dataesr/scientific-paragraphs-categorization huggingface dataset:
Indeed, very limited regions in the compositional space have been explored and experimental screening alone would be formidable. Numerous computational methods have been developed to predict the stability of single-phase solid solutions. Early models follow the Hume-Rothery theory  20, 21  and rely on simple descriptors such as atomic radius mismatch and tabulated mixing enthalpy to induce the empirical rules for the formation of multicomponent solid solutions  [22] [23] [24] [25]. More sophisticated models additionally take into account the free energy of IM compounds  [26] [27] [28]  , but are still oversimplified in that the IM phases are hypothetical and different definitions of the competing IM phases can lead to diverging predictions  25, 29. The CALPHAD (calculation of phase diagrams) method has been used to determine the phase formation of HEAs  [30] [31] [32]  although reliable thermodynamic databases are currently limited to a small number of elements  33.
Computational model and validations The thermodynamic stability of an alloy at a given temperature and pressure results from the competition between the Gibbs free energy of all competing phases. Here we use a regular solution model for all solid solution phases. The regular solution model combines an enthalpy model with a quadratic dependence in composition with an ideal configurational entropy (see Methods). We have previously shown that binary enthalpic interactions are sufficient to reproduce the mixing enthalpy of higher component (quaternary and quinary) random solid solutions  47. Within this model, the Gibbs free energy of any random solid solution can be computed from a series of binary interactions that can be fitted, for instance on DFT. We have built such a database for a set of 40 elements using the special quasirandom structure (SQS) approach  48.
Using these regular solution Gibbs free energies, the competition between all phases can be assessed with the convex hull construction which directly compares the free energy of a phase versus any linear combination of its subsystems. We additionally include competition from ordered, IM phases up to ternaries as provided by the AFLOW database  49. We assume no configurational entropy for the IMs as they have well-defined occupancy of the lattice, thus bearing no configurational degree of freedom. More computational details are provided in the Methods section and our database of regular solution enthalpic parameters are available via an online repository  50. The convex hull construction can be used to compute if an equimolar solid solution is stable for a given combination of elements. Our enthalpic model refrains from using any experimental parameters and is therefore fully ab initio.
Nevertheless, the solid-solution phase formed at high temperatures can still be retained at room temperature following normal cooling rates  52. So, the requirement to form a high-entropy single-phase equimolar solid solution will be here to show a (reasonable) temperature at which this single-phase is predicted to be stable according to our thermodynamic model. To validate the predictive power of our model, we use 134 equimolar quaternary and quinary alloys that have been synthesized and structurally characterized experimentally  [53] [54] [55]. This dataset includes 73 single-phase HEAs (Supplementary Table  2 ) and 61 multi-phase alloys (Supplementary Table  3 ). We use our Gibbs free energy model to see if a single-phase or multi-phase is predicted and if it agrees or disagrees with the experimental report.
We find our model attaining a predictive accuracy of 74% at the optimal T = 1350 K (Table  1  and Supplementary Table  2 ). Specifically, our model predicts correctly 70% of the single-phase HEAs and 79% of the multi-phase alloys, suggesting that the model performs equally well regardless of the actual phase. To put our model in perspective, we apply four empirical rules (ERs)  [22] [23] [24] 56  and two free-energy models  26, 27  developed previously to the same alloy dataset. In addition to the common criteria such as mixing enthalpy and entropy, the ERs rely mainly on atomic size mismatch whereas the two FEMs account for the formation of competing IMs (Supplementary Table  1 ). Notably, our model consistently outperforms all the ERs and the FEMs as shown in Table  1. Only  he ER1 22 achieves a higher TPR, but this comes at the cost of a markedly high FPR, showing that the model is strongly skewed towards the formation of single-phase solid solutions.
If we make no distinction between FCC and HCP and treat the two simply as close-packed (CP), the accuracy is further improved to 84%. Therefore, our model is more capable of predicting if a HEA is BCC or CP (FCC or HCP) as we will discuss more later. In summary, our regular solution model is at least as effective as previous models and rely on a physically-driven approach based on DFT. It will therefore likely extrapolate better than approaches trained on a small dataset.
Chemical map of high-entropy alloys We now set out to navigate the huge chemical space of quinary alloys from the combination of 40 elements. To set ourselves in the best scenario for the formation of single-phase solid solutions, we choose here T = 0. 9T m so that the entropic mixing contribution is maximized. As outlined before, we consider that HEA formed at high temperature can be quenched to room temperature preserving their single-phase nature. When tested with the same validation dataset, our model at 0. 9T m shows a high TPR of 84% but an FPR of 62%. The high TPR is more relevant in the current context of finding new HEAs. Applying our model to the 658,008 possible equimolar quinary alloys, we find 30,201 potentially stable HEAs at T = 0. 9T m , which amounts to 4. 6% of the quinary candidates.
These BCC refractory elements, when intermixed, consistently retain the BCC structure. FCC elements such as Al, Ga, or Pb favor as much BCC as CP structures despite their CP nature as elements. A similar effect is seen with HCP elements such as Zr, Hf, Ti, and Re. On the other hand, Mn, Os, and Ru are among the elements that are outstanding HCP formers, whereas Ag and Au are more likely to be found in FCC solid solutions. Apart from mixing energetics, the formation of HEAs is also determined by melting point and IM formation. A high melting point will offer the possibility to entropically stabilize the solid solution through a high synthesis temperature. This is especially important when strong IM formation could destabilize the solid solution. To clarify the statistical importance of these three factors, we perform a principal component analysis (PCA) on the quinary HEAs dataset (Fig.
The 16-atom SQS structures for the FCC, BCC, and HCP structures used in this work are generated by the ATAT suite of software  74  , whereby pair (triplet) interaction up to the 6th (3rd) nearest neighbor are taken into account. This Gibbs free energy of mixing is defined for a given structural lattice and computed on FCC, HCP, and BCC lattice. For the construction of an energy convex hull, the Gibbs free energy is used and can be easily obtained from ΔG mix ΔG = ΔG mix + X i c i E i : ð4Þ The convex hull analysis is carried out using pymatgen  75.
Competing intermetallics For a given quinary alloy, we search all its binary and ternary compounds using the AFLOW ICSD and LIB collections of IMs. We construct a convex hull of formation energy for the available IMs for a specific binary or ternary composition, from which the stable compounds and the unstable compounds with an energy above the hull of less than 10 meV/atom are chosen for a refining DFT computation using the same parameters as for the solid solutions. The 10 meV/atom cutoff threshold takes into account the uncertainties arising from the differences between the computation parameters (e. g. , pseudopotentials, kinetic energy cutoffs, and k-point samplings) used by the AFLOW dataset and our present calculations. Supplementary Fig. 3  shows that the threshold of 10 meV/atom suffices to include as many stable IMs as the numerical uncertainty of the formation energy is indeed typically within this value.
Acknowledgements The research was funded by the  Walloon Region  under agreement No. 1610154 -EntroTough in the context of the 2016 Wallinnov call. Computational resources were provided by the  Consortium des Équipements de Calcul Intensif (CÉCI) , funded by the  Fonds de la Recherche Scientifique de Belgique (F. R. S. -FNRS)  under Grant No. 2. 5020. 11and by the  Walloon Region. The present research benefited from computational resources made available on the Tier-1 supercomputer of the  Fédération Wallonie-Bruxelles , infrastructure funded by the  Walloon Region  under grant agreement No. 117545. G. H. acknowledges support as well from the  U. S. Department of Energy, Office of Science, Office of Basic Energy Sciences   Established Program to Stimulate Competitive Research (EPSCoR) program  under Award Number  DE-SC-0021347.
Medical diagnosis research has recently focused on feature selection techniques due to the availability of multiple variables in medical datasets. Wrapper-based feature selection approaches have shown promise in providing faster and more cost-effective predictors. However, selecting the most relevant features from medical datasets to increase disease classification accuracy remains a challenging research issue. To address this challenge, we propose an effective wrapper-based feature selection approach called BTLBO-KNN. It combines an improved Binary Teaching-Learning Based Optimization (BTLBO) algorithm with the K-Nearest Neighbor (KNN) classifier to accelerate the convergence rate in finding the near-optimal features subset. BTLBO-KNN incorporates two new efficient binary teaching and learning processes, an abandoned learner's replacement mechanism, and a teacher knowledge improvement method.
I. INTRODUCTION Feature selection approaches are pre-processing mechanisms in the data-mining process to select the optimal subset of features among all the existing ones. It eliminates irrelevant, redundant, and noisy features, keeping only the relevant and prominent features for subsequent data-mining tasks such as classification and regression in supervised learning  [1]. This selection process leads to effective machine learning models with high prediction accuracy. Furthermore, reducing the potential dimension of the datasets improves the processing efficiency  [2]. One can categorize feature selection methods into filters, embedded, and wrapper techniques  [3]. Filter techniques determine the relevance of the selected features independently of the learning technique. They The associate editor coordinating the review of this manuscript and approving it for publication was Santosh Kumar.
In  [14] , the authors propose a new feature selection approach based on the Genetic Algorithm (GA) combined with the back-propagation neural network classifier to select the most relevant and significant features in skin tumor diagnosis. The work of  [21]  uses Particle Swarm Optimization (PSO) to solve the feature selection problem in liver and kidney disease diagnosis. Moreover, the PSO hybridized with the non-parametric kernel density estimation-based classifier is also used to diagnose breast cancer disease in  [22]. The Moth Flame Optimization (MFO) algorithm combined with the KNN algorithm is applied to 23 medical datasets for medical diagnosis in  [23]  and 07 medical datasets with different sizes in  [9]. In  [2] , the authors introduce an improved Binary Dragonfly Algorithm (BDA) to escape local optima in a wrapper-based approach for the feature selection optimization problem.
Generally, these algorithms look into an excellent global search ability and fast convergence to maximize the intelligent system to generate feature subsets with improved diagnostic performance. In  [34] , the authors propose a feature selection approach using binary TLBO to improve the diagnosis performance of malignant and benign tumors for breast cancer disease. It requires only common control factors, such as the population size and the number of generations. They investigate various classifiers, including KNN, SVM, Naive Bayes, and Decision Tree. Results show that the classification accuracy is higher using the uncovered reduced feature sets instead of the original ones. A feature selection method based on an adaptive TLBO algorithm is proposed in  [35]. Features are extracted by an advanced gray-Level co-occurrence matrix, which retrieves texture, shape, and intensity-based features in the public Mammographic Image Analysis Society dataset.
2) Proposal of two new efficient binary teaching and learning processes based on binary logical operations to update the learners' knowledge, reducing computational cost for BTLBO-KNN. 3) Integration of an abandoned learner's replacement mechanism to enhance the diversification ability of BTLBO-KNN and prevent it from falling into local optima. 4) Utilization of a teacher knowledge improvement method to balance exploration and exploitation searches, and accelerate convergence rate. 5) Performance evaluation of the proposed BTLBO-KNN on real-world COVID-19 dataset, and 23 geneexpression and medical datasets from UCI and ASU repositories, including a comparison with recent stateof-the-art wrapper-based feature selection approaches. The remainder of this paper is organized as follows. Section II presents a literature review of relevant feature selection approaches.
More specifically, it discusses swarm and evolutionary optimization algorithms for medical diagnosis and related works on binary versions of the canonical TLBO algorithm. Section III introduces the basic TLBO algorithm for developing the proposed wrapper-based feature selection approach. Section IV describes its design in detail. Section V reports the comparative analysis of the proposed BTLBO-KNN with some recent state-of-the-art wrapperbased feature selection approaches on real-world datasets. Finally, Section VI presents the conclusion and some perspectives for future research.
propose an enhanced MFO algorithm as a search strategy within a wrapper feature selection framework to improve classification tasks in medical applications. It includes two stages of enhancement that aim to increase the diversity of the algorithm and support the exploration of the search space. This approach significantly outperforms other well-known wrapper and filter-based methods across multiple medical datasets. The paper also conducts an extensive investigation of the parameters and studies the effects of different settings on the performance of the feature selection process. Results of various comparisons reveal a significant impact of the LéB)vy flight operator and transfer functions on the performance of MFO. Sheikhpour et al. [22]  hybridized the PSO and the non-parametric Kernel Density Estimation (KDE) based classifier for diagnosing breast cancer disease.
[24]  propose a wrapper feature selection approach with and without incorporating a Greedy Crossover (GC) operator strategy to enhance the features' selection in medical diagnosis data. They performed experiments with 24 medical datasets, including a COVID-19 dataset. CHIO-GC, the approach integrating the greedy crossover operator strategy, demonstrates its exploration ability against the one without greedy crossover according to statistical metrics such as precision, accuracy, recall, specificity, F-measure, boxplot, convergence speed, and T-test. Comparisons with two wrapper-based feature selection techniques (LBMFO-V3  [23]  and HLBDA  [2] ) and four filter-based feature selection methods (Chi-Square, Relief, correlation-based feature selection, and Information gain) show that CHIO-GC outperforms its alternatives.
In  [13] , the authors propose a hybrid TLBO with the Salp Swarm Algorithm (TLBO-SSA) for the feature selection in digital mammography. They compare the basic TLBO, using 651 mammogram images, to the genetic algorithm using the WDBC dataset, and some existing wrapper-based feature selection approaches using both the WDBC and the 651 mammogram images. The TLBO-SSA shows a good performance. Also, an Improved TLBO (ITLBO) algorithm has been proposed to solve the feature selection for early diagnosis of chronic diseases  [31]. The ITLBO algorithm outperforms the basic TLBO in terms of the selected feature's size on an applied chronic kidney disease dataset. In  [32] , a Multi-objectives Binary TLBO (MBTLBO) that integrates the SVM with the radial basis function method as a classification model was proposed to select the relevant risk features with rheumatism disease.
MBTLBO is based on modifying the Binary TLBO (BTLBO) algorithm  [43]. Experiments conducted on a dataset of specific risk features for 523 Iraqi Rheumatoid Arthritis patients allowed us to assess the superiority of MBTLBO against BTLBO using five performance measures of disease classification, including precision, accuracy, recall, specificity, and F-measure. Furthermore, a New Modified Binary Teaching-Learning-Based Optimization (NMBTLBO) using the SVM classifier has been proposed to classify rheumatism disease  [33]. The experimental tests conducted on the Iraqi Rheumatoid Arthritis dataset demonstrate the performance of NMBTLBO against the BTLBO introduced by Akhlaghi et al. [43].
This bit-flip mutation operator introduces three variants of binary multiobjective TLBO algorithms for solving the feature selection problem. They applied three machine learning classifiers: the support vector machine, the extreme learning machine, and logistic regression to evaluate the performance of the proposed multiobjective TLBO approaches. The experiments performed on 12 datasets collected from the UCI machine learning repository and the Financial dataset obtained from the work of Pacheco et al. [54]  demonstrate the excellent performance of the Multiobjective TLBO with Minimum Distance (MTLBO-MD) version. Moreover, MTLBO-MD combined with logistic regression is compared with state-ofthe-art algorithms, including Non-dominated Sorting Genetic Algorithm (NSGA-II), Particle Swarm Optimization, Scatter Search, Greedy Search, and Tabu Search.
In terms of classification accuracy and size of the selected features, the comparison results show that MTLBO-MD and NSGA-II present almost similar performances, whereas MTLBO-MD outperforms the other algorithms. Furthermore, Hosseini and Khorashadizade  [55]  propose an efficient binary TLBO with a mutation operator (BMTLBO) for solving the feature selection problem. The experiments carried out on 14 benchmark datasets demonstrate the superiority of BMTLBO against the canonical TLBO algorithm and other existing optimization algorithms in terms of classification accuracy and the number of selected features.
In the experiments, α and β factors are set to 0. 99 and 0. 01, respectively. Indeed, this setting is commonly suggested in the literature  [8] ,  [23] ,  [56]. Like most wrapper-based feature selection approaches proposed in the literature  [2] ,  [8] ,  [9] , we use the popular KNN algorithm (with K = 5) to evaluate the classification error rate of the learners. Indeed, it is simple, easy to implement, and with low processing time costs. We use the stratified 10-fold cross-validation method to randomly partition the datasets processed by BTLBO-KNN into training and testing  [2] ,  [9] ,  [22]. More specifically, KNN is often used as the underlying machine learning model in wrapper-based feature selection methods for several reasons: • Simplicity: KNN is a relatively simple and intuitive algorithm that assigns a class label to a data point based on the class labels of its nearest neighbors.
It does not make assumptions about the underlying data distribution, making it versatile and applicable to various types of datasets. • Non-parametric nature: KNN is a non-parametric algorithm, meaning it does not assume any specific form of the data distribution. This makes it suitable for handling datasets with complex or nonlinear relationships between features and the target variable. • Feature relevance assessment: By using KNN in a wrapper-based feature selection method, the performance of the model can be directly evaluated based on how accurately it classifies the data using different subsets of features. The model's accuracy or other evaluation metrics can serve as an objective criterion to select the most relevant feature subset. • Flexibility: KNN can handle both classification and regression tasks, making it applicable to a wide range of feature selection scenarios.
It can be used with different distance metrics and varying numbers of nearest neighbors (k), providing flexibility in evaluating the relevance of features. • Interpretability: KNN allows for straightforward interpretation since the classification decision is based on the labels of the nearest neighbors. This interpretability aspect can be valuable in understanding the impact of individual features on the classification outcomes. It is important to note that while KNN is commonly used in wrapper-based feature selection methods, other machine learning algorithms can also be employed depending on the specific problem and data characteristics. The choice of algorithm may vary based on the nature of the dataset, the performance metric of interest, and the computational resources available.
V. EXPERIMENTS A. EXPERIMENTAL SETUP We perform the experiments with a real-world dataset of patients diagnosed with COVID-19, 1  and 23 gene-expression and medical datasets with different scales described in Table  3. These latter are collected either from the UCI 2 or the ASU 3  repositories. To validate the performance of the proposed algorithm and illustrate its robust wrapper-based feature selection approach, a series of comparisons are conducted on medical diagnosis on 24 datasets. These datasets of various diseases (breast, liver, heart, lymph, diabetes, Parkinson, Leukemia, covid-19,. etc. ) are used to perform a comparative evaluation of the disease diagnosis accuracy of BTLBO-KNN with five recent and efficient state-of-the-art wrapper-based feature selection approaches. Moreover, the comparative analysis is based on several performance metrics, including the best, worst, and average fitness values, the standard deviation of fitness values, classification accuracy, and the average number of the selected features.
Therefore, we adopt values commonly used in the literature for the N and the maximum number of iterations  [2] ,  [8]  (N = 10, MaxItr = 175). Nevertheless, we investigate the impact of the two remaining parameters (NonImpr and M ) on the performance of BTLBO-KNN. We consider four levels for each parameter reported in Table  5. Accordingly, 16 versions of BTLBO-KNN numbered from BTLBO-KNN 1 to BTLBO-KNN 16 are compared. Each version is executed in 20 independent runs to solve the medical feature selection process using the Leukemia dataset. This Dataset exhibits more sensitivity towards the parameter variation than the other medical or gene-expression datasets  [8] ,  [23]. Table  6  lists the results of the best, worst, average, and standard deviation (stdv) fitness values for the 20 runs of each BTLBO-KNN version.
The best results are in boldface in the table. To evaluate the influence of the various parameter levels, we use Minitab 4 to analyze the listed average fitness values of Table  6. Table  7  and Figure  2  illustrate the results of the statistical analysis resulting from the Taguchi Design Of Experiments (DOE). One can see that BTLBO-KNN achieves better fitness performances with NonImp = 100 and M = 5. Consequently, we perform the remaining experiments with this set of parameters. 24 remaining medical datasets. Each experiment involves 20 independent runs. Tables  8, 9 , 10, and 11 report respectively the best, worst, average, and standard deviation values of the fitness function for the techniques under evaluation. For clarity, the top results are highlighted in boldface. Let's first compare the fitness values for the best runs of the various algorithms reported in Table  8.