dataesr/scientific-paragraphs-categorization huggingface dataset:
applyAnalysis (R2): The chosen analysis method is being applied. This algorithm will transform activation map values while keeping the multidimentional aspect of the matrices. getModelPrediction (R3): The model predictions are collected to label data flows during the visualization encoding. buildSimilarityMatrix (R3, R4): In order to cluster the data, it is necessary to first vectorize each element of the evaluation dataset into their n-dimensional space imposed by each layer of the model. For example, a matrix M of size 16 × 16 × 64 resulting of a convolutional layer will be vectorized into V as: V = [M 1,1,1 , M 1,1,2 ,. , M 1,1,64 , M 1,2,1 ,. , M 16,16,64 ] T. Those vectors can be compared to each other using a similarity metric. Measuring similarity of one vector against each other builds up a similarity matrix which will be used to cluster data.
Instead, a KNN approach is presented, which will filter out low weighted edges from dense communities, while keeping the connexity of the graph. As for the k factor of the KNN algorithm, it was arbitrary considered that a pattern could not be similar to more than D/N other samples, D being the dataset size and N the number of different classes present in the evaluation dataset. The edges filtered out by KNN were set at a weight of 0. applyMCL (R3, R4, R5): The final operation is to cluster the graph in order to obtain a list of clusters and their composition. Along with the prediction data computed earlier and the evaluation dataset, there is enough information to trace how the evaluation data Algorithm 2 Visualization construction procedure DRAWDATA(C, pred, gt) % Parameters: % C: clusters grouped by layer belonging % pred: predictions given by the model % gt: ground truths of the evaluation dataset C[ pred ] ← generateClusters(pred) C[ gt ] ← generateClusters(gt) G ← buildDAG(C) G ← orderDAGVertices(G) G ← mergeEdgesIntoFlows(G) drawFlows(G ) end procedure was processed by the model.
CASE STUDIES This section sets out several realistic use cases to validate the method. They rely on two distinct convolutional neural networks for classification: -A simple model inspired from  LeNet5 (LeCun et al. , 1998)  which is a fairly popular, simple and efficient model designed to recognize handwritten digits. It serves as an example to illustrate the proposed method. -An adapted version of VGG16  (Simonyan and Zisserman, 2014)  to work on 32 × 32 pictures. It is more complex and has been designed to classify the ImageNet dataset with high accuracy  (Krizhevsky et al. , 2012) , which is featuring thousands of different classes out of 14 million pictures. Since training such a model has a high computational cost  (Simonyan and Zisserman, 2014) , convolutional layers of the original model were resized to work with the MNIST dataset while keeping the training results of ImageNet (ie.
neuron weights). Model training and evaluation were done on Ten-sorFlow  (Abadi et al. , 2015)  on an nVidia GeForce GTX 1080Ti using the Keras API  (Chollet et al. , 2015). The computer cluster is composed of 51 machines for a total of 2. 7TB RAM, using Hadoop for data transfers and Spark for task distribution, without optimizations such as efficient memory and computing resources management. The clustering process uses the MCL program proposed by its creator  (Dongen, 2000). Finally, the visualization process is implemented as a Web application using the HTML Canvas API. A demonstration of this interface can be found at http://pivert. labri. fr. Table  1  summarizes the performance results of the various scenarios experimented. Scenario 1: LeNet5 trained and evaluated on MNIST. This illustrative scenario aims to explain how this visualization method helps to understand inner work of a classification model and to determine which classes of the dataset are easier to classify than others.
By looking at the previous layer, it can be seen that the convolutional layer is incorrectly splitting those items leading the Dense 128 into errors. Scenario 2 : LeNet5 and Fashion-MNIST. The same experiment has been run using the Fashion-MNIST  (Xiao et al. , 2017)  dataset. It is a proposed as an alternative to the classic MNIST dataset, featuring clothing pictures instead of handwritten digits; they share the same input and output shapes and number of classes in order to be interchangeable and is supposed to be more complex. The model was trained with 60000 samples and evaluated with 10000 samples, and reached an accuracy score of 87. 9%. Results are not shown due to space issues but are available online. They prove the system works by giving a result similar to the previous scenario with more mixed clusters toward the end of the model.
Looking at the convolutional layers shows that data was less sparse before reaching the Dense layers. Scenario 3 : Detection of bad model -LeNet5 model trained with MNIST and evaluated on Fashion-MNIST. The model was trained to achieve high accuracy on MNIST and is expected to fail on Fashion-MNIST because of the different nature of the processed data. In this case, we use the visualization results to analyze the behavior of the proposed method in a worst case scenario (5. 6% accuracy). Figure  3  depicts the visualization result; if differs greatly from the others by the number of clusters generated and drawn. Furthermore, processed data doesn't seem to be equally distributed across computed clusters despite the balanced composition of the training dataset. When looking at the convolutional layers, it seems that a few visual traits have been identified by the model, but wrongly associated with the classes in the later Dense layers.
Scenario 4 : Simplification direction for complex models -VGG16 with MNIST. To adapt the model to the MNIST dataset, we applied some modifications on both VGG16 and the MNIST dataset: (i) MNIST images are considered to be colored image by duplicating the gray channel, (ii) MNIST images are padded to use a shape of 32 × 32 × 3 in order to avoid issues with the latest pooling operation of VGG16 (pooling area larger than the input tensor), (iii) end of the network has been modified to classify 10 classes instead of 1000, (iv) only this latest layer is trained, while the weights of the other layers are transferred from public ImageNet training. These steps do not replace a full training process of VGG16 on the MNIST dataset, but it still gives us an accurate enough model with an accuracy score of ≈ 97%.
Since VGG16 is more complex than the previous model, we assume there are unnecessary computations in the model to achieve similar accuracy results. With this experimentation, we expect to see early merged data fluxes in our visualization, meaning that the data is being overprocessed since the activation maps are already similar enough to be predicted as a same class. Figure  4  presents the results. The higher number of axis displayed is justified by the model's higher complexity. Using transfer learning, although those layers have been trained on ImageNet, the first convolution layers have nicely discerned a majority of classes except of the 5/3, 4/9 and 0/6 couples, which is a behavior really similar to LeNet5. The classification then get stagnant with both improvements and regressions at each pooling operation.
As the current visualization system gives good hints on the inner working of a model, experts may need to access more low-level and detailed information about the classification. Usage of distributed computing infrastructure is not a long-term solution to R1 and R2 when using distance matrix computation, since its complexity is quadratic and thus will be an issue when processing very large evaluation datasets and/or models. Concerning clustering quality, the method used in the previous scenario, namely cosine similarity, presents a few unsatisfactory clustering results, such as the difference between the decision layer's clusters and the actual predictions made by the model. An extensive study on combining similarity and cluster computing method would surely improve the method results. The current flow encoding is limited by the color palette and could lose in efficiency in the case of complex classification networks recognizing numerous classes.
Data collection and processing procedure PREPAREDATA(M, D, f ) % M: a DNN to inspect % D: an evaluation dataset % f : an analysis function % act, res, pred,C: empty associative lists for all x ∈ D do act[x] ← getActivationMaps(m, x) res[x] ← applyAnalysis( f , act[x], m) pred[x] ← getModelPrediction(m, x) end for for all L I ∈ M. layers do V ← ∀x ∈ D : res[x][L I ] M ← buildSimilarityMatrix(V ) M ← applyKNN(M, k) C[l] ← applyMCL(M ) end for return (C, pred) end procedure.
Algorithm 1 1 Data collection and processing procedure PREPAREDATA(M, D, f ) % M: a DNN to inspect % D: an evaluation dataset % f : an analysis function % act, res, pred,C: empty associative lists for all x ∈ D do act[x] ← getActivationMaps(m, x) res[x] ← applyAnalysis( f , act[x], m) pred[x] ← getModelPrediction(m, x) end for for all L I ∈ M. layers do V ← ∀x ∈ D : res[x][L I ] M ← buildSimilarityMatrix(V ) M ← applyKNN(M, k) C[l] ← applyMCL(M ) end for return (C, pred) end procedure.
, (k -1) and Y i (t s ) = 1 for s = k and then the time to event is t i ∈ I k = (t (k-1) , t k ]. As a motivating study we consider the Tandmobiel study which is a longitudinal prospective oral health study conducted in Flanders (Belgium) from 1996 to 2001. A cohort of 4430 randomly sampled school children who attended the first year of the primary school at the beginning of the study were examined annually (6 times). The response was time to the emergence of the permanent upper left first premolars (tooth 24 in European dental notation). When emergence occurs between annual follow-ups the exact time of emergence is not known and the time to the emergence is said to be interval censored. Modelling such data presents a variety of challenges. MacKenzie and Peng (2013) developed interval censoring methods for parametric models, some of which were non-PH and they compared the use of standard right censored likelihoods based on midpoints with interval censored likelihoods.
Data analysis We analysed a subset of data from the Signal Tandmobiel study. Following other authors (e. g. ,  Gómez et al. (2009) ), time to emergence, T , was measured as "child's age minus five years" (i. e. , age -5) since emergence of pre-molars does not occur before age five; more generally, of course, this threshold parameter could be estimated. Two covariates were analysed, namely, sex, where 0 = boy (52%) and 1 = girl (48%), and dmf, where 0 (57%) indicates that the primary predecessor tooth was sound and 1 (43%) indicates that it was decayed, missing due to caries, or filled. Gómez et al. (2009)  excluded 44 (1%) school children in whom the dmf status was unknown thus leaving 4386 children for our analysis. It should be noted that a more extensive data set from the Signal Tandmobiel study has been analysed by  Bogaerts et al.
(2002) ,  Lesaffre and Komárek (2005)  and  Komárek and Lesaffre (2009). We investigated four covariate structures: (I) sex only, (II) dmf only, (III) sex and dmf together, and (IV) sex and dmf together along with their interaction term. Each of these covariate structures were included in the six different model types designated by: PH, PHF, PHDM, MPR, MPRF, MPRDM (see Table1). Once the best-fitting model type is identified (using the mean AIC averaged over covariate structures as a guide), covariate 0. 30 0. 09 0. 33 -0. 10 0. 06 -1. 55 † The true parameters: λ = 2. 0, β 1 = 0. 5, β 2 = 0. 3; α = 2. 0, α 1 = 0. 25, α 2 = -0. 1. Thus, there are 24 initial models in total defined by the combination of four covariate structures in each of six model types. These models were fitted to the data using a specially written R programme (R Core Team, 2018) which called the routine nlm to maximize the likelihood function (3.
Experimental and pseudo-experimental data GENERIC learns the sloshing dynamics of the liquids from the measurements of the state variables at discrete time steps. We have obtained pseudo-experimental data from simulations We assume the existence of a slow manifold M on which each fluid lives. We extract synthetic data as vectors in R D from computational simulations. These data are possibly noisy, see the zoomed detail. An example sloshing phenomenon is represented as the red line in phase space. Given the inherent high-dimensionality of the manifold, nonlinear dimensionality reduction techniques will also be applied. This will project the data to a lower dimensionality embedding space in R d , with d � D. We develop structure-preserving integration schemes to integrate the evolution of the system in this low-order manifold.
These are then mapped back to the physical space in R D so as to obtain meaningful results. https://doi. org/10. 1371/journal. pone. 0234569. g001 performed by employing Smoothed Particle Hydrodynamics (SPH,  [35] ) for training and test. Once it reaches the test phase, the twin learns previously unseen trajectories from experimental data. Here, we generalize the scope of our first work  [4]  to identify the dynamics of a wider database. It has been specifically constructed with pseudo-experimental results of water, glycerine, butter, honey, mayonnaise and chocolate. Our intention is to cover different viscosities and densities, as well as behaviors. The different fluid constitutive models are sketched in Fig 2. Chocolate, mayonnaise and blood are considered shear thinning  [36]  [37] [38]  [39].
We have selected the Herschel-Bulkley model  [40]  to reproduce their rheology. It follows the next expression: τðtÞ ¼ k _ g n ðtÞ þ τ 0 ; in which τ is the shear stress, k the consistency index, _ γ the shear rate, n the flow index, and τ 0 the yield stress. We have simulated four different sloshing trajectories for each liquid assuming Smooth Particle Hydrodynamics discretization  [35] , according to the parameters in Table  1. This approach provides discrete data of the properties of each particle. Data have been extracted from snapshots taken every 0. 005 seconds to capture the important features of the dynamics and avoid the effect of overfitting as well. When learning Newtonian fluids, we only need the position r j , velocity v j and internal energy E j of each particle at discrete time instants.
When running the digital twin, this information comes from the scene. We make use of computer vision techniques to track the movement of the glass. For these purpose, we have added texture to it to track its features. See the details in the Appendix. This information has to be converted to an interpretable input for the integrator. The simulations of the database have been obtained by defining different input velocities of the glass to trigger the sloshing. Therefore, we relate the initial state of the virtual fluid with the tracked velocity of the container as an interpolation. With this information, we can perform the computation of the next state of the liquid. There are some features of the algorithm that also require data acquisition of the free surface. Albeit the use of sensors is widely spread, image analysis is an attractive option for experimental data acquisition.
Fluid clustering The digital twin should be able to mimic the behavior of any type of fluid, not necessarily in the database. Then, in future applications, it must perceive and recognize the fluid as well as explain what it is watching in understandable terms for a human. This is called interpretable machine learning  [46]. We expect to classify the fluid with only a few observations and, knowing which fluid it isor interpolating between the closest neighbors in the phase space-, make the calculations in the appropriate reduced order manifold. The high dimensionality of the problem would make unfeasible to perform the classification as fast as the application requires. We address this problem by applying model order reduction techniques. This allows us to perform the classification in a lower-dimensional manifold.
Dimensionality reduction is a common preprocessing step for classification tasks. This process entails a noticeable time reduction in the classification. In addition, if the dataset has a We choose again k-PCA to perform the reduction of our problem  [31]. k-PCA enables us to project the data onto a low dimensional manifold. In our case, and despite the smooth decay in the eigenvalues, see Fig  5 , some 3 dimensions have shown to provide with good clustering results. The different types of fluids remain clustered in the new projection, as can be seen in Fig 6. k-PCA is able to unveil the features that make the behavior of each fluid unique with respect to the others. We expect this fact to be advantageous for the classification process. In our case, we employ random forests  [47]  for classifying our dataset.
This technique consists of constructing several decision trees in different subspaces of the training set to generalize the classification and, as a result, avoid the overfitting that usually appears in single regression tree techniques. We also apply k-fold cross validation as part of the learning process. The method suggests to split the database into two parts, one assigned for training and the rest saved for testing. This process is repeated iteratively k loops, changing the distribution data of training and test sets, to improve the fitting. We need enough data to recognize the underlying trend, but we also need to leave sufficient for testing so as to avoid high variance error. According to this criteria, we establish a relation of 80% of snapshots for training, and 20% for test, in our algorithm.
Understanding the detailed timing of crop phenology and their variability enhances grain yield and quality by providing precise scheduling of irrigation, fertilization, and crop protection mechanisms. Advances in information and communication technology (ICT) provide a unique opportunity to develop agriculture-related tools that enhance wall-to-wall upscaling of data outputs from point-location data to wide-area spatial scales. Because of the heterogeneity of the worldwide agro-ecological zones where crops are cultivated, it is unproductive to perform plant phenology research without providing means to upscale results to landscape-level while safeguarding fieldscale relevance. This paper presents an advanced, reproducible, and open-source software for plant phenology prediction and mapping (PPMaP) that inputs data obtained from multi-location field experiments to derive models for any crop variety.
This information can then be applied consecutively at a localized grid within a spatial framework to produce plant phenology predictions at the landscape level. This software supports the development of process -oriented and temperature-driven plant phenology models by intuitively and interactively leading t he user through a step-by-step progression to the production of spatial maps for any region of interest. Maize (Zea mays L. ) was used to demonstrate the robustness, versatility, and high computing efficiency of the resulting modeling outputs of the PPMaP. The framework is implemented in R, providing a flexible and easy-to-use GUI interface. Since this allows appropriate scaling to the larger spatial domain, the software can effectively be used to determine the spatially explicit length of growing period (LGP) of any variety.
Introduction The recent rise and evolution of data analytics have greatly modernized the worldwide agriculture environment thereby improving the efficiency of monitoring farming environments  [1, 2]. Mathematical and statistical modeling tools embedded within computer programs and packages have been used intensively over the last decade with the intent to enhance agricultural production at scale  [3] [4] [5] [6] [7] [8]. The output of such technologies has revolutionized the empirical optimization of production and accurate predictions of output which has aided in precision agriculture planning and management  [7, 9, 10]. This paper contributes a reproducible and practical software capable of providing plant phenological phase period prediction and mapping (PPMaP). The PPMaP package, freely available at https://github.
The modules with which the PPMaP software was developed w ere cognizant of the nexus between stages of plant development and the various variables that influence each stage. Plant development denotes the scheduling of occurrences in the life cycle of a plant that can be described as the increase in weight, volume, length, or area of some of the parts or the whole plant  [11]. These plant growth and developmental processes are used to delineate the phenological stages of a crop. However, for modeling purposes, it is essential to separate the two main processes i. e. rate of biomass accumulation and the length of growth, as they are affected by different environmental variables even within intra-species  [12, 13]. On one hand, the rate of biomass accumulation is primarily determined by the amount of light captured by plants over a range of temperatures, whereas the length of growth for a specific variety is typically dependent on daily temperatures.
For instance, the complex role of genetic factors in determining the performance of genotypes in different environments and selecting superior genotypes in target environments was demonstrated by  Dia et al. (2016)   [7]. In their study, the Genotype x Environment int eraction (G×E) analysis was applied to describe the stability of genotypes and the response of crop in a multiplication context. This method helps to estimate the statistical parameters which guide on the selection of genes that have more adapted environmental and agronomic traits  [7]. Additionally, other several applications and online tools for plant image identification, analy sis, and sharing of leaf images to interpret and predict potential yield have been proposed  [10, 24, 25]. All these tools provide mechanisms to handle large datasets and further facilitate the distribution of information among the growing scientific community.
Additional examples of efforts and software that were developed to improve agricultural modeling include the CN-CLASS  [21]  that was initially developed to study Carbon (C) stock in forest ecosystems but was later modified to link crop phenological development and C allocation during the growth of maize. Also, CropScape is a w eb service-based application for discovering and disseminating geospatial cropland data products for decision making  [4]. Other software include the LEAF-E that was developed to analyze plant leaf growth through function fitting, while TIPS is an automated computer system for processing image-based phenotyping of maize tassels  [26]. However, the weakness of all these methods is that they generalize and facilitate the extrapolation of the potential areas for the optimum growth of the variety based on the known genotype, thus missing the fundamental location-specific parameters.
Therefore, we introduce new software that solves the limitations of the existing phenology determining platforms. The PPMaP is a framework that enables multi-location field experiments for plant phenology to derive temperature-dependent models for any crop variety and then provide a grid specific recommendation domain for the variety. This enables the successful extrapolation of the length of growing periods (LGPs) for any varieties with high levels of accuracy with the lowest potential risk of failure  [14]. This software also counters the traditional methods in which breeders find the best varieties by planting them in a diverse set of locations to measure performance over many seasons. The number of locations that these breeders can test the new varieties is however limited and can cause uncertainty when trying to choose the best genotypes for farmers  [27, 28].