices is used frequently with the aim of robustness, either to detect the coreness of data [data depth and multivariate median,  Liu (1990) ;  Aamari et al.
A common approach to do so is the screeplot (or elbow) test in principal components analysis, where a notable drop in the proportion of variance (or distance) explained can be taken as a cutoff, and as the most relevant dimension. High-dimensional biological datasets challenge this strategy, because fine-scale structure confounds in practice downstream analyses. Because of this, authors often use an arbitrary large set of 10, or sometimes 20 or 50 components  (Astle and Balding, 2009; Barfield et al. , 2014; Demmitt et al. , 2017; Sakaue et al. , 2020; Arciero et al. , 2021; Deng et al. , 2021). Power analyses based on simulations also provide a way to assess an adequate number of components  (Barfield et al. , 2014). In this work, we proposed an alternative approach, by exploiting the structure of the dataset to determine essential versus non-essential dimensions.
Limitations of DeCOr-MDS include the non-automated choice of the cutoff parameter c. This parameter sets the maximum tolerated number of standard deviations σ before a point is considered an outlier. A value for c = 3, which corresponds approximately to the 0. 1% most extreme points in a Gaussian distribution, may be selected, for instance. Dimension detection is also imperfect for heterogeneous datasets where the distribution of regular points (e. g. with distant clusters may prevent the height criterion for outlier detection to be effective. In this case a possible solution would be to first perform a clustering analysis (for instance k-means) to assess if the distance between clusters is comparable with the distance between the outlier and the main subspace, and if that's the case separately perform our method on each cluster.
There are various potential directions to improve the dimension detection in real datasets of high dimension. This may be achieved by studying the behaviour of the Cayley-Menger determinant, which is central in the procedure, in higher dimensions. One may also associate the height criterion with a distribution criterion  (Legrand, 2017) , which would be sensitive to clusters or other notable structure, as was apparent in the HMP dataset. Another beneficial improvement would be to reduce computing time, for instance by implementing a parallelized version or using a call to a compiled program. Finally, one could optimize the cutoff parameter c automatically, either through a hyperparameter search, or by using a data-driven procedure, during the exploration phase of the algorithm.
gloeosporioides complex from either a symptomatic leaf ('diseased', encoded 0 or 1 when a strain is present), a leaf without symptoms ('healthy', encoded 0 or 1 when a strain is present), or present in either plant leaf ('global', encoded 0 or 1 when present). Samples were the following: 222 leaves with symptoms and 350 asymptomatic leaves (some sampled plants had only leaves presenting symptoms, while most had only asymptomatic leaves). We first produced logistic regression models in R, investigating either prevalence (diseased, healthy, global) as dependent Statistical analyses. Data were organised following their natural order: environment (riparian, deep, edge, hill), stratum (floor, understory, canopy), altitude (in m), and recorded presence of a strain belonging to C. gloeosporioides complex from either a symptomatic leaf ('diseased', encoded 0 or 1 when a strain is present), a leaf without symptoms ('healthy', encoded 0 or 1 when a strain is present), or present in either plant leaf ('global', encoded 0 or 1 when present).
However, a persistent response creates more clients for SNRPB and therefore necessitates higher levels of this spliceosomal component. This is supported by the observation that SNRPB knockdown cells fail to induce the levels of Sec16A under condition of cargo overload. Thus, our data identify a role for core splicing in the regulation of ER-proteostasis. Mutations in SNRPB were shown to be linked to a rare genetic disease called Cerebrocosto-mandibular syndrome (CCMS). Skeletal abnormalities are a hallmark of CCMS, but there was no obvious link between mutations in a spliceosomal component and bone abnormalities. Our results provide mechanistic insights into the pathophysiology of the disease. Based on our observations, we propose that the mechanism of bone deformations is due to a perturbation of ER homeostasis and the trafficking of collagen-I.
RNA-Seq analysis Libraries were sequenced on an Illumina HiSeq3000 flow cell, using 2-lanes. This yielded ~ 35-40 million paired-end 150 nt reads for biological triplicates and technical duplicates of siCTRL and siSNRPB samples. These were analyzed for gene expression and alternative splicing using independent pipelines. For differential gene expression reads were aligned to the human genome using salmon (version 1. 5. 1)  (Patro et al, 2017). Salmon quantifications of gene expression were imported into RStudio using tximport and analyzed for differential gene expression using Deseq2 (version 1. 12. 3)  (Love et al, 2014). Genes associated with the GO terms 'COPII-coated vesicle budding' and 'regulation of regulated secretory pathway' were downloaded from Panther GO and merged with the Deseq2 output using standard Python code.
95 and a deltaPSI > 0. 15. To investigate exon features, exon and intron-length were calculated using standard Python code. Splice site coordinates were extracted from the rMATS output table in bed format (-20 to +3 for 3'-ss; -3 to +6 for 5'ss) and splice site sequences were extracted using bedtools. Sequences were input to MaxEntScan  (Yeo & Burge, 2004) , using the Maximum Entropy Model to score.
Cartilage and skeletal preparation of embryos To investigate cartilage formation, embryos were stained with Alcian Blue. For skeletal staining, the skin was removed from freshly dissected E17. 5 embryos and neonatal pups and stained as described by  (Wallin et al, 1994). Cartilage and skeletal preparations were imaged and analyzed using Lecia stereomicroscope (Lecia MZ6). Measurements were taken using Fiji ImageJ and statistical analysis was carried out on Graphpad, Prism (https://www. graphpad. com/scientific-software/prism/).