Functional factorial K-means analysis

Modeling the evolution of deaths from infectious diseases with functional data models: The case of COVID-19 in Brazil

In this paper, we apply statistical methods for functional data to explore the heterogeneity in the registered number of deaths of COVID-19, over time. The cumulative daily number of deaths in regions across Brazil is treated as continuous curves (functional data). The first stage of the analysis applies clustering methods for functional data to identify and describe potential heterogeneity in the curves and their functional derivatives. The estimated clusters are labeled with different "levels of alert" to identify cities in a possible critical situation. In the second stage of the analysis, we apply a functional quantile regression model for the death curves to explore the associations with functional rates of vaccination and stringency and also with several scalar geographical, socioeconomic and demographic covariates. The proposed model gave a better curve fit at different levels of the cumulative number of deaths when compared to a functional regression model based on ordinary least squares. Our results add to the understanding of the development of COVID-19 death counts.

Ensemble calibration model of near-infrared spectroscopy based on functional data analysis

As a nondestructive detection technology, near-infrared spectroscopy has been widely applied in various fields. With the wide application of near-infrared spectroscopy, the research on data processing has attracted more attention. Different from the existing discrete data model and based on the functional data analysis method, an ensemble calibration model FDA-EM-PLS (functional data analysis-ensemble learning-partial least squares) of near-infrared spectroscopy is proposed in this paper. Firstly, the near-infrared spectroscopy of each sample is divided into several intervals, and the functional data analysis is carried out on each interval. Then, the samples are clustered according to the generated functions, which can not only reduce the influence of noise, but also provide a theoretical basis for selecting variables. Further, Monte Carlo sampling is used to generate training subsets from clustering samples for ensemble learning, which not only solves the problem of small samples, but also improves the robustness of the model. The relevant experimental results show that the absolute relative error of FDA-EM-PLS for the corn and soil data are both less than 10%.