A modified generalized lasso algorithm to detect local spatial clusters for count data

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.

Extraction of Continuous and Discrete Spatial Heterogeneities: Fusion Model of Spatially Varying Coefficient Model and Sparse Modelling

Geospatial phenomena often have spatial heterogeneity, which is caused by differences in the data generation process from place to place. There are two types of spatial heterogeneity: continuous and discrete, and there has been much discussion about how to analyze one type of spatial heterogeneity. Although geospatial phenomena can have both types of spatial heterogeneities, previous studies have not sufficiently discussed how to consider these two different types of spatial heterogeneity simultaneously and how to detect them separately, which may lead to biased estimates and the wrong interpretation of geospatial phenomena. This study proposes a new approach for the analysis of spatial data with both heterogeneities by combining the eigenvector spatial filtering-based spatially varying coefficient (ESF-SVC) model, which assumes the continuous spatial heterogeneity and generalized lasso (GL) estimation, which assumes discrete spatial heterogeneity and proposes the ESF-GL-SVC model. The performance of ESF-GL-SVC was evaluated through experiments based on a Monte Carlo simulation and confirms that the ESF-GL-SVC showed better performance in estimating coefficients with both types of spatial heterogeneity than the previous two models. The application of the apartment rent data showed that the ESF-GL-SVC outputs the result with the smallest BIC value, and the estimated coefficients depict continuous and discrete spatial heterogeneity in the dataset. Reasonable coefficients were estimated using the ESF-GL-SVC, although some coefficients by ESF-SVC were not.

Point Event Cluster Detection via the Bayesian Generalized Fused Lasso

Spatial cluster detection is one of the focus areas of spatial analysis, whose objective is the identification of clusters from spatial distributions of point events aggregated in districts with small areas. Choi et al. (2018) formulated cluster detection as a parameter estimation problem to leverage the parameter selection capability of the sparse modeling method called the generalized fused lasso. Although this work is superior to conventional methods for detecting multiple clusters, its estimation results are limited to point estimates. This study therefore extended the above work as a Bayesian cluster detection method to describe the probabilistic variations of clustering results. The proposed method combines multiple sparsity-inducing priors and encourages sparse solutions induced by the generalized fused lasso. Evaluations were performed with simulated and real-world distributions of point events to demonstrate that the proposed method provides new information on the quantified reliabilities of clustering results at the district level while achieving comparable detection performances to that of the previous work.

Identifying local differences with fused-MCP: an apartment rental market case study on geographical segmentation detection

As the variety and quality of spatial data increase in recent times, the potential to analyze local characteristics based on spatial data is getting stronger. Previous spatial analysis methods structuralize the spatial autocorrelation of data by the distances between data observation points and the contiguity of the data-observed regions. It is significant for the estimation of global characteristics of spatial data. However, these approaches are not suitable for identifying local differences from the data since they assume a smooth spatial autocorrelation structure. Generalized fused lasso, which can detect local differences in spatial data, has been proposed in machine learning studies. Its limitation is that the estimated parameters are biased toward zero; however, methods that overcome the limitation have also been proposed. Fused-MCP is one of those methods and is expected to be useful in spatial analyses. This study applies fused-MCP to spatial analyses. As an example of spatial analyses based on fused-MCP, this study analyzes the structure of geographical segmentation of the real estate market in central Tokyo. Fused-MCP is utilized to extract areas where the valuation standard is the same. The results reveal that the geographical segmentation displays hierarchal patterns. Specifically, the market is divided by municipalities, railway lines and stations, and neighborhoods. The case study confirmed the applicability of fused-MCP to spatial analyses.