Eigenvector Spatial Filtering Research Articles

Incorporating Spatial Autocorrelation into GPP Estimation Using Eigenvector Spatial Filtering

Terrestrial gross primary productivity (GPP) is a critical part of land carbon fluxes. Accurately quantifying GPP in terrestrial ecosystems and understanding its spatiotemporal dynamics are essential for assessing the capability of vegetation to absorb carbon from the atmosphere. Nevertheless, traditional remote sensing estimation models often require complex parameters and data inputs, and they do not account for spatial effects resulting from the distribution of monitoring sites. This can lead to biased parameter estimation and unstable results. To address these challenges, we have raised a spatial autocorrelation light gradient boosting machine model (SA-LGBM) to enhance GPP estimation. SA-LGBM combines reflectance information from remote sensing observations with eigenvector spatial filtering (ESF) methods to create a set of variables that capture continuous spatiotemporal variations in plant functional types and GPP. SA-LGBM demonstrates promising results when compared to existing GPP products. With the inclusion of eigenvectors, we observed an 8.5% increase in R2 and a 20.8% decrease in RMSE. Furthermore, the residuals of the model became more random, reducing the inherent spatial effects within them. In summary, SA-LGBM represents the first attempt to quantify the impact of spatial autocorrelation and addresses the limitations of underestimation present in existing GPP products. Moreover, SA-LGBM exhibits favorable applicability across various vegetation types.

Eigenvector spatial filtering enhancing natural hazards vulnerability assessment in a susceptible urban environment: A case study of Izmir earthquake in Turkey

The increasing risk of earthquakes in urban areas has made it crucial to develop accurate vulnerability models for city infrastructure and systems. We aimed to assess and compare the effectiveness of different models and vulnerability analysis techniques in predicting earthquake vulnerability in the specific context of Izmir, Turkey. One central hypothesis in this research aimed to determine whether integrating Eigenvector Spatial Filtering (ESF) into both regression models and machine learning algorithms would yield a comparable enhancement in model performance. We performed earthquake vulnerability modeling (EVM) by considering (ⅰ) only seismic-related variables (SRV) and (ⅱ) integrating ESF by using Moran's eigenvector maps (MEMs). For each approach, we evaluated the predictive performance of two simple regression-based models; generalized linear model (GLM) and generalized additive model (GAM), and two complex machine learning ones; generalized boosting model (GBM), and random forest (RF). The study utilized five primary indicators encompassing geotechnical, physical, structural, social, and facilities data. The predictive performance of the models was assessed using evaluation metrics including Root Mean Square Error (RMSE), Mean Absolute Error (MAE), and adjusted R2. The results indicated that the optimal candidate model consisted of five key variables: altitude, building height, distance to safety gathering places, Peak Ground Acceleration (PGA), and population density. We found that decision-tree-based methods performed better than regression-based methods for both modeling schemes. RF exhibited the highest predictive performance for the training data (RMSE = 0.59, adjusted R2 = 0.71), while GBM outperformed other models for the test data (RMSE = 0.79, adjusted R2 = 0.78). However, incorporating ESF to the EVM analysis revealed that regression-based methods, particularly the GLM, obtained highest improvement in accuracy (RMSE 0.94 vs 0.76 and adjusted R2 0.56 vs 0.71 for the SRV and SRV + MEMs modeling approach). Significant differences were observed between GLM-GBM and GLM-RF comparisons, as well as GAM-GBM and GAM-RF comparisons. The findings of this research are expected to be helpful for informed decision-making, targeted risk reduction, and the development of effective policies and strategies to enhance preparedness and resilience in the face of seismic events in highly susceptible urban systems.

Do shifts in the racial and ethnic composition of a neighborhood lead to extreme changes in commuting times? evidence from New York City

From 2000 to 2016, NYC average commuting times increased by a marginal 0.24 s across all transit modes. Depending on one’s viewpoint, this could be a policy success due to no significant increase in commuting times or it could be a policy failure due to no substantial decrease in commuting time over almost two decades. Nevertheless, many census tracts actually experienced extreme increases or decreases in commuting times. The goal of this paper is to examine these extreme changes by focusing on understanding how changes in census tracts', racial and ethnic compositions influence commuting time changes. Analyzing NYC as a case study, we use logistic regressions with eigenvector spatial filtering (ESF) to identify the likelihood of extreme changes in commuting time from 2000 to 2016 given changes in various neighborhood characteristics. Overall, census tracts experiencing increases in Black, Asian, and Hispanic or Latino residents, female-headed households, and workers in professional occupations as well as higher highway densities are likely to have experienced extreme increases in commuting times. Meanwhile, census tracts experiencing increases in White residents, income, rental occupancy, housing burden, and proportions of their census tract within a subway shed are likely to have experienced extreme decreases in commuting times. The results for race and ethnicity support existing research indicating that racial and ethnic minorities are likelier to experience longer commuting times compared to White residents. The importance of our research, though, lies in showing that even when overall commuting times remain relatively stable, racial/ethnic minorities still face commuting disadvantages.

Sub‐Model Aggregation for Scalable Eigenvector Spatial Filtering: Application to Spatially Varying Coefficient Modeling

This study proposes a method for aggregating/synthesizing global and local sub‐models for fast and flexible spatial regression modeling. Eigenvector spatial filtering (ESF) was used to model spatially varying coefficients and spatial dependence in the residuals by sub‐model, while the generalized product‐of‐experts method was used to aggregate these sub‐models. The major advantages of the proposed method are as follows: (i) it is highly scalable for large samples in terms of accuracy and computational efficiency; (ii) it is easily implemented by estimating sub‐models independently first and aggregating/averaging them thereafter; and (iii) likelihood‐based inference is available because the marginal likelihood is available in closed‐form. The accuracy and computational efficiency of the proposed method are confirmed using Monte Carlo simulation experiments. This method was then applied to residential land price analysis in Japan. The results demonstrate the usefulness of this method for improving the interpretability of spatially varying coefficients. The proposed method is implemented in an R package spmoran.

Multiscale Continuous and Discrete Spatial Heterogeneity Analysis: The Development of a Local Model Combining Eigenvector Spatial Filters and Generalized Lasso Penalties

Two types of spatial heterogeneity can exist simultaneously: continuous variations across an entire space and significant changes that occur only in specific spatial units. Moreover, each of these can act across multiple spatial scales. To effectively detect both continuous and discrete spatial heterogeneity across different scales, this study proposes a novel approach that combines the random effects eigenvector spatially filtering‐based spatially varying coefficient (RE‐ESF‐SVC) model and the generalized lasso (GL) technique. Additionally, a restricted maximum likelihood estimation (REML)‐based two‐step iterative algorithm is developed for parameter estimation. Simulation experiments and an empirical application using rental price data confirm the ability of the proposed model to identify multiscale continuous and discrete spatial heterogeneity.

Supply–Demand Imbalance in School Land: An Eigenvector Spatial Filtering Approach

The spatial flows of school-age children and educational resources have been driven by such factors as regional differences in population migration and the uneven development of the education quality and living standards of residents in urban and rural areas. This phenomenon further leads to a supply–demand imbalance between the area of school land and the number of school-age children in the geographical location of China. The georeferenced data characterizing supply–demand imbalance presents an obvious spatial autocorrelation. Therefore, a spatial data analysis technique named the Eigenvector Spatial Filtering (ESF) approach was employed to identify the driving factors of the supply–demand imbalance of school land. The eigenvectors generated by the geographical coordinates of all primary schools were selected and added into the ESF model to filter the spatial autocorrelation of the datasets to identify the driving factors of the supply–demand imbalance. To verify the performance of the technique, it was applied to a county in the southwest of Shandong Province, China. The results from this study showed that all the georeferenced indicators representing population migration and education quality were statistically significant, but no indicator of the living standards of residents showed statistical significance. The eigenvector spatial filtering approach can effectively filter out the positive spatial autocorrelation of the datasets. The findings of this research suggest that a sustainable school-land-allocation scheme should consider population migration and the possible preference for high-quality education.

Are seed dispersal and seedling establishment distance- and/or density-dependent in naturally regenerating larch patches? A within-patch scale analysis using an eigenvector spatial filtering approach

The success of natural regeneration in silviculture depends on the complex interactions between interventions of stand structure, the natural seed-dispersal processes, and seedling development. Particularly, the spatial patterns of seed dispersal, seedling establishment and growth, and microenvironmental factors are closely interrelated, controlling the outcomes of natural regeneration practices. wWe performed a within-patch scale spatial analysis and modeling for seed dispersal and seedling development on four different natural regeneration patches (seed tree, grouped seed tree, reserved seed tree, and strip clear-cut methods) of Japanese larch (Larix kaempferi) using an eigenvector spatial filtering (ESF) approach. Our spatial analysis allowed us to determine whether seed fall, seedling establishment, and seedling growth are distance- rather than density-dependent, corresponding to the Janzen–Connell hypothesis. The ESF model revealed that gentle slope, moderate soil moisture, and low crown closure were essential in achieving potential seedling establishment and growth. In addition, the ESF based spatially varying coefficient (ESF-SVC) model provided the difference in impacts of those environmental factors across the regeneration patches. The strategy of planting a large number of evenly distributed remnant seed trees in the regeneration patch of the reserved seed trees was effective in improving seed dispersal, while no remnant seed tree in the regeneration patch of the strip clear-cut method contributed to seedling growth. These findings indicate that ESF-based approaches may represent a feasible way of natural regeneration modeling with more reliable statistical estimations and interpretations by accounting for spatial autocorrelation and heterogeneity.

Intraurban Geographic and Socioeconomic Inequalities of Mortality in Four Cities in Colombia.

Mortality inequalities have been described across Latin American countries, but less is known about inequalities within cities, where most populations live. We aimed to identify geographic and socioeconomic inequalities in mortality within the urban areas of four main cities in Colombia. We analyzed mortality due to non-violent causes of diseases in adults between 2015 and 2019 using census sectors as unit of analysis in Barranquilla, Bogotá, Cali, and Medellín. We calculated smoothed Bayesian mortality rates as main health outcomes and used concentration indexes (CInd) for assessing inequalities using the multidimensional poverty index (MPI) as the socioeconomic measure. Moran eigenvector spatial filters were calculated to capture the spatial patterns of mortality and then used in multivariable models of the association between mortality rates and quintiles of MPI. Social inequalities were evident but not consistent across cities. The most disadvantaged groups showed the highest mortality rates in Cali. Geographic inequalities in mortality rates, regardless of the adults and poverty distribution, were identified in each city, suggesting that other social, environmental, or individual conditions are impacting the spatial distribution of mortality rates within the four cities.

Applying the Geostatistical Eigenvector Spatial Filter Approach into Regularized Regression for Improving Prediction Accuracy for Mass Appraisal

Prediction accuracy for mass appraisal purposes has evolved substantially over the last few decades, facilitated by the evolution in big data, data availability and open source software. Accompanying these advances, newer forms of geo-spatial approaches and machine learning (ML) algorithms have been shown to help improve house price prediction and mass appraisal assessment. Nonetheless, the adoption a of ML within mass appraisal has been protracted and subject to scrutiny by assessment jurisdictions due to their failure to account for spatial autocorrelation and limited practicality in terms of value significant estimates needed for tribunal defense and explainability. Existing research comparing traditional regression approaches has tended to examine unsupervised ML methods such as Random Forest (RF) models which remain more esoteric and less transparent in producing value significant estimates necessary for mass appraisal explainability and defense. Therefore, the purpose of this study is to apply the supervised Regularized regression technique which offers a more transparent alternative, and integrate this with a more nuanced geo-statistical technique, the Eigenvector Spatial Filter (ESF) approach, to more accurately account for spatial autocorrelation and enhance prediction accuracy whilst improving explainability needed for mass appraisal exercises. By undertaking such an approach, the research demonstrates the application of this method can be easily adopted for property tax jurisdictions in a framework which is more interpretable, transparent and useable within mass appraisal given its simple and appealing approach. The findings reveal that the integration of the ESFs improves model explainability, prediction accuracy and spatial residual error compared to baseline classical regression and Elastic-net regularized regression architectures, whilst offering the necessary ‘front-facing’ and flexible structure for in-sample and out-of-sample assessment needed by the assessment community for valuing the unsold housing stock. In terms of policy and practice, the study demonstrates some important considerations for mass appraisal tax assessment and for the improvement of taxation assessment and the alleviation of horizontal and vertical inequity.

Estimating Regional PM2.5 Concentrations in China Using a Global-Local Regression Model Considering Global Spatial Autocorrelation and Local Spatial Heterogeneity

Linear regression models are commonly used for estimating ground PM2.5 concentrations, but the global spatial autocorrelation and local spatial heterogeneity of PM2.5 distribution are either ignored or only partially considered in commonly used models for estimating PM2.5 concentrations. Therefore, taking both global spatial autocorrelation and local spatial heterogeneity into consideration, a global-local regression (GLR) model is proposed for estimating ground PM2.5 concentrations in the Yangtze River Delta (YRD) and in the Beijing, Tianjin, Hebei (BTH) regions of China based on the aerosol optical depth data, meteorological data, remote sensing data, and pollution source data. Considering the global spatial autocorrelation, the GLR model extracts global factors by the eigenvector spatial filtering (ESF) method, and combines the fraction of them that passes further filtering with the geographically weighted regression (GWR) method to address the local spatial heterogeneity. Comprehensive results show that the GLR model outperforms the ordinary GWR and ESF models, and the GLR model has the best performance at the monthly, seasonal, and annual levels. The average adjusted R2 of the monthly GLR model in the YRD region (the BTH region) is 0.620 (0.853), which is 8.0% and 7.4% (6.8% and 7.0%) higher than that of the monthly ESF and GWR models, respectively. The average cross-validation root mean square error of the monthly GLR model is 7.024 μg/m3 in the YRD region, and 9.499 μg/m3 in the BTH region, which is lower than that of the ESF and GWR models. The GLR model can effectively address the spatial autocorrelation and spatial heterogeneity, and overcome the shortcoming of the ordinary GWR model that overfocuses on local features and the disadvantage of the poor local performance of the ordinary ESF model. Overall, the GLR model with good spatial and temporal applicability is a promising method for estimating PM2.5 concentrations.

Spatial-Statistical Analysis of Landscape-Level Wildfire Rate of Spread

The objectives of this study were to evaluate spatial sampling and statistical aspects of landscape-level wildfire rate of spread (ROS) estimates derived from airborne thermal infrared imagery (ATIR). Wildfire progression maps and ROS estimates were derived from repetitive ATIR image sequences collected during the 2017 Thomas and Detwiler wildfire events in California. Three separate landscape sampling unit (LSU) sizes were used to extract remotely sensed environmental covariates known to influence fire behavior. Statistical relationships between fire spread rates and landscape covariates were analyzed using (1) bivariate regression, (2) multiple stepwise regression, (3) geographically weighted regression (GWR), (4) eigenvector spatial filtering (ESF) regression, (5) regression trees (RT), and (6) and random forest (RF) regression. GWR and ESF regressions reveal that relationships between covariates and ROS estimates are substantially non-stationary and suggest that the global association of fire spread controls are locally differentiated on landscape scales. Directional slope is by far the most strongly associated covariate of ROS for the imaging sequences analyzed and the size of LSUs has little influence on any of the covariate relationships.

Spatial autocorrelation may bias the risk estimation: An application of eigenvector spatial filtering on the risk of air pollutant on asthma

Air pollutants are major risk factors for respiratory diseases, particularly asthma, socially and spatially correlated. Many existing environment-asthma-related studies, however, have evaluated the impact of crude trends at the largest district level, which accounts only for temporal effects and may produce biased results with spatial autocorrelation. This study aimed to investigate how the spatial autocorrelation affects the air pollution effect estimations (sulfur dioxide [SO2], nitrogen dioxide [NO2], carbon monoxide [CO], and particulate matter [PM10]) on daily asthma emergency department (ED) visits in two metropolitan areas in Korea (Seoul Metropolitan Area [SMA] and Busan Metropolitan City, Ulsan Metropolitan City, Gyeongsangnamdo [BUG]). We applied eigenvector spatial filter (ESF) to the spatio-temporal model to remove spatial autocorrelation and distributed lag nonlinear model (DLNM) to explore nonlinear patterns between air pollutant concentration and lagged days on the three models including aggregated model (a temporal model), spatial model without ESF, and spatial model with ESF (both are spatio-temporal models). The effect of SO2 was not statistically significant for asthma ED visits in the aggregated model for SMA (cumulative relative risks [CRR] = 0.99, confidence intervals [CI]: 0.93–1.05), while the effect was statistically significant in the spatial model with ESF (CRR = 1.10, CI: 1.08–1.12). NO2 and CO were positively correlated to asthma ED visits in the spatial model without ESF (CRR = 0.84, CI: 0.81–0.86; 0.91, 0.89–0.94, respectively), but the spatial model with ESF showed significant risks (CRR = 1.21, CI: 1.18–1.24; 1.13, 1.11–1.16). Moreover, the spatial model with ESF successfully removed spatial autocorrelation (P-values for Moran's I 0.83–0.98) and demonstrated the highest model fit (McFadden's pseudo R2 0.42–0.43 for SMA and 0.26–0.27 for BUG) among the three models. Our findings demonstrate how ESF can be introduced into spatial correlation to remove bias and construct more reliable models.

Spatial Regression in the Presence of a Hierarchical Transportation Network: Application to Land Price Analysis

Transportation networks have a hierarchical structure, and the spatial scale of their impact on urban growth differs depending on the hierarchy. However, in empirical analyses of the impacts that transportation has on land use and prices, such hierarchy is often examined using dummy variables, and the network dependence and heterogeneity of impacts are often ignored. Thus, this study develops a spatial regression method that considers not only spatial dependence, but also network dependence within a hierarchical transportation network. This method was developed by extending the random effects eigenvector spatial filtering approach. Subsequently, it was applied to a pre-existing analysis that focused on the impacts that high-speed rail (HSR) had on residential land prices in Japan over the last 30 years. The results of the analysis suggested that HSR lines had hierarchical effects on residential land prices. The results also provide interesting insight into the ongoing problem of Japanese urban hierarchy; that is, the excessive concentration of population and industry in the Tokyo metropolitan area.

Identifying Multiple Scales of Spatial Heterogeneity in Housing Prices Based on Eigenvector Spatial Filtering Approaches

Interest in studying the urban real estate market, especially in investigating the relationship between house prices and related housing characteristics, is rapidly growing. However, this increasing attention is handicapped by a limited consideration of the multi-scale spatial heterogeneity in these relationships. This study uses the rental price data of 72,466 apartments in the Tokyo metropolitan area to examine spatial heterogeneity in the real estate market at multiple spatial scales. Within the framework of spatially varying coefficient (SVC) modeling, we utilized a random effect eigenvector spatial filtering-based SVC (RE-ESF-SVC) model, an approach not previously employed in real estate studies, and compared it with the traditional ESF-SVC model, which has no random effects. Our results show that: (1) except for one housing characteristic that impacts prices consistently throughout the Tokyo metropolitan area, relationships between other characteristics and prices vary from local to global spatial scales; (2) because of the utilization of random effects, RE-ESF-SVC has the unique advantage of making estimations flexibly while maintaining a high performance.

Incorporating Spatial Autocorrelation in Machine Learning Models Using Spatial Lag and Eigenvector Spatial Filtering Features

Applications of machine-learning-based approaches in the geosciences have witnessed a substantial increase over the past few years. Here we present an approach that accounts for spatial autocorrelation by introducing spatial features to the models. In particular, we explore two types of spatial features, namely spatial lag and eigenvector spatial filtering (ESF). These features are used within the widely used random forest (RF) method, and their effect is illustrated on two public datasets of varying sizes (Meuse and California housing datasets). The least absolute shrinkage and selection operator (LASSO) is used to determine the best subset of spatial features, and nested cross-validation is used for hyper-parameter tuning and performance evaluation. We utilize Moran’s I and local indicators of spatial association (LISA) to assess how spatial autocorrelation is captured at both global and local scales. Our results show that RF models combined with either spatial lag or ESF features yield lower errors (up to 33% different) and reduce the global spatial autocorrelation of the residuals (up to 95% decrease in Moran’s I) compared to the RF model with no spatial features. The local autocorrelation patterns of the residuals are weakened as well. Compared to benchmark geographically weighted regression (GWR) models, the RF models with spatial features yielded more accurate models with similar levels of global and local autocorrelation in the prediction residuals. This study reveals the effectiveness of spatial features in capturing spatial autocorrelation and provides a generic machine-learning modelling workflow for spatial prediction.

Removing spatial autocorrelation in urban scaling analysis

Analyzing urban scaling relations can help predict the future development of cities and derive scale adjusted metropolitan indicators (SAMIs) to characterize the city's performance. However, existing studies treat cities as individual systems but ignore the spatial autocorrelation between them. Here, we propose a framework that incorporates the influence of spatial autocorrelation into urban scaling analysis. We use an eigenvector spatial filtering (ESF) model to capture the spatial effect when modeling the scaling relations of cities. Based on the residuals of the ESF model, we propose a new set of urban indicators—spatial and scale adjusted metropolitan indicators (SSAMIs)—to address the effect of spatial autocorrelation on SAMIs. The results of our experiments in China and the United States show that compared with non-spatial models, the ESF model could generate better-fitted results when estimating the scaling relations. The results also reveal that using SSAMIs could avoid overestimations of cities in developed regions and underestimations of cities in less developed regions. This study proposes a novel attempt to deal with the spatial autocorrelation effect in urban scaling analysis. It provides insights for understanding the urban scaling law and enhanced indicators for the evaluation of cities.

Incorporating spatial information in machine learning: The Moran eigenvector spatial filter approach

AbstractSpatial statistical models are highly effective for modeling geospatial data as they consider spatial information of geographic spaces and other non‐spatial covariates, enabling them to minimize spatial autocorrelation by addressing spatial dependence. In contrast, machine learning (ML) models are highly effective for predicting non‐spatial data, but they are not as effective for modeling and predicting geospatial data because of spatial autocorrelation issues. One of the frequently reported limitations of ML models for geospatial data modeling is that there is no standard method of incorporating spatial information of geographic space into the model, and consequently they cannot minimize spatial autocorrelation. In this study, we have presented a local spatial information‐embedded ML method capable of minimizing spatial autocorrelation by addressing spatial dependence while predicting a geospatial phenomenon. Our study applied the eigenvector spatial filter method to extract approximated eigenvectors from spatial coordinates and embed them within ML models as a set of vectors along with the selected non‐spatial covariates. We have also presented a comparison of relative prediction performance between traditional spatial statistical and ML‐based models. The experiment demonstrates that incorporating spatially filtered eigenvectors to represent spatial information in ML model specification significantly improves the prediction performance.

Using an Eigenvector Spatial Filtering-Based Spatially Varying Coefficient Model to Analyze the Spatial Heterogeneity of COVID-19 and Its Influencing Factors in Mainland China

The COVID-19 pandemic has led to many deaths and economic disruptions across the world. Several studies have examined the effect of corresponding health risk factors in different places, but the problem of spatial heterogeneity has not been adequately addressed. The purpose of this paper was to explore how selected health risk factors are related to the pandemic infection rate within different study extents and to reveal the spatial varying characteristics of certain health risk factors. An eigenvector spatial filtering-based spatially varying coefficient model (ESF-SVC) was developed to find out how the influence of selected health risk factors varies across space and time. The ESF-SVC was able to take good control of over-fitting problems compared with ordinary least square (OLS), eigenvector spatial filtering (ESF) and geographically weighted regression (GWR) models, with a higher adjusted R2 and lower cross validation RMSE. The impact of health risk factors varied as the study extent changed: In Hubei province, only population density and wind speed showed significant spatially constant impact; while in mainland China, other factors including migration score, building density, temperature and altitude showed significant spatially varying impact. The influence of migration score was less contributive and less significant in cities around Wuhan than cities further away, while altitude showed a stronger contribution to the decrease of infection rates in high altitude cities. The temperature showed mixed correlation as time passed, with positive and negative coefficients at 2.42 °C and 8.17 °C, respectively. This study could provide a feasible path to improve the model fit by considering the problem of spatial autocorrelation and heterogeneity that exists in COVID-19 modeling. The yielding ESF-SVC coefficients could also provide an intuitive method for discovering the different impacts of influencing factors across space in large study areas. It is hoped that these findings improve public and governmental awareness of potential health risks and therefore influence epidemic control strategies.

The Moran Spectrum as a Geoinformatic Tupu: implications for the First Law of Geography

ABSTRACT Geoinformatic Tupu, or Geoinformatic graph spectrum, is a theoretical as well as a technical framework for generalizing geographic knowledge and solving real world problems. Geoinformatic Tupu is a promising platform for capitalizing on the technical advances of Geographic Information Systems, and to integrate the Chinese traditional way of thinking with modern information technology. It has been one of the major research topics in the Chinese GIScience community in recent decades, with an evolving epistemological development. A core objective of Geoinformatic Tupu is to recover and represent geographic principles with the Tupu approach, which is adopted in this paper to formulate the First Law of Geography (FLG) [i.e. the law of spatial autocorrelation] as the Moran Spectrum – a combination of sequential diagrams, graphs, and numeric components. Using the Moran Spectrum as a conduit, we present the theory of Moran Eigenvector Spatial Filtering (MESF), a distinct branch of spatial statistics that has demonstrable advantages in statistical modelling and machine learning, but has yet to be widely disseminated due to its conceptual and computational complexity. This paper demonstrates the effectiveness of the Tupu approach in enriching the representation of the FLG as well as deepening its applications. It also suggests inclusion of the Moran Spectrum as a core component in Geoinformatic Tupu.

Self-adaptive bandwidth eigenvector spatial filtering model for estimating PM2.5 concentrations in the Yangtze River Delta region of China.

PM2.5 concentrations are commonly estimated using geographically weighted regression (GWR) models, but these models may suffer from multi-collinearity and over-focus on local feature problems. To overcome these shortcomings, a self-adaptive bandwidth eigenvector spatial filtering (SA-ESF) model utilizing the golden section search (GO-ESF) and genetic algorithm (GA-ESF) was proposed. The SA-ESF model was applied to estimate ground PM2.5 concentrations in the Yangtze River Delta (YRD) region of China both seasonally and annually from December 2015 to November 2016 using remotely sensing data, factory locations, and road networks. The results of the original eigenvector spatial filtering (ESF), GO-ESF, GA-ESF, and GWR models show that the GA-ESF model offers better performance and exhibits a better average adjusted R2 which is 26.6%, 15.3%, and 10.8% higher than for the ESF, GO-ESF, and GWR models, respectively. We next calculated stochastic site indicators that can describe characteristics of regional concentration from interpolated concentration maps derived from the GA-ESF and GWR models. The concentration maps and stochastic site indicators point to major differences in the PM2.5 concentrations in mountainous areas. There are notably high concentrations in those areas using the GWR model, in contrast with the GA-ESF results, indicating that there may be overfitting problems using the GWR model. Overall, the proposed SA-ESF model with the genetic algorithm technique can capture both global and local features and achieve promising results.