dataesr/scientific-paragraphs-categorization huggingface dataset:
Comparison to PLS-DA, Random Forests and SVM using 2 datasets To compare PD-CR to the standard PLS-DA, Random Forests and SVM classification methods in terms of accuracy and feature selection, we tested the four methods on two metabolomic datasets named "BRAIN" and "LUNG". Accuracies and feature selection for each method were obtained using 4 fold-cross validation with varying random seeds. We also provide the results with a a new version of PD-CR minimizing the ℓ2 norm PD-CR ℓ2 (See Algorithm 6 https : //arxiv. org/pdf/1902. 01600. pdf).
LUNG dataset The LUNG dataset was provided by Mathe et al. This dataset includes metabolomics data concerning urine samples from 469 Non-Small Cell Lung Cancer (NSCLC) patients prior to treatment and 536 controls collected from 1998 to 2007 in seven hospitals and in the Department of Motor Vehicles (DMV) from the greater Baltimore, Maryland area. Urine samples were analyzed using an unbiased metabolomics LC-MS/MS approach. This dataset is available from the MetaboLights database (study identifier MTBLS28) Mathe et al. used Random Forests to classify patients as lung cancer patients or controls  [10]. The aim was to create a new screening test for lung cancer, based on metabolomics data from urine. Lung cancer is one of the most common cancers and it is well established that early diagnosis is essential for treatment.
BRAIN dataset The BRAIN dataset was obtained from a metabolomic study performed by our biological team (TIRO) on frozen samples of glial tumors. The samples were provided by the university hospitals of Nice and Montpellier (France). Metabolite extracts were prepared and analyzed in the TIRO laboratory (Nice, France). With this dataset, the goal was to create a model that accurately discriminated between mutated isocitrate dehydrogenase  (6) ρ(x) = d 1 -d 2 d 1 + d 2 (7) Label =    -1 if ρ(x) < -ǫ 0 if -ǫ < ρ(x) < ǫ 1 if ρ(x) > ǫ (IDH) and IDH wild-type glial tumors. This mutation is a key component of the World Health Organization classification of glial tumors  [29]. The mutational status is usually assessed by IDH1 (R132H)-specific (H09) immunohistochemistry. Yet this technique can lead to False-Negative results  [30] , which can only be identified by sequencing.
Data Filtering and Pre-processing Our laboratory performed the LC-MS/MS analysis for the BRAIN dataset. Therefore, we could apply different levels of filtering on this dataset. After processing of the raw data using MZmine 2. 39 software, two types of filtering were applied to the BRAIN dataset, minimal and maximal filtering. The minimal filtering only removed metabolites for which a spike was detected in less than 10 percent of the samples. The maximal filtering removed all unidentified metabolites as well as metabolites that did not have an isotopic pattern. This filtering method is frequently used for metabolomic studies and diminishes the number of noisy features in the dataset. Furthermore, it diminishes the time necessary for data processing because it diminishes the data volume. Unfortunately, any filtering will necessarily come with a high risk of removing some relevant features which is also the case with this filtering method.
Comparison to other methods Before comparison, the data were pre-processed as follows: (i) Log-transformation for the following benefits: Reducing heteroscedasticity and thus the bias on regression and transforming multiplicative noise into additive noise, (ii) Mean centering and scaling  [31]. PD-CR  [13]  was compared to PLS-DA  [32] , Random Forests (with 100 and 400 trees)  [9]  and SVM using the sklearn python package. Additionally, we evaluated the impact of the use of the Huber loss in PD-CR compared to the use of the ℓ2 loss. Parameters σ , τ , δ and ρ were set according to results obtained using various datasets in an initial step  [13]  and were not further tuned. Parameter η , which affects the feature selection step was manually tuned to fit the number of features in the datasets and to maximize accuracy after cross validation.
We computed the accuracy of the 4 classification methods for the two metabolomics datasets using 4-fold cross-validation (Script "PD-CR vs PLS-DA, RF and SVM" on https:// github. com/ tirol ab/ PD-CR). The selected metabolites were analyzed and compared between methods for the metabolomics datasets. For PD-CR, we plotted the histograms of the CSP ρ(x) and the probability distribution function (PDF) as well as the False Discovery Rate (FDR =(FP+FN)/total) and the rate of rejected samples (RRS = rejected samples/total samples) depending on epsilon (the CSP threshold) (Script "rhoComputing" on https:// github. com/ tirol ab/ PD-CR).
Results The characteristics of the two metabolomics datasets are presented in Table  1. The LUNG dataset included a large number of patients (a little over 1,000) with an equivalent number of features (a little under 3,000) and the BRAIN dataset included a smaller number of patients (88) with a much higher number of features. While obtaining metabolomics data concerning as many patients as there are in the LUNG dataset is remarkable, the number of patients in the BRAIN dataset is closer to the number of patients in most metabolomics studies.
Minimally filtered dataset As shown in Table  4 , PD-CR outperformed PD-CR ℓ 2 , PLS-DA, Random Forests (400 trees) and SVM by 1. 1% , 7. 7% , 2. 7% and 4. 3% , respectively for the BRAIN dataset. For this high dimensional dataset, the number of features (25,286) significantly exceeded the number of samples (88) giving a significant drop in the PLS-DA accuracy. Furthermore, as shown in Fig. 3  the accuracy obtained with PD-CR could be further improved by using the CSP to perform classification with rejection. Indeed, most of the samples were classified with a high CSP and if we apply a CSP threshold ǫ of 0. 45, the FDR drops to 0 while only rejecting 10% of the samples. This shows that all the missclassified samples had a low CSP. As shown in Table  5 , most of the top features selected with the 3 methods correspond to different isotopes and adducts of 2-hydroxyglutarate.
Indeed, POS_ MZ131. 0342, POS_MZ132. 0375 and POS_MZ133. 0384 all correspond to the  2-Hydroxyglutarate is a well-known oncometabolite produced in high quantities by mutated IDH1/2 in gliomas  [33]. It is therefore expected that this compound will have a high weight when classifying mutated vs wild-type gliomas as it should be significantly increased in IDH mutated gliomas (as shown in Fig. 4 ). Here all four methods selected this important feature among a high dimensional dataset  (25, 287  features in this case). Adducts and isotopes of 2-hydroxyglutarate with low levels are top selected features using PD-CR indicating that our method is a very sensitive way to identify significant molecules. This result on the minimally filtered dataset also suggest that PC-CR avoids overfiting as no unexpected feature was selected.
Comparison to the highly filtered dataset As shown in Table  6  the accuracies of the different methods were equivalent and very high when using the highly filtered version of the BRAIN dataset (accuracy being a little lower with SVM). When PD-CR was used on the highly filtered BRAIN dataset, it lead to similar results as with PD-CR using an ℓ2 loss, PLS-DA, Random Forests and SVM. In contrast, it out- performed these methods when using the minimally filtered dataset. In this case, as shown in Table  7  more features were selected. When using the BRAIN dataset for the   IDH-mutated vs wild-type classes, most of these additional features were adducts of 2-hydroxyglutarate and are therefore known to be biologically relevant. The additional features that are not adducts of 2-hydroxyglutarate will be investigated in a future study.
Discussion Machine learning methods are of particular interest for metabolomics studies and are being used increasingly for other omics studies. Herein we introduce a new primal-dual method for supervised classification and feature selection. To our knowledge, a primaldual method had never been used in this way. We compare this method to three of the most frequently used methods: PLS-DA, Random Forests and SVM, on two metabolomics datasets. Metabolomics datasets tend to be sparse datasets including highly correlated features. PD-CR is particularly suited for this data structure. Hence, for metabolomics, PD-CR appears to be more accurate than the three other methods while selecting biologically relevant features and providing a confidence score for each prediction. An important upside associated with the inclusion of a confidence score for each prediction is that it enables classification with rejection.
We have shown that PD-CR outperformed the common PLS-DA, Random Forests and SVM methods on both LUNG and BRAIN datasets. We believe that this is partly due to the fact that PD-CR uses a Huber loss. Indeed, the use of the Huber loss with PD-CR leads to a better accuracy than the use of a common ℓ1 or ℓ2 loss  [13]. Note that the l1 loss is not derivable in zero. Moreover the drawback of the term �Y µ -XW � 1 of the l1  (8) ρ(x) = 1 -k Min(d 1 , d 2. , d k ) d 1 + d 2 +. d k loss is that it enforces equality of the two matrices out of a sparse set. Moreover the use of the Huber loss reduces the impact of the presence of outliers in the training set, and therefore leads to a better accuracy than the ℓ2 loss, as shown in Tables  2  and 4. Furthermore we show in Tables  2  and 4  that using PD-CR with an ℓ2 loss provides bet- ter results than PLSDA which uses the same ℓ2 loss.
This is probably due to the fact that PLS-DA does not perform feature selection and is known to be prone to overfitting  [5]. Moreover, when comparing methods with the minimally filtered and the more filtered versions of the BRAIN dataset, all methods suffered a decrease in accuracy with the minimally filtered dataset (PD-CR keeping the higher accuracy). However the results obtained using the PLS-DA method appeared to be more impacted than those of the Random Forests, SVM and PD-CR. Indeed, the accuracy of PLS-DA significantly decreased when the less filtered dataset was used dropping from 93. 18% to 84. 09%, compared to a mild decrease in accuracy for the other methods. This can also be explained by the fact that PLS-DA does not perform feature selection and is known to be prone to overfitting  [5].
For this reason, several strategies are commonly used to reduce the number of features in metabolomics datasets. Features can be filtered according to the number of detected peaks in all samples, the correct identification of the compound (using the most common adduct) or the presence of isotopes. Working with filtered data has some advantages, including the fact that it appears more biologically relevant to work on less noisy and more reliable data. However, filtering also has some important drawbacks, the most important being the high risk of removing interesting metabolites from the dataset. In the case of the BRAIN dataset, 2-Hydroxyglutarate is a well known metabolite associated to IDH mutation. However, in many metabolomic studies, the goal is to discover potentially unidentified metabolites associated to particular conditions which can only be achieved by including unidentified metabolites.
As shown in this work, PD-CR can be applied to both minimally filtered and highly filtered metabolomics datasets. As it has been previously reported, when designing prediction models, some methods may lead to a more accurate model for a specific dataset while others may be more adapted with other datasets  [35]. Indeed, even though we can discuss which machine learning method is the best, most often, researchers try out several machine learning methods on their metabolomics datasets and report the results of the most accurate one. This process has even been automated by some authors  [36]. PD-CR is an advanced method, based on recent development in convex optimization and we believe it should be considered by researchers when designing prediction models for metabolomics studies. Much like the commonly used methods PLS-DA, Random Forests and SVMs, available with  [37] , our python implementation of PD-CR only requires the tuning of one parameter: η.
This makes the use of PD-CR quite simple, even for non machine learning experts, much like PLS-DA. Note that the tuning of the η parameter must be done care- fully since it modifies feature selection. When comparing misclassified patients between methods in an additional analysis, it appeared that in the minimally filtered BRAIN dataset 16/88 tumors were misclassified with at least one method. 2 tumors were misclassified with all methods, 6 with two or three methods and 8 with only one method (3 were misclassfified only with PLS-DA, 4 with Random Forests, 1 with SVM and none with PD-CR). In the LUNG dataset 702/1005 patients were misclassified with at least one method. 68 patients were misclassified with all methods, 240 with two or three methods and 394 with only one method (15 were misclassfified only with PLS-DA, 63 with Random Forests, 305 with SVM and 11 with PD-CR).
Furthermore, relevant feature selection is necessary for a correct understanding of the biological mechanisms underlying classification. It is well established that when expressed, mutant IDH 1/2 reduces 2-oxo-glutarate to 2-hydroxyglutarate  [42]. It was therefore expected for 2-hydroxyglutarate to be a feature of importance as was the case when using PD-CR on the BRAIN dataset for the classification of IDH-mutated vs wildtype gliomas. As the biologically relevant features are known in advance, the BRAIN dataset is a good testing set for this new method. Furthermore, as we described, the features selected with PD-CR in the LUNG dataset are identical to the ones described by Mathé et al. in their original study, which also validates the accurate feature selection performed by PD-CR.
Conclusion Herein we propose a recently introduced primal-dual method (PD-CR) for feature selection and classification with rejection. To our knowledge, the primal-dual method has never been used in such fashion. PD-CR includes a sparse regularization factor which is particularly appropriate for high dimensional sparse datasets such as metabolomics datasets. We highlight the two main results. First, PD-CR is more accurate than PLS-DA, Random Forests and SVM and leads to the selection of biologically relevant features.
Acknowledgements The authors thank  Xuchun Zhang  and  Axel Gustovic  for his collaboration to the development of python software during their 2018 and 2021 internships respectively,  Pr Antonin Chambolle  and  Pr Jean-Baptiste Caillau  for fruitfull discussions concerning the Primal-dual method,  Dr Jean-Marie Guigonis  ( Bernard Rossi facility ) for the LC-MS analyses and  Pr Hugues Duffau  and  Dr Catherine Goze  for validation, and formal analysis.
Funding This work has been supported by the  French government , through the  UCA-JEDI Investments  in the  Future  project managed by the  National Research Agency (ANR)  with the reference number  ANR-15-IDEX-01. Equipment for this study was purchased through grants from the  Recherche en matières de Sûreté Nucléaire et Radioprotection program  from the  French National Research Agency  and the  Conseil Départemental 06. David Chardin  was funded by a grant from  GIRCI Méditéranée.
Acknowledgements Funding by the  National Natural Science Foundation of China  ( 21805166 ), the 111 Project ( D20015 ) and the  Engineering Research Center of Eco-environment in Three Gorges Reservoir Region, Ministry of Education, China Three Gorges University  ( KF2019-05 ), the outstanding young and middle-aged science and technology innovation teams,  Ministry of Education, Hubei province, China  ( T2020004 ),  Foundation of Science and Technology Bureau of Yichang City  ( A21-3-012 ), the  Fundamental Research Funds for the Central Universities  (lzujbky- 2019-74 ), the  "Double First-Class" Research Start-up Funds of Lanzhou University  ( 561119203 ), the  University of Bordeaux  and the.
15 and 18). An ideal gas thermodynamic model was arbitrarily chosen. Formation standard enthalpies and standard entropies were taken from the DIPPR databank for each compound present in the model. Mass balances for each species on a control volume within the catalytic bed leads to a set of ordinary differential   equations. Stationary regime is reached. This problem is then discretised and solved thanks to the LSODE program. 19, 20 netic scheme A network of 61 reactions was developed to represent the transformations between 27 compounds (including 25 hydrocarbons, H 2 and the inert tracer, He). Olefins and C 8 compounds representing less than 2. 5% of the GC FID chromatograms area, they were considered as trace species and excluded from the kinetic model. The 25 selected species are referred to as xLy.
The model is fitted on the data that are provided by the FID GC analysis only whereas experimental dihydrogen consumption was calculated from the thermo-conductivity detector (TCD) GC analysis. The accuracy of predictions is comparable between catalysts. No catalyst formulation nor support nature variations were associated to bias in model predictions. As shown in Fig. 5  in the case of a single example catalyst (P-egg_0. 3% wt Pt_1. 3% wt Cl), the effect of temperature and contact time variations is reproduced by the model. The quality of model predictions is comparable between different catalysts. The individual significance of each parameter was assessed by performing a student's t-test. In this study, the parameters were considered statistically different from zero, when the estimates dispersion exceeds 95% of the reference tabulated value at the same degree of freedom.
Lipids Incorporating VLCFAs To illustrate the importance and distribution of VLCFAs in plants, we quantified all fatty acid and fatty acid derivatives in different tissues of arabidopsis using GC-MS and -FID for identification and quantification, respectively. Data for roots and stems were calculated from a previous study [60], while new analyses were performed for leaves and dried seeds for this study. For global acyl-chain profiling, tissues were directly transmethylated in 5% sulfuric acid in methanol for 3 h at 85 • C, and the released acylchains were extracted and silylated before GC analysis. This procedure allows for an estimation of all the major acyl-chains present either in classical membrane phospholipids (as unmodified fatty acid), in the sphingolipids of the plasma membrane (as 2-hydroxy fatty acids) or in surface lipids (as waxes and cutin/suberin monomers).
Groundwater has become a major source of irrigation in the past few decades in India, but as it comes from millions of individual borewells owned by smallholders irrigating small fields, it is difficult to quantify the actual irrigated area across seasons and years. This study's main goal was to monitor seasonal irrigated cropland using multiple optical satellite images. The proposed research was performed over the Berambadi watershed, an experimental site in southern peninsular India. While cloud cover during crop growth is the greatest obstacle to optical remote sensing in tropical regions, the cloud-free images from multiple optical satellite platforms (Landsat-8 (OLI), EO1 (ALI), IRS-P6 (LISS3 and LISS4), and Spot5Take5 (HRG2)) were used to fill data gaps during crop growth periods. The seasonal cumulative normalized difference vegetation index (NDVI) was calculated and resampled at 5 m spatial resolution for various cropping seasons.
Remote Sensing Data Collection and Image Pre-Processing Clouds are the greatest obstacle to using the images from the same satellite for an entire study period. To address the unavailability of time-series images from the same satellite due to cloud cover, we obtained optical images from several platforms, including LS8, S5T5, EO1-ALI, and the Indian Remote Sensing (IRS) satellite IRS-P6 (Figure  2 ). LS8 OLI images, EO1-ALI images, High Resolution Geometrical sensor images from S5T5, and Linear Imaging Self Scanning Sensor (LISS-3 and LISS-4) images from IRS-P6 (Resourcesat-2) were obtained from the summer season of 2014 to that of 2016. All images obtained were pre-processed for atmospheric correction using the Second Simulation of a Satellite Signal in the Solar Spectrum  [43] [44] [45]  radiative transfer model, followed by a geometric correction.
Ground Observation Data We collected ground observation data from farmers for all seven monitored cropping seasons (summer 2014, kharif 2014, rabi 2014-2015, summer 2015, kharif 2015, rabi 2015-2016, and summer 2016). Due to limited funds, the ground survey was performed in the middle of the kharif and rabi seasons in 2014 and 2015. During these surveys, farmers also provided data for the summer seasons of 2014 and 2015. Summer 2016 crop data were collected during the kharif season of 2016. The quality of the data collected was maintained while performing the surveys (e. g. , data were collected only if the farmer was certain of his/her answers). The ground survey was performed to collect a maximum amount of data about crop and water management at the field scale. A variety of data were collected from the survey while processing the datasets and generating results.
The main data collected during the field survey included: (i) seasonal crop type (ii) irrigation practices (e. g. , number of irrigation events) (iii) crop sowing dates (iv) crop harvest dates (v) whether the crop was irrigated, rainfed, or partially irrigated (vi) source of irrigation water (own borewell or neighbor's borewell) The spatially distributed survey was performed throughout the entire watershed. The survey indicated that farmers performed unplanned partial irrigation during crop growth when rainfall was absent, depending on their irrigation system  [38]. After finishing all ground observations, the data were divided into two categories to decrease heterogeneity in cropping practices in the watershed: (i) annually irrigated croplands (irrigated in all three cropping seasons) (ii) others (rainfed, partially irrigated, and left fallow for one cropping season) The total number of fields surveyed for 2014-2015, 2015-2016, and summer 2016 were 628, 731, and 604, respectively (Table  1 ).
The intensively irrigated crops included longduration crops that grow in all three cropping seasons (e. g. , banana, sugarcane, irrigated coconut), crops that grow in two seasons (e. g. , turmeric, ginger (kharif and rabi), and single-season crops (e. g. , beetroot, onion, garlic, cabbage, carrot, watermelon, vegetables). Spatially-distributed intensively-irrigated croplands were surveyed in 2014, 2015, and 2016 in the Berambadi watershed (Figure  3 ), and all samples were divided evenly and randomly into training (calibration) and validation samples. These data were used to classify the irrigated croplands and validate the classification outputs, respectively.
This NDVI correction was performed to reduce the uncertainty among the NDVI products  [51, 52]. The coefficients of determination (R 2 ) of these regressions were high (Figure  6 ). A high R 2 (0. 85) was obtained for images acquired on the same day from S5T5 and EO1-ALI satellites. Since the IRS LISS-3 and IRS LISS-4 images were acquired with a two-day difference, their R 2 was lower (0. 67). The linear regression equations were applied to the NDVI datasets derived from the other satellite images (EO1 (ALI); Spot5Take5; IRS-P6 (LISS3); IRS-P6 (LISS4)). Equations (  1 )-(  4 ) represent the equations obtained from linear regression between NDVI values obtained from Landsat-8 (OLI) and other satellite datasets. These equations were further implemented over other satellite datasets to calculate refined NDVI images.