Eötvös Loránd Research Network - University of Pannonia Complex Systems Monitoring Research Group, University of Pannonia, Veszprém, Hungary.
Plasma Chemistry Research Group, Institute of Materials and Environmental Chemistry, Research Centre for Natural Sciences, Centre of Excellence, Hungarian Academy of Sciences, Budapest, Hungary.
PLoS One. 2023 Apr 13;18(4):e0284078. doi: 10.1371/journal.pone.0284078. eCollection 2023.
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.
非负矩阵分解 (NMF) 有效地降低了多维数据的维度，适用于多目标排序问题。在多目标优化中，只要存在三个或四个冲突观点，就可以通过找到帕累托前沿来确定最优解。当目标数量增加时，多目标问题就会演变成一个多目标优化任务，其中帕累托前沿变得过度饱和。关键思想是，NMF 聚合目标，以便可以应用帕累托前沿，而和和和和和和和和和和和和和和和和和和和和和和和和和和和和和和和和和和和和和和和和和和和和和和和和和和和和和和和和和和和和和和和和和和和和和和和和和和和和和和和和和和和和和和和和和和和和和和和和和和和和和和和和的和和和和和和和和和和和和和和和和和和和和和和和和和和和和和的和和和和和和和和和和中除了被提出之外，其他地方你没有提供足够的信息，因此我无法理解你的问题。
