dataesr/scientific-paragraphs-categorization huggingface dataset:
g. sandy banks). At the modular stage, the combination of occurrence classes of Colour-Material led to a large number of potential classes (142 identified in the present study). If additional observables (e. g. texture) and similarities (e. g. endmember fractions, patch geometry) were to be computed, this number could even increase dramatically. As a consequence, the automatic definition of IDs, colours and labels for an increasing number of modular classes may become an issue. We suggest the IDs could be handled in bit flag arrays as in the quality assurance data associated with MODIS Land Products (GSFC-NASA, 2020). Bit flag arrays contain multiple flags (e. g. binary values) stored in fixed bit positions of the array depending on the characteristic they measured. The binary strings can then easily be converted in numeric decimal values.
Improving end-user and remote sensing expert knowledge Due to these operational limitations, as for now, the main advantage of ontologies may actually lie in its ability to formalize, aggregate and share expert knowledge about the symbolic definitions of land cover classes. This would firstly concern the symbolic descriptions from a remote sensing perspective. For example, similarly to spectral libraries used to store numeric knowledge about spectral signatures of target objects, we argue that our system could serve as a basis to build libraries of symbolic definitions of the representation of land cover classes in remote sensing images. Performing additional tests in other contexts would indeed make it possible to accumulate symbolic definitions of land cover classes in order to build a remote sensing expert knowledge database to be stored in ontologies.
Acknowledgments This work was supported by the  French National Centre for Space Studies (CNES)  through the  TOSCA CASTAFIOR  project (grant agreement  181670 ), by the  European Union 's  Horizon 2020 Research and Innovation Program  under the  Marie Sklodowska Curie grant ODYSSEA  (no  691053 ), by the  GUYAMAZON LandCoverMap project  (grant agreement  304459/00 ) and by the  French National Centre for Scientific Research (CNRS)  through the  International Emerging Action SCOLTEL project  (grant agreement  231438 ).
Tensile test To determine the mechanical properties, monotonic tensile tests are carried out on dog-bone specimens. Samples are designed according to ISO 6892-1 standard and manufactured using water jet cutting machine. The load is measured by a load cell of 50 kN capacity. Cauchy stress is calculated by the ratio of the load over the current section of the sample before necking. The logarithmic strain is measured by a field measuring system by 3D Digital Image Correlation (DIC) software, Aramis  [36]. To prepare specimens for DIC, the sample surface is cleaned and spray-painted with a white and black stochastic pattern using a spray can with acrylic paint. Two high speed cameras equipped with 50 mm lenses are used to acquire the images for the DIC. Tensile tests are conducted under extensometer-based strain control at a constant technical strain rate of ε = 10 -3 s -1.
For the tensile test, since experimentally the fracture was initiated from the edge, a tiny imperfection (0. 03 mm) has been done in the FE model geometry to trigger numerically the deformation localization also on the edge. The boundary conditions are applied in two different ways. For the first case (model M1), non-zero displacements (  ,   and   ) are imposed on the lower and upper sides of specimen as shown in Fig. 4-a. These values are obtained from the displacement field recorded by Aramis on the specimen surface. An automatic procedure is developed to apply the experimental local displacements to the FE model with a Python script. Such a procedure leads to a more realistic model, in which the misalignment of the specimen during the test is reproduced. For the second case (model M2), the nodes located on the lower side are clamped while those located on the upper side are moved along  axis with a smooth increasing displacement as shown in Fig.
Simultaneously, evolution of stress triaxiality  and Lode parameter  is obtained from the numerical analysis. Although, specimens are designed to achieve a constant stress state,  and  may vary during test. Therefore, to assign a specific stress state to each fracture test it is convenient to calculate the average of stress triaxiality   and Lode parameter   by the following relations: 𝜂 𝑎𝑣𝑔 = 1 ε𝑓 ∫ ε𝑓 0 𝜂 𝑑 ε𝑝 and 𝐿 𝑎𝑣𝑔 = 1 ε𝑓 ∫ ε𝑓 0 𝐿 𝑑 ε𝑝 (7) A. Kacem et al. A Python script is developed for the presented methodology. It makes it possible to determine ( ε ,   ,   ) for each specimen in the post-processing phase. The failure indicator  at the critical element can be calculated for each test through Eq. (  4 ) by using the loading history extracted from the numerical simulation of the tests and the fracture strain ε determined by the hybrid approach.
Therefore, to calibrate the fracture criterion, the fracture parameters are optimized using a generalized reduced gradient (GRG) algorithm tool by minimizing the following error function defined in the least square sense 𝐸𝑟𝑓 = 𝑁 𝑠 ∑ 𝑖=1 ( 1 -𝐷 𝑖 ) 2 (8) where   denotes the number of samples used for the calibration and   corresponds to the failure indicator of the th test which is calculated numerically through Eq. (  4 ). Three sets of experimental data are used to calibrate the fracture criterion: set 1 (SH, H-R4 and N-R5), set 2 (SH, H-R4 and N-R15) and set 3 (SH, H-R4, N-R15 and N-R5). For sets 1 and 2 the minimum number of tests (  = 3) required to identify the fracture parameters is used whereas for set 3 all fracture specimens (  = 4) are employed for calibration. It should be noted that the dog-bone specimen is not utilized for calibration and serves mainly the purpose of validation.
From state-of-the-art visualization algorithms, we distill six working principles which are, by hypothesis, sufficient to produce visual projections qualitatively similar to those obtained with these state-of-the-art algorithms. These working principles are presented through the geometrical reasoning of the classical Multidimensional Scaling algorithm, and their effectiveness is illustrated through a novel straightforward algorithm for data visualization. We show, using several datasets originated from various applications, that our algorithm can produce visual projections qualitatively similar to those obtained with these state-of-the-art algorithms. Besides, under the same motivation (of simplification), the problem of visualizing large datasets is tackled through a companion algorithm which is able to embed new input patterns.
More recently, the replacement of dissimilarities in MDS with geodesic distances imposed by weighted graphs, as in the Isometric Feature Mapping (ISOMAP)  [3]  and similar approaches, renewed the public interest in visualization tools, in a turning point when the flow of high dimensional data was growing through the Internet, in the form of images, sounds and a The associate editor coordinating the review of this manuscript and approving it for publication was Rashid Mehmood. myriad of behavioral signals easily acquired with hand-held devices such as mobile phones. In that scenario, ISOMAP adapted MDS to compare geodesic distance matrices, which allowed 2D or 3D projection of points lying in possibly curved nonlinear manifolds. In ISOMAP, as in typical MDS formulation, once all pairwise distances (e.
g. Euclidean, geodesic, L-metrics, Minkowski, rank-image) are computed, the choice of a convex stress cost function  [1]  allows the application of the Classical MDS efficiently, through eigenvalue decomposition of a double centered distance matrix  [4]. Alternatively, whenever the cost function associated to the low dimensional projection problem is not convex, the steepest descent (or gradient) method can be used instead, through computational iterations  [1] ,  [5]. That is the same approach used in the visualization algorithm Stochastic Neighbor Embedding (SNE)  [6] , proposed in 2003, which can be loosely regarded as another steepest descent version of the MDS. This new method was further improved, a few years later, becoming the state-of-the-art t-distributed Stochastic Neighbor Embedding (t-SNE, where the ''t'' comes from the Student's t-distribution)  [7] , which quickly gained broad notoriety among data analysts, in part because of its visually attractive results, with many examples of labeled datasets forming self-organized clusters corresponding to known labels.
Moreover, t-SNE was made available in many versions of programming languages, such as Python and Matlab, which possibly further boosted its popularization. More recently, new visualization algorithms such as the LargeVis, an acronym used in the paper entitled Visualizing Large-scale and High-dimensional Data  [8] , and the Uniform Manifold Approximation and Projection (UMAP)  [9]  were proposed with evident inspiration in t-SNE, as they approximately follow its recipe. Indeed, besides the graph based reasoning already used in ISOMAP, they also make use of probabilities instead of distances. UMAP further includes some elements of fuzzy models in its theoretical background. It is noteworthy that much older works based on MDS also included sounding probabilistic background, such as  [1] , but possibly the principal aspect shared by SNE, t-SNE, LargeVis and UMAP is the joint effect of: (a) a probabilistic perspective where distances between points are replaced either with conditional probabilities (in SNE, t-SNE and LargeVis), or with probabilistic norms (in UMAP), (b) and an imposed constraint of (almost) uniform density of projected points.
This vectorial perspective clearly shows that all neighbors of y i have their influence on the composition of the resultant vector determined by the difference between P i,j and Q i,j. For large values of D X , this causes a well-known problem for visualization (where D Y = 2 or 3), the crowding problem, where many points tend to be projected in the same spot because most weights tend to cluster around similar values. As an illustration, in Fig. 1  we consider Euclidean distances between image patterns from the emblematic MNIST dataset  [11]. Each image is coded as a 784D vector (28 × 28 monochromatic pixels), and we randomly selected 3000 images for this illustration. The first image is taken as x i , and 2999 distances are computed, corresponding to the first row of P, whose values are represented in the upper plot in Fig.
1 , the crowding of weights can be avoided. For instance, for the MNIST dataset, and again for the first row of P, the division of all N distances by 200 yields about 36 non-negligible entries. Unfortunately, because the density of points is rarely the same everywhere, the same scaling factor may not be suitable for all rows of P. The use of Gaussian functions to replace Euclidean distances suggests a probabilistic reasoning where P i,j can be regarded as a conditional probability of picking x j as the next sample, given that the current sample is x i. This was indeed the probabilistic framework used in  [6]  by Hinton and Roweis to propose the SNE. Besides, although SNE is not presented as a case of MDS, the application of the following three changes on MDS helps palliating the crowding problem, while it also makes MDS more similar to SNE: C1 The adaptation of a specific scaling factor for each row of P, thus yielding a constant effective number of relevant values per row.
WP3 Pairwise distances are either shrunk or expanded by a local scale factor, σ i , so that a similarity measure f X (x i , x j ) yields negligible values for far neighbors, where f X (•) is a positive Radial Basis Function with maximum at f X (0). For instance, in t-SNE f X (x i , x j ) = exp -1 2σ 2 i x i -x j 2 2. As illustrated in Fig. 1 , for the MNIST dataset, σ 1 = 200 is a local scale factor for x 1 that retains only 36 near neighbors with similarities above 1% of the maximum, and 14 near neighbors with similarities above 5%. As expected, according to (C1), for this same scale factor the corresponding Perplexity  [6]  is about 25, thus in the same range. This local distance scaling yields non-symmetrical metrics, as illustrated in Fig. 2 , where points within two regions with discrepant densities highlight the need for a symmetrization strategy.
The detail in Fig. 2  shows that the Euclidean distance d i,j is differently scaled around point x i and x j with scale factors σ i and σ j , respectively. This induces a density equalization effect, also illustrated, where the resulting average density is controlled by the Perplexity parameter, in t-SNE. On the flip side, the symmetry requirement for a metric to be a distance is violated, as  space, whereas irregularly distributed regions, such as between-clusters gaps and between-densities boundaries cannot be properly handled to yield an equalized density, as illustrated in Fig. 2. Therefore, beyond the intended dimension reduction, when D X > D Y , two remarkable effects are observed in t-SNE, namely: density equalization and density-sensitive clustering, as highlighted in Fig. 2. Note that, in this illustration there is no dimension reduction, as D X = D Y = 2, but although the original dataset has no remarkable gap, the projected data-points have a distinguishable one, d proj , resulting from the projection of cross-densities distances, whereas most points are packed in almost uniform density clusters.
These visually attractive effects can be roughly induced by the flagging of K near neighbors (KNN) for each data point (as in WP1), followed by the normalization of the volume occupied by these KNN, thus inducing local space shrinking or expansion. This raw simplification of WP3 is used in Section III. WP4 Matrix P = {p i,j } is filled with symmetrized similarities between locally scaled pairwise distances in the input dataset, X , where similarities are obtained through a given Radial Basis Function (RBF) f X : R D X → R + , and elements of matrix Q are obtained as similarities between instances of the projected low-dimensional dataset, Y, through another RBF f Y : R D Y → R +. WP5 Symmetric matrices P and Q are compared, and projected points are adjusted according to rules similar to  (5).
Besides, points in Y tend to be density-equalized, as illustrated in Fig. 2. Therefore, in Algorithm 2, except for step 1, even near neighbours of elements in X are always found through Euclidean distances between corresponding (projected) elements of Y, which is an originality of this piecewise linear interpolator. All distances in Algorithm 2 are Euclidean. The motivation for having an approximation of g 0 is two-fold: first it allows the visualization of new incoming data without any projection re-adaptation, thus g plays the role of a data compressor, or an encoder. Besides, because the current version of the SVA is not adapted to large datasets (for naive manipulation of N by N matrices P and Q may become prohibitive), Algorithm 2 can also be used to tackle large datasets, by applying SVA to a small subsample of it, and then encoding all remaining data with g.
V. EXPERIMENTAL RESULTS Most experimental results presented here are visual evidences that, with an adequate choice of the parameters, the SVA, which is a simple implementation of the WP listed in Section II, yields results visually similar to those obtained with t-SNE (which is itself a baseline for LargeVis and UMAP, as presented in  [8]  and  [9] , respectively). We start by using two publicly available datasets, MNIST  [11]  comprising of of 28 × 28 grayscale 10-class handwritten digits, and Fashion-MNIST  [12] , a more challenging dataset than MNIST, in terms of classification, although it is also composed of 28 × 28 grayscale images split in 10 classes. In Fashion-MNIST each class corresponds to a fashion product category. Both databases have two non-overlapping subsets, one labeled ''training'', with 60,000 images, and another labeled ''test', with 10,000 images.
As the standard version of t-SNE (see Section 5 of  [7] ), the current version of SVA is not adapted to large datasets. Therefore N = 3000 images were randomly drawn from each test dataset, and the same set, under the same initialization of Y was used in all experiments in this section, to yield better visual comparison of results. Fig. 3  is to be compared to the 2D t-SNE projection shown in Fig. 4 , with perplexity parameter set to 40, whereas Fig. 5  and Fig. 6  are to be  compared to the 2D t-SNE projection shown in Fig. 7 , also with perplexity parameter set to 40. Regarding Algorithm 2, Fig. 8  illustrates its use, where just 3000 images sampled from the ''test'' MNIST dataset, along with their projections were used as parameters X and Y of g. Then, all 60,000 new images from the ''training'' dataset were projected (without further adaptation of the visualization projection).
The experimental results presented in this paper were chosen as visually representative of experiments done so far. Some more results, along with suggestions of implementations of the SVA and the encoder g in some usual computer languages can be found as supplemental material posted on IEEE Xplore. https:// ieee-dataport. org/documents/supplementary-material-paperstraightforward-working-principles-behind-modern-data Visual evaluation is obviously the most usual approach for comparisons between visualization algorithms, insofar as visualization experiments are typically concerned with subjective (visual) aspects of classes and clusters dispersion, hardly replaced with any objective index. One may even conjecture that visualization algorithms are popular because there is not yet an objective index capable of replacing human cognition.
Nevertheless, by considering that the goal of all visualization algorithms considered in this work (including the SVA) is to preserve as much as possible the local neighboring structure of points before and after projection, and knowing that it can be a very difficult goal for points lying in manifolds with local dimensions much higher than 2 or 3, we crafted a simple index, namely, the Near-Neighbors Coincidence Rate (NNCR), which is computed as in  (9). C(X , Y; V ) = 1 N × V N n=1 |X n ∩ Y n | ( 9 ) where V is an index parameter representing the number of near neighbors to be considered, X n stands for a subset of X whose elements are the V near neighbors of x n. Like- To test this new measure, we consider four public datasets whose points represent very diverse signaling phenomena. We used the following constant parametrization of methods across all next experiments, to allow better comparisons of results: • t-SNE: Perplexity = 30.
• UMAP: n = 30 (the number of neighbors), mindist = 0. 1 (desired separation between close points in the embedding space) and nepochs = 200 (number of training epochs to use when optimizing the low dimensional representation). • SVA(a): K = 30, R η = 3, η = 0. 1 and f T 2 (r) = 1 1+r 2. • SVA(b): K = 30, R η = 3, η = 0. 1 and RBF f UMAP (r) = 1 1+ar 2b. In all experiments, points were projected into R 2 , and the number of iteration for t-SNE, SVA(a) and SVA(b) was set to 1000. Fig. 9  illustrates one projection with each algorithm of the emblematic Iris dataset used in  [13] , with 150 4D vectors numerically representing sepal and petal measurements (length and width) for flowers from 3 species, namely: Iris setosa, Iris versicolor and Iris virginica. Thus, data points were labeled here with Setosa, Versicolor or Virginica.
For the second set of comparative experiments, we took the recently published dataset explained in  [14] , here referred to as Meat volatiles, where an array of 10 sensors (8 Metal Oxide gas sensors plus temperature and humidity sensors), i. e. an e-nose was used to acquire multivariate signals through time from 7 controlled mixtures of beef and pork, (always 100 g of fresh ground meat per acquisitions sessions of 120 s). In this dataset, only 60 instances of each mixture are available, but each instance corresponds to a sequence of 60 10D measurements vectors taken every 2 seconds. Thus, from this dataset we randomly drawn 3000 measurement vectors and projected them from 10D into 2D, as illustrated in Fig. 10. A fine analysis of each dataset is beyond the scope of this paper, where the comparison between 2D projections across methods is the main concern.
However, it is worth noticing that all projections in Fig. 10  seem to present the same inconsistency, namely: that similar proportions of beef and pork are not projected in near clusters. As for this matter, one should be aware that, for e-noses based on Metal Oxide sensors, robust feature extraction from raw signals is yet a relevant research subject. In any case, in spite of these apparent raw signal inconsistencies, all four projection in Fig. 10  are in agreement with each other. Fig. 11  illustrates one projection per algorithm for the dataset here referret to as Newsgroups, 2 where each of 16242 postings (texts in natural language) is encoded as a 100D binary vector, where the occurrence for 100 relevant words (e. g. cancer, baseball, car, children) is flagged with 1. Thus, each binary vector is labeled with comp.
*, rec. *, sci. * or talk. *, corresponding to the group name in which it was posted. For the projections presented in Fig. 11 , 3000 vectors were randomly drawn along with their corresponding labels. Finally, a public dataset of male and female clean-speech utterances in Brazilian Portuguese  [15] , was used to yield 19 Mel-Frequency Cepstral Coefficients (MFCC) per short speech frames of 25 ms, taken from all utterances, from 2 Also labeled as ''20 Newsgroups,'' and publicly available at https://cs. nyu. edu/roweis/data. html. all speakers. The first element of each MFCC vector was systematically discarded (for it does not carry relevant acoustic information), thus yielding around 200,000 18D MFCC vectors, from which only 3000 were randomly drawn and labeled according to the corresponding speaker gender.
In this paper, this dataset is referred to as Speaker gender, and its projection in 2D is presented in Fig. 12. The NNCR for all 16 projections (4 per dataset) are gathered in Table  1. As compared to the corresponding visual aspects, the NNCR seems to yield meaningful comparative values. For instance, for the datasets Iris and Meat volatile, most clusters concentrate unmixed classes, and NNCR values above 0. 7 confirm that, on average, more than 70 % of the local structures in the corresponding original datasets were preserved. This further suggests that the corresponding underlying manifolds in Iris and Meat volatile datasets are more easily projected into 2D than the ones in the Newsgroup and the Speaker gender datasets, where only less than 45% of the local neighboring structures were preserved.
VI. CONCLUSION State-of-the-art visualization approaches are based on elaborated probabilistic and fuzzy models. By contrast, in this work we assume that a few simple working principles would be sufficient to yield similar results, which was corroborated by experiments done with an algorithm where these principles were straightforwardly implemented. This algorithm was applied to several public datasets corresponding to various application domains. The proposed reduction to simple principles has a first useful aspect in terms of potential boosting of new developments in visualization tools, because the simplicity of the six listed working principles allows for new contributions and improvements from researchers with a broad range of different backgrounds. For instance, we observed that the choice of an RBF, f Y , is not restrained to probability distributions, and the knowledge of the exact cost function (and its gradient) is not imperative for a visualization result qualitatively similar to that yielded with t-SNE.