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This article aims to integrate ${k}$ -NN regression, false-nearest neighborhood (FNN), and trustworthiness and continuity (T&C) neighborhood-based measures into an efficient and robust feature selection method to support the identification of nonlinear regression models. The proposed neighborhood ranking-based feature selection technique (NRFS) is validated in three problems, in a linear regression task, in the nonlinear Friedman database, and in the problem of determining the order of nonlinear dynamical models. A neural network is also identified to validate the resulting feature sets. The analysis of the distance correlation also confirms that the method is capable of exploring the nonlinear correlation structure of complex systems. The results illustrate that the proposed NRFS method can select relevant variables for nonlinear regression models.

The parameter identification of failure models for composite plies can be cumbersome, due to multiple effects as the consequence of brittle fracture. Our work proposes an iterative, nonlinear design of experiments (DoE) approach that finds the most informative experimental data to identify the parameters of the Tsai-Wu, Tsai-Hill, Hoffman, Hashin, max stress and Puck failure models. Depending on the data, the models perform differently, therefore, the parameter identification is validated by the Euclidean distance of the measured points to the closest ones on the nominal surface. The resulting errors provide a base for the ranking of the models, which helps to select the best fitting. Following the validation, the sensitivity of the best model is calculated by partial differentiation, and a theoretical surface is generated. Lastly, an iterative design of the experiments is implemented to select the optimal set of experiments from which the parameters can be identified from the least data by minimizing the fitting error. In this way, the number of experiments required for the identification of a model of a composite material can be significantly reduced. We demonstrate how the proposed method selected the most optimal experiments out of generated data. The results indicate that if the dataset contains enough information, the method is robust and accurate. If the data set lacks the necessary information, novel material tests can be proposed based on the optimal points of the parameters' sensitivity of the generated failure model surface.

The utility function-based sum of ranking differences (uSRD) method is proposed as a utility function-based multi-criteria decision analysis tool. Our idea is that the transformation functions can be represented by a utility function that can be aggregated with multi-attribute utility functions. We present a framework incorporating utility values as the basis for three different but interconnected analyses. The exemplary application focuses on greenhouse gas emissions and economic indicators of 147 countries. First, the uSRD is applied to the utility values to uncover the hidden relationships of the 40 indicators. A ranking of countries is established to see which sample performs the best and the worst in both emissions and economy. Lastly, mitigation actions are delegated to countries through a three-stage assignment that connects emissions to utilities, sectors, and mitigation actions. The results show that the uSRD excels as a support tool for decision-making.

Non-negative matrix factorization (NMF) efficiently reduces high dimensionality for many-objective ranking problems. In multi-objective optimization, as long as only three or four conflicting viewpoints are present, an optimal solution can be determined by finding the Pareto front. When the number of the objectives increases, the multi-objective problem evolves into a many-objective optimization task, where the Pareto front becomes oversaturated. The key idea is that NMF aggregates the objectives so that the Pareto front can be applied, while the Sum of Ranking Differences (SRD) method selects the objectives that have a detrimental effect on the aggregation, and validates the findings. The applicability of the method is illustrated by the ranking of 1176 universities based on 46 variables of the CWTS Leiden Ranking 2020 database. The performance of NMF is compared to principal component analysis (PCA) and sparse non-negative matrix factorization-based solutions. The results illustrate that PCA incorporates negatively correlated objectives into the same principal component. On the contrary, NMF only allows non-negative correlations, which enable the proper use of the Pareto front. With the combination of NMF and SRD, a non-biased ranking of the universities based on 46 criteria is established, where Harvard, Rockefeller and Stanford Universities are determined as the first three. To evaluate the ranking capabilities of the methods, measures based on Relative Entropy (RE) and Hypervolume (HV) are proposed. The results confirm that the sparse NMF method provides the most informative ranking. The results highlight that academic excellence can be improved by decreasing the proportion of unknown open-access publications and short distance collaborations. The proportion of gender indicators barely correlate with scientific impact. More authors, long-distance collaborations, publications that have more scientific impact and citations on average highly influence the university ranking in a positive direction.

Non-negative matrix factorization (NMF) efficiently reduces high dimensionality for many-objective ranking problems. In multi-objective optimization, as long as only three or four conflicting viewpoints are present, an optimal solution can be determined by finding the Pareto front. When the number of the objectives increases, the multi-objective problem evolves into a many-objective optimization task, where the Pareto front becomes oversaturated. The key idea is that NMF aggregates the objectives so that the Pareto front can be applied, while the Sum of Ranking Differences (SRD) method selects the objectives that have a detrimental effect on the aggregation, and validates the findings. The applicability of the method is illustrated by the ranking of 1176 universities based on 46 variables of the CWTS Leiden Ranking 2020 database. The performance of NMF is compared to principal component analysis (PCA) and sparse non-negative matrix factorization-based solutions. The results illustrate that PCA incorporates negatively correlated objectives into the same principal component. On the contrary, NMF only allows non-negative correlations, which enable the proper use of the Pareto front. With the combination of NMF and SRD, a non-biased ranking of the universities based on 46 criteria is established, where Harvard, Rockefeller and Stanford Universities are determined as the first three. To evaluate the ranking capabilities of the methods, measures based on Relative Entropy (RE) and Hypervolume (HV) are proposed. The results confirm that the sparse NMF method provides the most informative ranking. The results highlight that academic excellence can be improved by decreasing the proportion of unknown open-access publications and short distance collaborations. The proportion of gender indicators barely correlate with scientific impact. More authors, long-distance collaborations, publications that have more scientific impact and citations on average highly influence the university ranking in a positive direction.

A novel visualization technique is proposed for the sum of ranking differences method (SRD) based on parallel coordinates. An axis is defined for each variable, on which the data are depicted row-wise. By connecting data, the lines may intersect. The fewer intersections between the variables, the more similar they are and the clearer the figure becomes. Therefore, the visualization depends on what techniques are used to order the variables. The key idea is to employ the SRD method to measure the degree of similarity of the variables, establishing a distance-based order. The distances between the axes are not uniformly distributed in the proposed visualization; their closeness reflects similarity, according to their SRD value. The proposed algorithm identifies false similarities through an iterative approach, where the angles between the SRD values determine which side a variable is plotted. Visualization of the algorithm is provided by MATLAB/Octave source codes. The proposed tool is applied to study how the sources of greenhouse gas emissions can be grouped based on the statistical data of the countries. A comparison to multidimensional scaling (MDS)-based ordering is also given. The use case demonstrates the applicability of the method and the synergies of the incorporation of the SRD method into parallel coordinates.