dataesr/scientific-paragraphs-categorization huggingface dataset:
Full-field measurements could be used on heterogeneous state configuration to enrich material state databases with more complex configurations. However, as it has been mentioned above, the stress analysis of complex tests requires the coupling with FE simulations that need a constitutive model. This is disappointing to observe that these 2 advanced methods (one that extracts material data from experiments and the other that makes use of material state data to perform simulations) cannot help each other. At this point, one ends up with the following fundamental question: Is it possible to measure stress fields? In general, it has not yet been possible. There exist some optical techniques, like photoelasticity, caustics, or more recently diffraction contrast tomography, that allow to measure elastic stress fields, but non-elastic stress evaluation is out of their scope.
This set consists in more than 600 000 points in the space defined by the components of stress, strain, and anelastic strain tensors. For visualization purposes, one needs to reduce the dimensionality of this database. Because it is assumed that von Mises plasticity holds, the von Mises stress is computed as well as the deviatoric part of the elastic strain and the norm of the anelastic strain. In Figure  17A , the evolution of the von Mises stress is plotted as a function of the norm of the plastic strain for a few points. The typical loading unloading scenario of elastoplasticity is captured. In Figure  17B , von Mises stress is plotted as a function of the deviatoric part of the elastic strain and the norm of the plastic strain. The shape of the domain of admissible material states agrees well with the one considered in the numerical simulations to generate the images.
CONCLUSION A methodology is proposed to build, in a general case, a parametric description of the displacement and stress fields based on an anelastic strain field. Digital image correlation is used to obtained the displacement parameters whereas the stress parameters are obtained thanks to thermodynamic assumptions on the deformation process leading to an auxiliary problem. The method thus allows for measuring displacement, strain, and stress fields. Further, an anelastic strain field measuring the distance between the actual local constitutive behaviour and elasticity according to a given but arbitrary elastic tensor is obtained. The ability of the method to measure stress fields in different situations is illustrated. The raw data extracted from the measurement are admissible material states in a space of dimension 9 (3 components for the strain, stress, and anelastic strain tensors) for 2D problems.
Acknowledgements: We all thank the  Royal Society of London  ( International Exchange grant   IE130506 ), the Paris group thanks the  Agence Nationale Reseaux  (grant  09-JCJC-0022-01 ),  La Ville de Paris  (grant  Programme Emergence ) and the  CNRS  (grant PEPS PTI) while FV thanks the  US Air Force (AFOSR  grant  FA9550-12-1-0294 ) and the  European Research Council  ( ERC grant   SP2- GA-2008-233409 ). Data accessibility: All data and methods are reported within this paper and with the electronic supplementary material.
Acknowledgments: We would like to warmly thank  P. Biagioni ,  D. Neshev , and  A. Zayats  for fruitful discussions and  S. Suffit  for help in fabrication. Funding:  Erasmus Mundus NANOPHI  ( 2013 5659/002-001 ),  NanoSpectroscopy COST Action MP1302, CARIPLO Foundation SHAPES Project  ( 2013-0736 ), and " Double Culture" Ph. D. Program of Sorbonne Paris Cité  ( V. F. Gili ). We acknowledge the financial support from the  SEAM Labex  (" Programme d'investissements d'avenir " of the  French Government) , within the  PANAMA  Project.
12. The binned ML-analysis (dashed-dotted line on diagrams) yields T 1/2 = 76. 5 ± 17. 8 s for 211 Tl, T 1/2 = 30. 9 ± 8. 0 s for 212 Tl and T 1/2 = 11. 0 ± 2. 4 s for 214 Tl. An almost negligible contribution from the much slower decay of the daughter nuclei ( 211,212,214 Pb) can be observed in these three cases. The most exotic thallium nuclei 215,216 Tl were measured with rather limited statistics of only 281 and 99 implants, respectively. In this case, we noticed a slight improvement of the signal-to-background ratio in the correlation histograms when the correlation area was enlarged from 3 × 3 mm 2 to 5 × 5 mm 2. The ML analysis also shown in diagrams of Fig. 12  yielded a half-life of T 1/2 = 9. 7 ± 3. 8 s for 215 Tl and T 1/2 = 5. 9 ± 3. 3 s for 216 Tl. The neutron data analysis showed the presence of only one correlated implant-β-neutron event for each of 211,212,215 Tl, which yields neutron branching ratios of 2.
ACKNOWLEDGMENTS This work was supported by the  Spanish Ministerio de Economia y Competitividad  under grants No. FPA2011-28770-C03-03 ,  FPA2008-04972-C03-03 ,  AIC-D-2011-0705 ,  FPA2011-24553 ,  FPA2008-6419 ,  FPA2010-17142 ,  FPA2014-52823-C2-1-P ,  FPA2014-52823-C2-2-P, CPAN CSD-2007-00042  ( Ingenio2010 ), and the program  Severo Ochoa  ( SEV-2014-0398 ). I. D and M. M were sup-.
Acknowledgements The authors thank  Gobierno de Aragón-Fondo Social Europeo (Grupos de Investigacion  Consolidados  T12  and  T87 ) and  MINECO-FEDER  ( MAT2013-46505-C3-1-R ) for financial support. Authors acknowledge the use of  Servicio General de Apoyo a la Investigación-SAI, Universidad de Zaragoza. This work was also supported by  "le Syndicat Mixte de la Côte d'Opale" and "la région Nord Pas de Calais ".
Supervised classification systems used for land cover mapping require accurate reference databases. These reference data come generally from different sources such as field measurements, thematic maps, or aerial photographs. Due to misregistration, update delay, or land cover complexity, they may contain class label noise, i. e. , a wrong label assignment. This study aims at evaluating the impact of mislabeled training data on classification performances for land cover mapping. Particularly, it addresses the random and systematic label noise problem for the classification of high resolution satellite image time series. Experiments are carried out on synthetic and real datasets with two traditional classifiers: Support Vector Machines (SVM) and Random Forests (RF). A synthetic dataset has been designed for this study, simulating vegetation profiles over one year.
The real dataset is composed of Landsat-8 and SPOT-4 images acquired during one year in the south of France. The results show that both classifiers are little influenced for low random noise levels up to 25%-30%, but their performances drop down for higher noise levels. Different classification configurations are tested by increasing the number of classes, using different input feature vectors, and changing the number of training instances. Algorithm complexities are also analyzed. The RF classifier achieves high robustness to random and systematic label noise for all the tested configurations; whereas the SVM classifier is more sensitive to the kernel choice and to the input feature vectors. Finally, this work reveals that the cross-validation procedure is impacted by the presence of class label noise.
The supervised strategy requires a training input dataset in order to learn a decision rule, which is used to predict the labels of new unlabeled instances. Each training instance is defined by a feature vector and its related reference class label. More specifically, for land cover mapping, it has been established that Support Vector Machines (SVM) and Random Forests (RF) generally outperform other traditional supervised classifiers  [8]. Both SVM and RF classifiers obtain promising results on satellite image time series  [9] [10] [11]. Furthermore, the RF ensemble classifier has some advantages as described in  [12]. In particular, it has low sensitivity to feature selection  [13] , an easy parameterization  [14] , and a low computing time  [15, 16]. The reference dataset is crucial in order to train classification systems and to evaluate the produced land cover maps.
Accordingly, it is generally split into two sets in supervised classification schemes: one for training, and the other one for validation, i. e. , for assessing land cover map quality. Obtaining well-labeled data is an important challenge  [17]. Some methods such as active learning, where users select iteratively the best informative instances, have been proposed  [18, 19]. Unfortunately, these methods are hardly applicable for land cover mapping over large areas  [20]. Another strategy to obtain an accurate labeled dataset consists in using field collected data or interpreted data from very high spatial resolution satellite images or airborne photographs. However, the resulting datasets are time consuming to be produced, hardly feasible on large areas, and often expensive. Learning classification algorithms over large areas requires a substantial number of instances per land cover class describing landscape variability.
Accordingly, training data can be extracted from existing maps or specific existing databases, such as crop parcel farmer's declaration or government databases. When using these databases, the main drawbacks are the lack of accuracy and update problems due to a long production time. Volunteered geographic information, known as crowd-sourcing, referring to geospatial data created by citizens, has also been used as reference databases  [21]. However, such databases have generally high level of noise due to disagreements between the untrained volunteers. The quality of the reference databases plays a key role in the assessment of derived land cover maps. Theoretically, reference databases are considered as an ideal gold standard, that provide the "correct" label for each referenced instance. However, the term "ground truth" is avoided since real reference databases contain errors, artifacts and imprecisions  [22].
In the literature, the noise contained in reference datasets has been divided in two main categories  [23, 24]. The first category corresponds to the feature noise, which has been defined as an imprecision or a mistake introduced in the attribute values of the instances. Feature noise may be due to acquisition conditions (e. g. , cloudy day); data preprocessing, in particular with orthorectification, geometric and atmospheric corrections; registration differences caused by digitization or delineation; computation of features (e. g. , phenology estimation); or encoding problems. The second category corresponds to class label noise, i. e. , the instance label is different from the ground truth label. The corresponding instances are called corrupted or mislabeled instances. Some previous works have shown that feature noise is usually less adverse than class label noise  [23, 24].
Thus, mislabeling can occur while inexperienced personnel collects this kind of reference data. The combination of several existing databases-necessary to cover large areas-may lead to the emergence of mislabeled data due to disagreements in land cover definition. Misregistration between satellite images and reference databases may also contribute to class label noise  [22]. Similarly, the date gap, between the reference database production and the image acquisition, may involve new errors due to possible changes in land cover. The presence of class label noise has several consequences on supervised learning techniques  [25]. Most of the works study class label noise focusing on the influence on classification performances. They have shown that noisy labels could adversely impact the classification accuracy of the induced classifiers.
Some studies also discuss the learning classifier choice in the presence of noise  [36]. For instance, the robustness of eleven classifiers has been examined in the presence of feature and class label noise with several imbalanced datasets  [37]. In the context of land cover mapping, Decision Trees, 1-Nearest Neighbor and Linear Machine performances have been compared in  [31]. This last study has shown that the classification performances linearly decrease when the noise level increases. In addition, other consequences may emerge due to class label noise. The learning model complexity may be impacted for some classification algorithms. For example, the average path length of training instances may increase in the presence of class label noise, leading to increasing computational training time.
In order to evaluate the impact of class label noise on the classifier complexity, several measures, such as the class separability, have been studied in  [38]. The effect of noise presence has also been evaluated on different training conditions to study some specific requirements such as the number of training instances  [32]. Eventually, some related tasks, such as feature selection, may also be affected  [39]. Few works have proposed a detailed analysis of class label noise influence on classification tasks, and much less in remote sensing. As mentioned above, this is explained by the difficulty of having a clean real dataset or a real dataset where feature and label noise is clearly identified  [40]. To overcome such limitations, some studies have analyzed class label noise influence firstly on synthetic data, and then on real data  [38, 41, 42].
Experiments with synthetic data are needed since noise level is completely under control; whereas experiments with real datasets better represent data complexity, but are not guaranteed label noise-free. For the classification of remote sensing image time series, creating a synthetic dataset simulating realistic data is a tough task. In this study, a synthetic dataset is specifically designed to evaluate the influence of class label noise on classifier performances. It simulates vegetation profiles representing one year for ten land cover classes. More precisely, this work aims at studying RF and SVM performances in the presence of random and systematic class label noise. It focuses on the effect of training mislabeled data for satellite image time series classification on balanced problems.
Experiments on synthetic datasets are performed to corroborate obtained results on real datasets, that are composed of Landsat-8 and SPOT-4 images acquired during one year. Firstly, the random label noise problem is analyzed by considering several learning conditions. The effect of the number of classes is evaluated. Then, the impact of different input feature vectors and the number of training instances are studied for real datasets. The complexity of the learning algorithms is also analyzed to evaluate the impact of class label noise on classifier behaviors. Secondly, the influence of systematic label noise is analyzed for synthetic and real datasets. This paper is organized as follows: Section 2 details the experimental set-up, and in particular the generation of the synthetic dataset as well as the description of the noise injection procedure; Section 3 presents the classification scheme with the classifier algorithm presentation; Section 4 is devoted to results; and finally Section 5 draws the conclusion.
Data The experiments have been performed on two datasets. The first one is composed of synthetic data where class label noise is completely controlled and known. The second one corresponds to real data where instance feature vectors have been extracted from optical satellite image time series. Thus, the landscape diversity is well represented, but this dataset probably contains feature and class label noise. Both datasets cover one year describing a complete vegetation cycle, that facilitates the recognition of land cover classes such as croplands. The random noise is added to the two datasets (see Section 2. 2).
Synthetic Datasets The creation of synthetic optical satellite image time series describing the heterogeneity of the landscapes and close to reality is not a straightforward task. Although some works exist to predict surface reflectance  [43] , it is almost impossible to create realistic models ensuring that the statistical properties of the synthetic products are close to those of remote sensing images. However, some studies have shown that phenological vegetation characteristics can be modeled by using vegetation indexes, such as Normalized Difference Vegetation Index (NDVI). In the context of satellite image time series classification, NDVI has shown its ability to capture the vegetation growing  [44] , and its interest to detect phenology patterns  [45]. For these reasons, the proposed synthetic datasets are based on the generation of synthetic NDVI profiles describing vegetation classes.
In this study, it has been decided to use simulated NDVI profiles representing only one crop per year as feature vector. However, in order to create more realistic profiles, a vegetation regrowth has been simulated by adding a Gaussian function to the Equation  (1). Vegetation regrowth appears after the phenological cycle described by Equation  (1). Figure  1  displays an example of a main cycle followed by a vegetation regrowth. Finally, a uniform noise is added to Equation (1) in order to achieve a more realistic data variability. The model described by Equation (  1 ) is used to simulate the ten vegetation land cover classes that constitute the proposed synthetic dataset. There are five summer crops (corn, corn silage, sorghum, sunflower, and soy), three winter crops (wheat, rapeseed, and barley), and two forest classes (evergreen, and deciduous).
Rapeseed is a special case, which is simulated by the sum of two double logistic functions in order to reproduce rapeseed blooming. Each color represents profiles belonging to the same polygon. The vegetation regrowth simulation can be observed between DoY 175 and DoY 325. Considering the simulation procedure, the three datasets described in Table  2  are generated. These datasets are composed of different number of land cover classes since this study aims at evaluating the influence of the number of classes on classification performances in the presence of class label noise. Besides, the 2-class dataset, composed of two similar classes, will allow to study rule-based noise influence.
Real Datasets The studied real datasets have been obtained by extracting instance feature vectors from optical remote sensing images, and class label from real reference databases. Contrary to synthetic datasets, real datasets are not guaranteed label noise-free, but they better represent the land cover classification problem. In order to assess and validate results obtained on synthetic datasets, only vegetation classes have been studied in real datasets. For this purpose, images coming from SPOT-4, Take-5 experiment  [51] , and Landsat-8 satellites have been used. The available images in 2013 are displayed in Figure  3  for both sensors. The use of SPOT-4 and Landsat-8 images allows to cover almost a complete year, and thus a complete vegetation cycle. Landsat-8 images are spatially resampled at the 20 m spatial resolution of SPOT-4 images.
Both sensor images are orthorectified and converted from digital number values to top-of-atmosphere reflectances by USGS (United States Geological Survey) or Theia Land Data Center. Then, the images are converted into top-of-canopy reflectance values by using the MACCS processing chain (Multi-sensor Atmospheric Correction and Cloud Screening)  [52]. Cloudy data, identified by MACCS, are filled in with a temporal linear interpolation  [11, 53]. The French Land Parcel Information System database (Registre Parcellaire Graphique in French), has been used as reference database. This database annually maps French crop fields, which have been declared from the farmers. In this case, the used land cover classes correspond to two summer crops (sunflower and corn) and three winter crops (barley, wheat, and rapeseed).
To limit the presence of class label noise coming from the database, two preprocessing tasks have been performed. First, polygons have been eroded of 80 m, then the smallest polygons have been deleted. The total number of extracted polygons per land cover class is given by Table  3. In order to ensure that experimental configurations are comparable with those used for synthetic datasets, nbp polygons per land cover class are randomly selected in the reference database. Then, n instance feature vectors are randomly extracted for each selected polygon. Similarly to synthetic datasets, vegetation land cover classes are firstly represented by NDVI profiles computed from satellite image time series. However, more features can be used as input data in the classification scheme. Taking benefit from SPOT-4 and Landsat-8 spectral resolutions, different datasets may be extracted to enhance classification performances.
Accordingly, two other input spectral feature sets are studied: (1) spectral bands with NDVI (SB-NDVI); and (2) spectral bands with twelve spectral features including NDVI (SB-SF). Both input feature sets are described in  [54]. Increasing the number of features also allows to study the influence of different input datasets in the presence of class label noise. Table  4  presents the twelve configurations used for the experiments. As for the synthetic dataset, the total number of instances can be computed by multiplying the number of classes by n × nbp. Datasets 1 to 6 are composed of 1000 instances per land cover class, i. e. , the same number of instances than for synthetic datasets. However, this number of instances is close to the feature vector sizes of SB-NDVI and SB-SF. In these cases, the learning process can be affected by the curse of dimensionality because the size of feature vectors is close or higher than the number of instances.
Noise Injection Procedure To assess the classification results, a noise injection procedure generating artificial class label noise is required  [28, 31, 32]. The knowledge of noisy instances allows to study the influence of class label noise  [42] , and also the effectiveness of mislabeled instance detection methods or cleansing filters  [55, 56]. Random and systematic class label noises are implemented for this study. Both procedures consist in injecting artificial class label noise to the datasets created in Section 2. 1. It has been decided to generate class label noise for all the studied classes at several levels. Therefore, a x% noise level describes the percentage of instances affected by class label noise for each class. For example, a 5% noise level implies that all classes have 5% of their instances with wrong labels.
The random change considers that wrong label assignment is equiprobable between all the class labels except the original one. Thus, it prevents relabeling an instance with its original label contrary to  [23, 28]. This choice allows to have a current noise level equal to the theoretical one, which is independent of the number of classes. By contrast, the systematic label noise flips the label of corrupted instances belonging to the same class to an another class. In the case of binary classification, random and systematic label noise procedures are identical. Thus, the systematic label noise injection procedure is only applied on the 5-class datasets. Table  5  displays the corresponding flips applied for synthetic and real datasets. For the synthetic dataset, the noise class label has been selected randomly for each class.
For the real dataset, the confusions have been introduced between the winter crops (wheat, barley and rapeseed) and between the summer crops (corn and sunflower). The study of twenty noise levels ranging from 5% to 100% with 5% step is proposed. The noise will be generated for all the training datasets presented in Section 2. 1. It has been decided that each noise level is independent. Specifically, if a given instance is corrupted at 5% noise level, it does not imply that the same instance will be corrupted at 10% noise level. In the literature, the correlation between instances has not been taken into account during the noise generation. It means that traditional injection procedures operate at the instance level. Due to the specific nature of data coming from the remote sensing reference databases, this procedure can suffer from some limitations.