dataesr/scientific-paragraphs-categorization huggingface dataset:
There exist also some recent variants of SVD, for example, in  [39] , where the authors have used a Non-Negative Matrix Factorization (NNMF) to reduce the dimensionality of hyperspectral images for Saliency Detection. The same strategy was presented in  [40]  by using the Autoencoder Neural Network (ANN). Typically, in these approaches, different kinds of distances  [41]  are evaluated in order to calculate the reconstruction error (RE) between the reduced image and the original one. In the second stage, copulas theory  [42, 43]  is used to produce the LC map. There are several copula functions  [44]  that can model the dataset under study well and in the task of classification, each class can be modeled with a different copula. In this work, the results were found by testing different copulas, and the best ones, as we shall see, were obtained using the Bernstein copula, introduced in 2004 by Sancetta and Satchell  [30].
This copula was built on the basis of Bernstein's polynomials and had the advantage of arbitrarily approximating any copula. In order to demonstrate the best performance achieved by this methodology, we have performed the experiments on a real-world SITS dataset, called Reunion Island, used in  [18] , and we have compared the results with the same state-of-the-art competitors engaged in the same paper. The rest of this research work is structured as follows: Section 2 introduces the mathematical theoretical background of matrix factorization and copula employed in the LC classification of Reunion Island SITS, Section 3 describes the methodologies for building the copula-based classifier, Section 4 presents the description of the dataset, Section 5 goes into detail of the implemented algorithm, Section 6 gives the details of the experimental design, Section 7 provides an in-depth discussion of the results.
This drew us to consider the empirical way, and, in this sense, we have evaluated h by the Improved Sheather Jones (ISJ), which is a data-driven bandwidth selector. The mean integrated square error (MISE) is given by MISE(h) = E f (x; h) -f (x) 2 dx. The ISJ algorithm consists of looking for parameter h in such a way that minimizes the asymptotic mean integrated square error (AMISE) that represents the first-order asymptotic approximation of MISE. This quantity is given by a relation that involves the unknown quantity f (x) 2. This is obtained by the calculation of a sequence of estimates using a recursive formula  [58]. The benefit of a semi-parametric approach is that it is flexible. This allows us to adapt the algorithm to any type of dependency structure specific to a given dataset.
Data The dataset for the experiments, with the same preprocessing analysis carried out, is the same as considered in  [18]  and consists of a time series of 34 Sentinel-2 (S2) images acquired between April 2016 and May 2017 on Reunion's Island, a French department situated in the Indian Ocean, see Figure  1. All the S2 images used are available via (http://theia. cnes. fr) and are preprocessed in regards to surface reflectance via the MACCS-ATCOR Joint Algorithm  [59]  developed by the National Centre for Space Studies (CNES). In paper  [18] , the authors take into account only the 10 m bands, Blue (B2), Green (B3), Red (B4) and Near-Infrared (B8), and the NDVI radiometric index was calculated for each date  [6, 60]. The spatial dimension of the Reunion Island dataset provided in  [18]  consists of 6656 × 5913 pixels, and for each of these, four spectral bands and one index is deemed for each acquisition over time.
The dataset is constructed from a variety of sources, and the ground truth is available as a vector GIS file containing a group of polygons, each assigned with a single LC class. In order to ensure accurate spatial correspondence with the image data, all geometries were corrected by hand using the corresponding Sentinel-2 images as a reference. In addition, the GIS vector file, which holds the spatial information of the polygon, has been rasterized, bringing it to Sentinel-2 spatial resolution (10 m). The final truth dataset consists of 322,748 pixels and 2656 objects distributed over 13 classes of the dataset, Table  1. For data and details of the Reunion Island study site, please refer to  [61].
5. Separating the pixels of the training dataset by class and fitting the copula-based classifier to each class by using the Bernstein copula according to the procedure described in Sections 3. 2 and 3. 3. To find the parameter for the empirical Bernstein copula we refer to the procedure described in  [30]. 6. Once we have chosen the Bernstein copula that best fits each class of the training set, we use the testing set to evaluate the accuracy of the classification. In particular, for each observation of the testing set, we evaluate the discriminant functions and the predicted class by using Equations (  2 ) and (  4 ), in which c represents the previously fitted copula on the training set.
Experimental Settings In order to evaluate the behavior of the algorithm with the use of copulas, we took into account five state techniques deemed for the classification of SITS as competing methods. As a competitor machine learning tool, we considered the classical Random Forest (RF) algorithm  [6, 60]. This algorithm still represents a benchmark in the literature since it is widely used for multi-class land cover classification and with high-dimensional data, as in the case of the dataset of this work. It works with subsets of data and is parallelizable, plus the prediction speed is significantly faster than the training speed because we can save the generated forests for future use. Moreover, RF has methods for balancing the error in unbalanced class population datasets. In addition, to assess the proposed approach as a viable alternative for classification, algorithms using NN have been considered.
Moreover, it is worth noting that, for DuPLO and ConvLSTM, a patch-based strategy was used, while for other methods, the time-series information associated with each pixel was considered. In this work, for the experiments with CopCLF, the learning and test phase was conducted following the same strategy in the  [18]. More precisely, the dataset has been divided into 30% of the objects for the training phase, 20% of the objects for the validation set and the last 50% are employed for the test phase, with the imposition that all the pixels of the same object belong exclusively to one of the splits (training, validation or test) to shrink the spatial bias in the evaluation procedure. Commonly, the training set is used to learn the classifier, and the validation set is employed to improve the accuracy of the considered algorithm that will then be used with the test set.
For our CopCLF framework https://github. com/CrisDS81/CopCLF, accessed on 16 May 2022, we ran the experiments by using the Python package Scikit-learn, for the SVD process (https:// scikit-learn. org/stable/, accessed on 16 May 2022) we ran KDEpy (https://pypi. org/project/ KDEpy/, accessed on 16 May 2022), for the empirical estimation of the marginal densities we ran Copulae (https://copulae. readthedocs. io/en/latest/, accessed on 16 May 2022) and Openturns (https://openturns. github. io/openturns/latest/user_manual/_generated/ openturns. EmpiricalBernsteinCopula. html?highlight=bernstein/, accessed on 16 May 2022) for the estimation of the Bernstein copula. The accuracy of the different classifiers used may undergo changes depending on which strategy was used to divide the dataset. To mitigate this issue, for each dataset, and for each evaluation measure, we present the results for the average over ten different random splits performed with the strategy presented above.
As can be seen in Figure  4e  of the heat-map of CopCLF, each pair of classes achieves very good results compared to the other figures. Only DuPLO in Figure  4d  has a heat map similar to that produced with the method analyzed in this work, and this can also be seen from the quantitative analysis analyzed above. Furthermore, to complete the confusion matrix analysis, we see how the heatmaps of Random Forest, LSTM and ConvLSTM in Figure  4a-c  produce a less sharp diagonal, in which the colors for each pair of classes deviate from yellow, representing the absolute maximum value of precision. This leads us to conclude that the use of the copula in this task can be considered a really good alternative for SITS classification. To better complete the qualitative study, we decided to show some map classification in Figure  5 , choosing three representative examples from the entire dataset of tje Reunion Island dataset.
In this hypothesis, comparative approaches should rank equally. We run this test on the F-measure of the compared configurations on each k-fold of the dataset and reject the null hypothesis with a p-value ≤ 0. 05. Since the null hypothesis is rejected, we use a post-hoc test called the Nemenyi test, which is used for pairwise comparisons  [63]. In this test, we need to get the difference between the average rankings of all rankers. If this difference is greater than or equal to one critical distance (CD), we can say that these two classifiers are significantly different from each other. CD is calculated as: CD = q α k(k + 1) 6N. The q α term is obtained from (α = 0. 05), where k = 6 represents the numbers of classifiers and the relative q α is 2. 85. The results of this test, reported in Figure  6 , confirm that CopCLF is ranked higher than all of its baseline configurations.
In particular, the critical difference diagram, obtained using a 0. 05 significance level, shows that CopCLF is, on average, the best performing approach, with RF(DuPLO) as runner-up. Table  4  reports the total time spent completing the three steps of CopCLF (i. e. , dimensionality reduction, learning and predictive stage). The table shows the average times obtained by launching the algorithm 10 times, randomly choosing the training, validation and test set of the Reunion Island dataset with the same percentage of splitting described in Section 6. 1.
Conclusions In this research work, we have provided a novel approach for supervised classification based on copula functions. In particular, we applied this strategy to a Sentinel-2 Satellite Image Time Series. The approach, CopCLF, combines a strategy that allows the reduction of the dimensionality of the data through the matrix factorization via SVD and a classifier based on copula functions. In particular, the Bernstein copula was used. The experiments were carried out, taking into account the dataset and the classification methods presented in  [18]. In particular, the dataset is a real-world study site located in the Indian Ocean, and the classifiers against which we made a comparison are the machine learning benchmark algorithm Random Forest, and others based on NN, specifically a combination of RNN and CNN, called DuPLO.
Moreover, we plan to extend the method by considering a different strategy to reduce the dimensionality of SITS and extend the study by using other families of copula as Vine copulas  [44, 65] , which have proven to work very well in the presence of large datasets. Finally, the use of a multi-source scenario in which optical (Sentinel-2) SITS can be combined with Synthetic Aperture Radar (Sentinel-1) SITS data may represent a future development.
Everest's (Nepalese) Base Camp has not been assessed. Here, we utilize previously unpublished photos taken twice-daily by an automatic camera at the Base Camp AWS (Figure  1 ), alongside meteorological data, to examine the impacts of weather on the visibility of this iconic peak that draws visitors from all over the world. Using the seasonal timing identified by  Matthews et al. (2020a) , we investigate the conditions of both the 2019 and 2020 post-monsoon seasons (1 October to 30 November) using hourly measurements from five AWSs, at varying altitudes, along the Mt. Everest summit route (Figure  2a ): Phortse (3810m), Everest Base Camp (5315m), Camp II (6464m), South Col (7945m) and Balcony (8430m). Here, we examine data encompassing two postmonsoonal seasons, spanning 1 August 2019 to 31 January 2021, the time periods when the upper slopes of Mt.
Everest are least obscured by clouds. In addition to the numerical data recorded by the AWSs, a Campbell Scientific Canada CCFC Field Camera looking eastward toward the summit of Mt. Everest was also installed at Everest Base Camp during the 2019 Everest Expedition (Figure  1 ). As shown in Figure  2 (a), the camera's viewshed from left to right (north to south, respectively) primarily shows Mt. Everest's West Ridge (~7000-7200m), Mt. Everest's summit (8849m) and Nuptse's sub-peak (~7400m). The camera takes two photographs daily at 0937 Nepal time (NPT) (0352 utc) and at 1437 NPT (0852 utc), respectively. According to meteorological data, the summer monsoon brings significant changes to the Nepal Himalaya  (Khadka et al. , 2021) , and herein, we show that the monsoon's departure brings equally significant changes once more.
Acknowledgements This research was conducted in partnership with  National Geographic Society ,  Rolex  and  Tribhuvan University , with approval from all relevant agencies of the  Government of Nepal. We gratefully acknowledge the communities of the Khumbu Region and the  Sherpa climbing team  for their efforts in aiding the setup and maintenance of the AWSs, as this work would not be possible without them. We also thank the reviewers for their time and their helpful feedback which improved this manuscript.
Model Data 11 models contributed to the second part of SIREx with a total of 22 simulations and 36 simulated winters. The participating models cover a broad variety in terms of rheology, spatial grid resolution, temporal and spatial resolution of atmospheric boundary condition, ITD classes, and grid type (structured vs. unstructured, Lagrangian vs. Eulerian). Some important details of the model simulations are summarized in Table  1 ; for further information we refer to the specific references provided in Table  1. Note that the MERCATOR model participating in SIREx Part I does not participate in our analysis. In addition to the simulations presented in SIREx Part I, we analyze a MITgcm (2 km, ITD) simulation for the  year 1997 year and FESOM2 simulations (1997 year and 2008)). For all simulations sea ice drift, concentration, and thickness were provided for at least one SIREx winter (14 of the simulations cover both years and 8 simulations cover either 1997 or 2008).
Detection and Tracking of LKFs in the Model Data The LKF detection and tracking algorithms require the data to be on a regular grid  (Hutter et al. , 2019a). The output fields from the unstructured grid models were interpolated onto regular grids with spatial resolution similar to their original resolution (FESOM ice velocities to the grid of MITgcm 4. 5 km, FESOM2 ice velocities and deformation rates to the grid of MITgcm 2 km, and neXtSIM ice velocities to a grid with 10 km grid spacing in Polar Stereographic projection). All other model output was processed on the native model grids. We adapt the filtering technique of the LKF detection algorithm to account for the fact that the model and RGPS data do not have the same sampling frequencies (3 days for the RGPS and 1 day for the models).
Only the neXtSIM simulation contains LKFs with deformation rates lower than this threshold such that we use a threshold of d LKF = 0. 002 days -1 for this simulation. (c) The three daily deformation fields are combined into one binary map where a specific pixel is flagged as LKF if any of the three daily fields are flagged as LKF at this pixel position. (d) A morphological thinning algorithm is applied to the combined binary map to reduce all LKFs to a width of one pixel. By applying the morphological thinning algorithm explicitly after combining the daily LKF maps, we ensure that LKFs that move within 3 days are not detected more than once. A detailed discussion of the comparability of the RGPS LKF data set and the derived model LKF data sets with respect to spatial and temporal resolution is included in Appendix A.
Principles of the Model-Observation Comparison The RGPS data set covers most of the Arctic Ocean, but the coverage varies in time depending on the available synthetic aperture radar (SAR) imagery. Gaps in the deformation data can split long LKFs into multiple smaller LKFs or inhibit tracking of LKFs. This affects derived LKF statistics leading to, for instance, fewer LKFs with long lifetimes  (Hutter & Losch, 2020). In contrast, the model output fields provide deformation data for the whole study region without any gaps in time. Thus, we mask the LKFs detected in each simulation with the RGPS coverage in order to exclude any effects of varying RGPS coverage on the comparison between the model and observations. The tracking of LKFs is repeated only for the masked LKFs. We use the masked LKFs for all statistics presented in this paper because these results are directly or indirectly affected by the number, length, or lifetime of the LKFs.
The original unmasked LKFs are only used in the concentration and thickness anomaly analysis, as we do not compare to RGPS data in this analysis, and in the intersection angle analysis, because in the coarse resolution simulations there are otherwise too few LKFs available for this analysis. We tested with all high-resolution simulations that masking the LKFs with the RGPS coverage does not affect the distribution of simulated LKF intersection angles (not shown). A direct comparison of LKFs detected in RGPS and model output is not possible due to the chaotic nature of ice fractures  (Coon et al. , 2007; Kwok et al. , 2008). Instead, statistics of the spatial and temporal properties of the simulated features can be compared to the statistics derived from observations  (Hutter & Losch, 2020).
For clarity and consistency, we also use the same statistic to define the misfit in intersection angles, although the data is not heavy tailed. By using the log-scale in the skill metric, all parts of the intersection angle PDFs are weighted without overemphasizing the peak of the distribution. As not all simulations contributing to SIREx are run over the same time period, we use the RGPS years consistent with each simulation in the computation of the metric functional. In this manner, we take interannual variability of the LKF statistics between both SIREx winters into account. By definition, the skill metric increases with larger misfit between models and observations. Thus, a lower skill metric value indicates better model performance. For reference of the magnitude of the skill metric, we use the interannual variability of different LKF properties within the RGPS data set.
Data Availability Statement All published code and data products originating from the Sea Ice Rheology Experiment is organized in the SIREx data collection: https://zenodo. org/communities/sirex: this includes the model output in netCDF format (Bouchat et al. , 2022a), the model Lagrangian trajectories and deformation data  (Bouchat et al. , 2022b) , and the RGPS Lagrangian composite deformation data (Bouchat & Hutter, 2022)  as well as the LKF data  (Hutter et al. , 2022). The code of the LKF detection and tracking algorithm is available on github: https://github. com/ nhutter/lkf_tools. git (Hutter, 2019). The RGPS LKF data set is available on PANGAEA: https://doi. org/10. 1594/ PANGAEA. 898114 (Hutter et al. , 2019b). The daily fields from the 0. 08 HYCOM-CICE experiment are available at the HYCOM data server ftp://ftp.
Recent interdisciplinary cruises have taken place, providing more integrated knowledge on the importance of zooplankton to carbon sequestration  (Guidi et al. , 2016; Kiko et al. , 2020; Steinberg and Landry, 2017; Stukel et al. , 2019). No global study has yet been able to analyse community-level variations in zooplankton abundances, biomass and community composition in conjunction with assessments of vertical particle flux in the upper kilometre of the global ocean. Here, a homogeneous dataset of community-level zooplankton images generated from the TARA Oceans expeditions is explored together with associated measurements of their contextual environmental conditions to: (i) test whether zooplankton communities present consistent vertical variations in abundance and composition across the oceans and in different latitudinal bands, and (ii) investigate the main drivers of such vertical gradients and how they are coupled to the surface phytoplankton and estimates of particle flux.
The TARA Oceans expedition collected over 35000 samples encompassing the whole plankton community (i. e. , from viruses to jellyfish) across the global ocean from 2009 to 2013  (Karsenti et al. , 2011). Previous studies that analysed the TARA Oceans imaging dataset explored the global latitudinal gradients in richness and composition for the whole plankton community focusing on surface waters  (Ibarbalz et al. , 2019; Brandao et al. , in press). Here, we aim to describe the community composition of mesozooplankton down to 1000m depth on a global scale. As the imaging techniques used here cannot achieve a species-level identification of the zooplankton community composition, our approach is rather oriented towards larger taxonomic and /or functional groups that may be associated with broad ecological and biogeochemical functions.
(2006)  to estimate the contribution (%) of three pigment size classes (microphytoplankton, nanophytoplankton, and picophytoplankton;  _#$%&' ,  _()(' , and _ *$%' , respectively) to total phytoplankton biomass in the epipelagic layer. The median value of all hydrological and optical data together with imaging data were calculated for each of the five horizontal layers sampled by the Multinet for future data processing. The samples were classified as anoxic, hypoxic and normoxic according to the oxygen minimum value measured within the towed layer. We used a threshold of 5 µ  34 to classify the stations as anoxic  (Roullier et al. , 2014)  and 58. 5 µ  34  (Bode et al. , 2018)  to classify them as hypoxic.
The measurements of all these environmental variables are available on PANGAEA (https://doi. org/10. 1594/PANGAEA. 840721). To estimate the strength of the Diel Vertical Migration (DVM) at 10 stations, pairwise Wilcoxon tests were performed to compare in each layers the abundance and biomass of each taxa between day and night. For those 10 same pairs of stations, we used an analysis of similarities (ANOSIM) to test for significant variations in community composition between day and night samples. The ANOSIM tested whether the inter-groups difference (day and night groups) was higher than the intra-groups difference, by providing an R coefficient. An R coefficient close to one suggests dissimilarity between groups, while R value close to zero suggests an even distribution of high and low ranks within and between groups.
Significant axes were identified using the Kaiser-Guttman criterion  (Legendre and Legendre, 1998). Data manipulation and statistical analyses were performed with Matlab 2018b (MATLAB 9. 5) for the vertical profiles of abundance and biomass and statistical test (Wilcoxon test, Kruskal-wallis test), R environment v3. 5. 1 (using the following packages: vegan version 2. 5-5, ggplot2 version 3. 1. 1, ggrepel version 0. 8. 0 and ggfortify version 0. 4. 7) for the redundancy analysis and PRIMER6 (Version 6. 1. 12) and PERMANOVA+ (Version 1. 0. 2) for the ANOSIM test.