Quantification research proposes methods to estimate the class distribution in an independent sample. Quantification methods find applications in areas that rely on estimated aggregated quantities, such as epidemiology, sentiment analysis, political research, and ecological surveillance. For instance, epidemiologists are often concerned with the dynamics of the number of disease cases across space and time. Thus, while classification predicts individual subjects, quantifiers are the methods that directly estimate the number of cases. Although quantification is a thriving area of research, with numerous approaches proposed in the last decade, most focus has been on binary-class quantifiers. One common approach for multi-class quantification is the one-versus-all (OVA) approach, but empirical evidence suggests its performance is suboptimal. This paper's first contribution is to elucidate why OVA quantifiers struggle to perform well in multi-class settings due to a distribution shift. To circumvent this problem, our second proposal is two new multi-class quantifiers based on ensemble learning that significantly improve performance for binary and multi-class settings. Our comprehensive experimental setup with 37 state-of-the-art (single and ensemble) quantifiers shows that our ensembles are the best-performing quantifiers and rank first in a recent quantification competition.

The relationship between seed germination rate and environmental temperature is complex. This study assessed the effectiveness of multi-layer perceptron (MLP) and Particle Swarm Optimization (PSO) techniques in modeling and predicting the germination rate of two common bean cultivars as a function of distinct temperatures. MLP was utilized to model the germination rate of the cultivars and PSO was employed to determine the optimum temperatures at which the beans germinate most rapidly. The outcomes derived from implementing the MLP were compared with those obtained by means of a traditional statistical method. The MLP provided more accurate results than the conventional statistical regression in predicting germination rate values regarding the two common bean cultivars. The optimum germination rate values derived from implementing the PSO model were more accurate than those obtained by using the conventional quadratic regression.