Solution paths for the generalized lasso with applications to spatially varying coefficients regression

Spatio-temporal clustering analysis using generalized lasso with an application to reveal the spread of Covid-19 cases in Japan

This study addressed the issue of determining multiple potential clusters with regularization approaches for the purpose of spatio-temporal clustering. The generalized lasso framework has flexibility to incorporate adjacencies between objects in the penalty matrix and to detect multiple clusters. A generalized lasso model with two L 1 penalties is proposed, which can be separated into two generalized lasso models: trend filtering of temporal effect and fused lasso of spatial effect for each time point. To select the tuning parameters, the approximate leave-one-out cross-validation (ALOCV) and generalized cross-validation (GCV) are considered. A simulation study is conducted to evaluate the proposed method compared to other approaches in different problems and structures of multiple clusters. The generalized lasso with ALOCV and GCV provided smaller MSE in estimating the temporal and spatial effect compared to unpenalized method, ridge, lasso, and generalized ridge. In temporal effects detection, the generalized lasso with ALOCV and GCV provided relatively smaller and more stable MSE than other methods, for different structure of true risk values. In spatial effects detection, the generalized lasso with ALOCV provided higher index of edges detection accuracy. The simulation also suggested using a common tuning parameter over all time points in spatial clustering. Finally, the proposed method was applied to the weekly Covid-19 data in Japan form March 21, 2020, to September 11, 2021, along with the interpretation of dynamic behavior of multiple clusters.

Spatiotemporal variability and key influencing factors of river fecal coliform within a typical complex watershed

Fecal coliform bacteria are a key indicator of human health risks; however, the spatiotemporal variability and key influencing factors of river fecal coliform have yet to be explored in a rural-suburban-urban watershed with multiple land uses. In this study, the fecal coliform concentrations in 21 river sections were monitored for 20 months, and 441 samples were analyzed. Multivariable regressions were used to evaluate the spatiotemporal dynamics of fecal coliform. The results showed that spatial differences were mainly dominated by urbanization level, and environmental factors could explain the temporal dynamics of fecal coliform in different urban patterns except in areas with high urbanization levels. Reducing suspended solids is a direct way to manage fecal coliform in the Beiyun River when the natural factors are difficulty to change, such as temperature and solar radiation. The export of fecal coliform from urban areas showed a quick and sensitive response to rainfall events and increased dozens of times in the short term. Landscape patterns, such as the fragmentation of impervious surfaces and the overall landscape, were identified as key factors influencing urban non-point source bacteria. The results obtained from this study will provide insight into the management of river fecal pollution.