dataesr/scientific-paragraphs-categorization huggingface dataset:
For a given data series T and a given class C i , dCAM C j T ð Þ is defined as: À Á computations per kernel. Thus, the training time per epoch is higher for dCNN than CNN. However, given that the size of the input of dCNN is larger (containing D permutations of a single series) than CNN, the number of epochs to reach convergence is lower for dCNN when compared to CNN. Intuitively, dCNN trains on more data during a single epoch. This leads to similar overall training times. dCAM C j T ð Þ ¼ σ 2 M 0 C j T ð Þ t 0 Ã μ M C j T ð Þ t 0 … σ 2 M 0 C j T ð Þ t n Ã μ M C j T ð Þ t n : … : σ 2 M DÀ2 C j T ð Þ t 0 Ã μ M C j T ð Þ t 0 … σ 2 M DÀ2 C j T ð Þ t n Ã μ M C j T ð Þ t n σ 2 M DÀ1 C j T ð Þ t 0 Ã μ M C j T ð Þ t 0 … σ 2 M DÀ1 C j T ð Þ t n Ã μ M C j T ð Þ t n 0 B B B B B B @ 1 C C C C C C A (.
Datasets We conduct our experimental evaluation using real datasets injected with known discriminant patterns. We use the StarLightCurves (classes 2 and 3 only) and ShapesAll (classes 1 and 2 only) datasets from the UCR archive  (Dau et al. , 2019) , in which we inject subsequences that will generate discriminant features. We build two types of datasets to study the ability of the algorithms to identify the discriminant patterns guiding the classification decision, (1) when these patterns occur in a subset of the dimensions at different timestamps, and (2) when these patterns occur in a subset of the dimensions at the same timestamp. (1) For Type 1 datasets, we build each dimension of Class 1 by concatenating random instances from one class of one of our two UCR seed datasets. We build Class 2 by injecting in the series of the other class of our two UCR datasets a pattern in 2 random dimensions at a random position in the series.
(2) For Type 2 datasets, we build each dimension of Class 1 by concatenating random instances from one of the classes of our two UCR datasets and injecting patterns from the other class in x random dimensions and at different positions. We build Class 2 by injecting patterns at the same positions of 2 random dimensions. Examples of Type 1 and Type 2 5-dimensional datasets based on StarLightCurves are depicted in Figure  6a ,b, respectively. In our experiments, we generate 1000 time series for the Type 1 synthetic dataset and 1000 time series for the Type 2 synthetic dataset.
Evaluation measures We first evaluate the classification accuracy, C-acc. This measure corresponds to the ratio of correctly classified instances among all instances in the test dataset. We then evaluate the discriminant features accuracy, Dr-acc, for Class 1 (see Figure  6 ). We define Dr-acc as the PR-AUC for CAM/cCAM/dCAM obtained from the models and the ground-truth. The ground-truth is a series that has 1 at the positions of discriminant features (see Figure  6a. 2): ground-truth contains 1 at the positions of the injected patterns, marked with the red rectangles, and 0 otherwise). We motivate the choice of PR-AUC (instead of ROC-AUC) because we are more interested in measuring the accuracy of identifying the injected patterns (representing at max 0. 02 percent of the dataset) than measuring the accuracy of not detecting the noninjected patterns.
We are using kernel sizes equal to 8, 5, and 3 for each block for the three layers of the block. For dInceptionTime, we use the same architecture as originally defined  (Ismail Fawaz et al. , 2020). We also include MTEX-CNN  (Assaf et al. , 2019) (MTEX) as a baseline, representative of other kinds of architectures that can provide a multivariate CAM. The explanation is computed separately for discriminant features and timestamps using grad-CAM  (Selvaraju et al. , 2017)  (MTEX-grad). The latter is a variant of the usual CAM. We split our dataset into training and validation sets with 80 and 20 percents of the total dataset, respectively (equally balanced between the two classes). The training dataset is used to train the model, and the validation dataset is used as a validation dataset during the training phase.
We generate a fully new test dataset of 1000 time series (generated in the same manner as the initial 1000 time series used for the train and validation set) and evaluate C-acc and Dr-acc. We train all models with a learning rate α ¼ 0:00001, a maximum batch size of 16 instances (less if GPU memory cannot fit 16 instances), and a maximal number of epochs equal to 1000 (we use early stopping and stop before 1000 epochs if the model starts overfitting the test dataset). For dCAM, we use k ¼ 100 (number of random permutations), a value that we empirically verified (due to lack of space, a detailed analysis of the effect of k is in the full version of the article).
Accuracy evaluation We now evaluate the classification accuracy (C-acc) and the discriminant feature identification accuracy (Dr-acc) on synthetically built datasets. Table  1  depicts both C-acc and Dr-acc on Type 1 and 2 datasets when varying the number of dimensions from 10 to 100. Overall, we observe that all methods have better performance (both C-acc and Dr-acc) on Type 1 datasets than on Type 2 datasets. This was expected since discriminant features located in single dimensions are easier to find than discriminant features that depend on several dimensions.
e30-16 Paul Boniol et al. Type 1 10 1. 00 ( ± 0. 00) 1. 00 ( ± 0. 00) 1. 00 ( ± 0. 00) 1. 00 ( ± 0. 00) 1. 00 ( ± 0. 00) 1. 00 ( ± 0. 00) 20 1. 00 ( ± 0. 00) 0. 86 ( ± 0. 02) 1. 00 ( ± 0. 00) 1. 00 ( ± 0. 00) 1. 00 ( ± 0. 00) 0. 99 ( ± 0. 00) 40 0. 85 ( ± 0. 00) 0. 65 ( ± 0. 01) 1. 00 ( ± 0. 00) 1. 00 ( ± 0. 00) 1. 00 ( ± 0. 00) 1. 00 ( ± 0. 00) 60 0. 83 ( ± 0. 16) 0. 65 ( ± 0. 01) 1. 00 ( ± 0. 00) 1. 00 ( ± 0. 00) 1. 00 ( ± 0. 00) 0. 96 ( ± 0. 00) 100 0. 70 ( ± 0. 02) 0. 57 ( ± 0. 04) 1. 00 ( ± 0. 00) 0. 98 ( ± 0. 00) 1. 00 ( ± 0. 00) 0. 85 ( ± 0. 01) Type 2 10 0. 60 ( ± 0. 01) 0. 82 ( ± 0. 03) 0. 54 ( ± 0. 01) 1. 00 ( ± 0. 00) 1. 00 ( ± 0. 00) 0. 93 ( ± 0. 01) 20 0. 54 ( ± 0. 02) 0. 57 ( ± 0. 02) 0. 52 ( ± 0. 02) 1. 00 ( ± 0. 00) 1. 00 ( ± 0. 00) We then notice that for low dimensional (D ¼ 10) datasets, ResNet, dResNet, dCNN and dIncep-tionTime are performing nearly perfect C À acc.
Moreover, ResNet and MTEX-CNN are performing well for low-dimensional data series but start to fail for a more significant number of dimensions. While the drop is already significant for the Type 1 dataset built from the StarLightCurve dataset, it is even stronger for Type 2 datasets, for which ResNet fails to classify instances with a number of dimensions D ≥ 20. On the contrary, dCNN, dResNet, and dInceptionTime, which use the random permutations in the input, are not sensitive to the number of dimensions and have an almost perfect C-acc for most of Type 1 datasets. We observe a C-acc drop for dCNN, dResNet, and dInceptionTime as dimensions increase for Type 2 datasets. However, this drop is significantly less pronounced than that of ResNet. Overall, dCNN, dResNet, and dInceptionTime, which have on average the three highest ranks, are the most accurate methods.
Regarding cResNet, although it achieves a nearly perfect C-acc for Type 1 datasets, we observe that it fails to classify correctly instances of Type 2 datasets. As explained in Section 2, the input data structure is not rich enough to allow comparisons among dimensions, which is the main way to find discriminant features between the two classes of Type 2 datasets. We also observe that MTEX-CNN fails to classify instances of Type 2 datasets. Thus, this architecture is not correctly detecting the discriminant features across different dimensions. Overall, Figure  7a  shows that dCNN, dResNet, and dInceptionTime are equivalent to cResNet for Type 1 (Figure  7a. 1), outperforming all the baselines for Type 2 (Figure  7a. 2), and in general are better than the baselines (ResNet and cResNet) for both types (Figure  7a.
3) with F Type1,Type2 ð Þ ¼ 2ÃC-acc Type1 ð Þ Ã C-acc Type 2 ð Þ C-acc Type 1 ð Þ þ C-acc Type2 ð Þ ). We now compare the different methods using the Dr-acc measure. We observe that the baseline cCAM (computed with cCNN) is outperforming CAM (computed with ResNet) and dCAM (with all of dCNN, dResNet, and dInceptionTime) for Type 1 datasets. This is explained by the fact that these classes can be discriminated by treating dimensions independently. Thus, cCAM (with no comparisons between dimensions) is naturally the best solution. Nevertheless, as Type 2 datasets require comparisons among dimensions to discriminate the classes, cCAM fails on them, with a Dracc very similar to the one of a random classifier. This confirms that such a baseline cannot be considered as a general solution for multivariate data series classification.
We also observe that Dracc of the explanation method of MTEX-CNN (MTEX-grad) is lower than dCAM for Type 1 and close to Dr-acc of cCAM for Type 2, meaning that it cannot identify discriminant features of Type 2 datasets. We then compare CAM and dCAM (used with dCNN, dResNet, and dInceptionTime). We note that dCAM significantly outperforms CAM. As depicted in Figure  7b , we also observe that Dr-acc reduces for all models as the number of dimensions increases. Nevertheless, Dr-acc of dCAM remains relatively high for both Type 1 (Figure  7b. 1)) and Type 2 (Figure  7b. 2) datasets (for a number of dimensions under 60). This result demonstrates the superiority of dCAM over state-of-the-art methods. The superiority of dCAM is also confirmed by looking at the average ranks in Table  1 , which indicates that dCAM computed from dResNet has the highest rank of 2:15.
Dataset and use case description At this point, we need to create our datasets of abnormal data series (i. e. , vibrations) and anomaly-free data series. Following the suggestion of expert knowledge, we selected 120 sensors inside 12 subsystems of the nuclear power plants. Figure  8a  summarizes the subsystems analyzed and the number of sensors collected. We collected every unwanted vibration that happened in every French 1300 MW nuclear plant. In total, we have 444 vibrations. We then create our multivariate data series by selecting every sensor's measurement between 75 minutes before the vibrations and 5 minutes after. We set the acquisition rate to 1 point every 6 seconds. Each multivariate data series contains 96,000 points. Next, we note the set of data series containing a vibration T A M.
What we want to highlight are unexpected solicitations that would lead to vibrations later. This will trigger immediate and cost-effective corrective actions. We thus have in total 888 multivariate data series (for which 444 of them correspond to unwanted vibrations) of D ¼ 120 dimensions. In total, the dataset contains 85,248,000 points. Formally, we define the dataset as T M ¼ T N M S T A M , with T N M , T A M ∈ ℝ 444,120,800 ð Þ.
Quantitative evaluation We then evaluate the relevance of the subsequences identified by our proposed approach dCAM. We first start by measuring the consistency of the detection (or activation) as regards the (1) temporality (i. e. , are the subsequences detected close in time to the vibration?), (2) structural information (i. e. , are the sensors closely related to the vibrating system?). As the experts are interested in discriminant features across the entire dataset, we perform the analysis listed above on the entire T A M (i. e. , for time series included in the training and the validation set). As dCAM uses random permutations of the time series dimensions (resulting in inputs not used in the training set), the risks related to overfitting are limited and allow us to merge the training and validation set for this discriminant feature evaluation.
Conclusions and future work Even though data series classification using deep learning has attracted a lot of attention, existing techniques for explaining classification decisions fail in the case of multivariate data series. In this work, we describe a novel approach, dCAM, based on convolutional neural networks, which enables us to detect the discriminant subsequences within individual dimensions of a multivariate data series. The experimental evaluation with synthetic and real datasets demonstrates the benefits and superiority of our approach in discriminant feature discovery and classification explanation in multivariate time series. Our real use case applied to the nuclear power plants domain verifies applicability and the interest of our solution. In future work, we plan to study in detail the effect that using permutations in the input has on the overall approach.
Data availability statement. The data and code supporting this study's findings are openly available on GitHub. The code to reproduce the synthetic experiments can be found here: https://github. com/boniolp/dCAM. Restrictions apply to the availability of the data related to the industrial use case described in this article. Funding statement. This work was supported by EDF R&D and ANRT French program. Ethical standard. The research meets all ethical guidelines, including adherence to the legal requirements of the study country.
Study design and data sources We used a database including all COVID-19 laboratoryconfirmed cases in Portugal from 3 March 2020 until 16 July 2021. This database is compiled by the Portuguese  Directorate General of Health (DGS) and includes all first positive laboratory notifications for each patient. It also contains information related to CN and EI questionnaires for each LN if they were submitted. EI questionnaires can only be recorded and submitted if a clinical notification is previously submitted. We described the proportion of cases without CN nor EI and without EI overall (regardless of CN) in time, place, and person. We identified the factors associated with these outcomes in multivariable analysis using Poisson regression and presented adjusted relative risks, 95% confidence intervals, and p-value.
Most of the terms of Equation (  1 ) are estimated from radiative transfer codes using ancillary data (wind speed, atmospheric pressure, water vapor, etc. ). For the estimation of aerosol and marine contributions, the standard algorithm offers two cases (see  [5]  for details): For clear oceanic waters (case 1), the marine signal is assumed to be negligible in the NIR spectral domain (dark pixel method  [16] ), which allows to quantify the contribution of aerosols in the NIR. The spectral difference estimated at 748 and 869 nm (NIR MODIS wavelength) allows to select the two most suitable aerosol models that will be used to estimate the signal attributed to aerosols in the visible bands and to deduce the marine contribution. When the marine signal is not negligible in the NIR (case 2 waters), the iterative method of  [29]  is applied to simultaneously compute the aerosol contribution and the marine reflectance.
SOM-NV Processing of MODIS-Aqua Data Equation (1) can be written in terms of reflectance ρ, to reduce the effects of solar illumination and measurement geometry  [16] : ρ t (λ) -ρ R (λ) -Tρ g (λ) -tρ WC (λ) = [ρ a (λ) + ρ Ra (λ)] + tρ w (λ) (4) The terms on the left-hand-side in Equation (  4 ) are known with good accuracy for diffuse transmittance t  [30, 31] , Rayleigh scattering ρ R  [31] , glitter ρ g  [32] , and whitecaps effects ρ WC  [33] ; see also  [18]  for more details. NASA has made available a Multi-Sensor Level-1 to Level-2 (MSL12) tool for atmospheric correction (l2gen contained in the SeaDAS software), which compute the different terms of Equation (4). We used the standard l2gen process (see SeaDAS 7. 5. 3 version) to generate the various left terms and partially correct the satellite measurement, which now depends only on aerosols (ρ A = ρ a + ρ Ra ) and marine (tρ w ) terms for each wavelength: ρ cor (λ) = ρ A (λ) + tρ w (λ) (5) where ρ A is the atmospheric reflectance due to aerosols as well as due to molecule-aerosol diffusion and ρ cor is the quantity we seek to estimate from the approach  [26] , here applied to MODIS, whose sensor's wavelengths are close to the SeaWiFS spectral bands (Table  1 ).
2. 2. 1. Algorithm Description is a two-steps algorithm that uses two different statistical models applied sequentially: the Self-Organizing Map (SOM) and the NeuroVaria method. SOM is an unsupervised learning classification model  [34]. It is well suited for visualizing and clustering highdimensional datasets. NV is a variational inversion allowing the retrieval of accurate optical thickness and ocean surface Chl. NV is based on an iterative method described in  [22, 35, 36]. It uses a neural network family called MultiLayer Perceptron (MLP), allowing the retrieval of accurate oceanic and atmospheric constituents. One of the great difficulties of this method is to find the accurate input parameters (for the atmosphere and for the ocean), which allow to minimize the cost function. In basic versions of NV, a dedicated MLP inverts the signal from the PIR to determine the input parameters for aerosols, while they are arbitrarily fixed for the ocean.
Two datasets are used for the SOM-NV algorithm: Data obs and a synthetic expert data (Data expert ), both composed of the reflectance and geometry variables. Reflectance is given at eight wavelengths for SeaWiFS and seven for MODIS (Table  1 ) and for two angles: the sun zenith angle θ s and the scattering angle γ, defined as follows: γ = arccos(-cos θ v cos θ s + sin θ v sin θ s cos(∆φ)) (6) where ∆φ = φ sφ v and φ s and φ v are the solar and sensor azimuthal angles, respectively. The collection of these nine-dimensional vector (7 reflectances + 2 angles) constitutes the observation dataset defined as Data obs. Data expert includes three additional geophysical variables, i. e. , the type of aerosol, the AOT, and Chla. This database contains nearly 12,000,000 simulations using the two-layer radiative transfer code of  [16] , eight SeaWiFS bands, the two angles, and aerosol models.
AOT and Chla values and constitutes what will be called the Look-Up Table (LUT). A set of one-year data (Learn obs ) is used to train SOM and build a SOM-Angle-Spectrum (SOM-A-S) map. The vectors of the learning dataset are then organized into 600 clusters (20 × 30 neurones), allowing a highly discriminative representation of the data. Data obs and Data expert (representing the expertise whose associated parameters or labels-Chla, AOT, and aerosol type-are known), are used to label the 600 clusters of SOM-A-S. A labeling of SOM-A-S has evolved since  [23]. It is now based on the simultaneous projection of reflectance and angles described in  [26]. At the end of this labeling phase, each cluster of SOM-A-S map has captured a set of "expert reflectance" (ρ exp ) and takes the corresponding label.
Adaptation to MODIS Data The SOM-NV algorithm is then adapted to MODIS measurements. Seven of the eight SeaWiFS spectral bands are close to those of MODIS (see Table  1 ). The SeaWiFS sensor crosses the Equator at 12:00 in a descending mode, whereas MODIS crosses it at 13:30 in an ascending mode. See more information on the NASA Ocean Color ( https: //oceancolor. gsfc. nasa. gov/ accessed on 17 February 2023). The two angles and seven reflectances measured on board MODIS are then projected onto the clusters defined in SOM-A-S. Since different conventions apply to SeaWiFS and MODIS, we modify the azimuthal angle of MODIS (Φ = 180 -Φ). This adaptation also implies that:.
• The 510 nm band used by SOM-A-S (finding no equivalent on MODIS sensor) is replaced by the 531 nm during the projection of the image; • The 765 nm wavelength column of SeaWIFS is replaced by a null vector; • F 0 values are taken from the version 7. 5 of SeaDAS software to remain in the same standard as SeaWiFS. According to the methodology described in the previous section, each pixel of the image is associated with a cluster for which the corresponding atmospheric and oceanic variables are known. Finally, we project the portion of each swath contained in our domain on a fixed grid of 1/96 degrees resolution (1. 1 km). The variables saved in the SOM-NV archive of MODIS-Aqua are reflectance, AOT at 869 nm, and Chla and geographical coordinates for each pixel.
In Situ Data AERONET Data NASA has commissioned a network of stations called AERONET (for AErosol RObotic NETwork) to assess aerosols by measuring optical thickness, using ground-based photometers  [40]. Although most of these data are located on the mainland, coastal stations can serve to validate AOT given by the water color algorithms. In this study, we used data from two AERONET stations: Mbour (14. 394 Pigment concentration is obtained from the High Performance Liquid Chromatography (HPLC) method, which is a technique of analytical separation of molecules present in a complex mixture. Depending on organic matter concentration, one to two liters of sea water were filtered onto 25 mm Whatman GF/F filters stored at -80 • C for later analysis. The pigments were separated and quantified according to the method described by  [42] , adapted from  [43].
Multispectral Fluorometer Data (FluoroProbe) The bbe Moldaenke FluoroProbe (hereafter FP) is a multispectral fluorometer which illuminates a sampling chamber at six different wavelengths centered at 370, 470, 525, 570, 590, and 610 nm. Emission fluorescence is measured at 680 nm. The sequential and differentiated illuminations provide a fluorescence spectrum used to differentiate four algae groups: green, brown, and blue-green algae, and cryptophytes  [44]. The 370 nm LED is used to evaluate and correct the contribution of yellow substances to the fluorescence signal. The inversion of this information to determine the Chla contribution for each algal group is detailed in  [44]. FP data were collected continuously (3 s interval) at the surface along the tracks of MiniSCOPES 2015 and 2017. Data are averaged over a radius of 1 km around the position of the satellite pixels to be compared with estimates produced by SOM-NV and STD.
Aerosol Optical Thickness Derived from the SOM-NV Algorithm Diouf et al. [26]  showed that the SOM-NV algorithm applied to SeaWiFS provided a better estimate of AOT than the STD processing (better correlation coefficient) using two stations of the AERONET observation network in Mbour and Cabo Verde. We also evaluated the MODIS AOT estimates made from the STD and SOM-NV processing for these two coastal stations: Mbour, which is located on "la petite côte" of Senegal, and Cabo Verde, which is located in an open oceanic region (Figure  1 ). In total, 1435 (261) and 1690 (181) collocated retrievals are used for SOM-NV (STD) over the 16-year dataset at Cabo Verde and Mbour, respectively. As for SeaWiFS, absorbing Saharan dusts are generally characterized by high AOT, which are not decoded by the STD MODIS algorithm (threshold for the dust mask set at 0.
To the extent that the properties of the water color signal are improved by this processing scheme, the Chla estimates should also be greatly improved by this approach. However, dedicated and numerous in situ data are still necessary to conclude on this point. SOM-NV Chla is closer to HPLC Chla, as shown in March for two different years. Chla, AOT at 869 nm, reflectance at 412, 443, 488, 531, and 547 nm resulting from the SOM-NV processing of MODIS-Aqua from 2003 to 2018 are archived in netcdf format as a regional dataset that is published in https://zenodo. org/, last access on 17 June 2023 (DOI: https://doi. org/10. 5281/zenodo. 7971187).
Acknowledgments:  K. Correa  was supported for this study by a scholarship from  IRD  ( Institut de Recherche pour le Développement)  and by a grant from  Région Bretagne. The  French National Research Agency (ANR)  partly funded this research ( SOLAB  project; grand  ANR-18-CE32-0009 ). The authors also acknowledge support from the  International Joint Laboratory ECLAIRS. The authors thank  S. M. Sall  for their constant support to this work. We thank  NASA Ocean Biology Processing Group. (2017). MODIS-Aqua Level 2 Ocean Color Data  Version R2018. 0 [OC]. NASA Ocean Biology Distributed Active Archive  Center. https://doi. org/10. 5067/AQUA/MODIS/L2/OC/2018. We would like to thank  Aida Beye  (aida. beye@ird. fr) for processing the FP data. We thank also  Didier Tanré  and their staff for establishing and maintaining the Dakar, Senegal site used in this investigation.