The non-stationarity, nonlinearity and complexity of the PM_2.5 series have caused difficulties in PM_2.5 prediction. To improve prediction accuracy, many forecasting methods have been developed. However, these methods usually do not consider the importance of data preprocessing and have limitations only using a single forecasting model. Therefore, this paper proposed a new hybrid decomposition–ensemble learning paradigm based on variation mode decomposition (VMD) and improved whale-optimization algorithm (IWOA) to address complex nonlinear environmental data. First, the VMD is employed to decompose the PM_2.5 sequences into a set of variational modes (VMs) with different frequencies. Then, an ensemble method based on four individual forecasting approaches is applied to forecast all the VMs. With regard to ensemble weight coefficients, the IWOA is applied to optimize the weight coefficients, and the final forecasting results were obtained by reconstructing the refined sequences. To verify and validate the proposed learning paradigm, four daily PM_2.5 datasets collected from the Jing-Jin-Ji area of China are chosen as the test cases to conduct the empirical research. The experimental results indicated that the proposed learning paradigm has the best results in all cases and metrics.

In recent years, healthcare has attracted much attention, which is looking for more and more data analytics in healthcare to relieve medical problems in medical staff shortage, ageing population, people living alone, and quality of life. Data mining, analysis, and forecasting play a vital role in modern social and medical fields. However, how to select a proper model to mine and analyze the relevant medical information in the data is not only an extremely challenging problem, but also a concerning problem. Tuberculosis remains a major global health problem despite recent and continued progress in prevention and treatment. There is no doubt that the effective analysis and accurate forecasting of global tuberculosis prevalence rates lay a solid foundation for the construction of an epidemic disease warning and monitoring system from a global perspective. In this paper, the tuberculosis prevalence rate time series for four World Bank income groups are targeted. Kruskal–Wallis analysis of variance and multiple comparison tests are conducted to determine whether the differences of tuberculosis prevalence rates for different income groups are statistically significant or not, and a novel combined forecasting model with its weights optimized by a recently developed artificial intelligence algorithm—cuckoo search—is proposed to forecast the hierarchical tuberculosis prevalence rates from 2013 to 2016. Numerical results show that the developed combination model is not only simple, but is also able to satisfactorily approximate the actual tuberculosis prevalence rate, and can be an effective tool in mining and analyzing big data in the medical field.

The spatial distribution of mean daily maximum boundary layer height (BLH) from 1900 to 2010, and three climatic subzone boundaries. (The white line represents the annual average precipitation contour and the fill colour represents the average BLH).