Predicting GDP of Indonesia Using K-Nearest Neighbour Regression

The impact of the global recession in 1998 that originated from the recession in the US will affect the projected economies in Asia, including Indonesia, both direct and indirect nature. In this study, we predicted Indonesia's GDP in the event of the economic crisis that hit Indonesia starting in 1998. Instead of using the famous prediction algorithm as a neural network and linear regression. K-Nearest Neighbour is selected because it is easy and fast to use in the small dataset. We use a dataset from 1980-2002, consisting of rice prices, premium prices, GDP of Japanese country, American GDP, currency exchange rates, Indonesian government consumption, and the value of Indonesia's oil exports. For evaluation, we compare k-NN regression prediction result with prediction result using back propagation neural network and multiple linear regression algorithm. Result show, k-NN regression is able to predict Indonesia's GDP using small dataset better than the neural network, and multiple linear regression method

A generalization of the Minkowski distance and a new definition of the ellipse

In this paper, we generalize the Minkowski distance by defining a new distance function in n-dimensional space, and we show that this function determines also a metric family as the Minkowski distance. Then, we consider three special cases of this family, which generalize the taxicab, Euclidean and maximum metrics respectively, and finally we determine circles of them with their some properties in the real plane. While we determine some properties of circles of the generalized Minkowski distance, we also discover a new definition for the ellipse.Comment: 18 pages, 18 figure

Road distance and travel time for an improved house price Kriging predictor

The paper designs an automated valuation model to predict the price of residential property in Coventry, United Kingdom, and achieves this by means of geostatistical Kriging, a popularly employed distance-based learning method. Unlike traditional applications of distance-based learning, this papers implements non-Euclidean distance metrics by approximating road distance, travel time and a linear combination of both, which this paper hypothesizes to be more related to house prices than straight-line (Euclidean) distance. Given that – to undertake Kriging – a valid variogram must be produced, this paper exploits the conforming properties of the Minkowski distance function to approximate a road distance and travel time metric. A least squares approach is put forth for variogram parameter selection and an ordinary Kriging predictor is implemented for interpolation. The predictor is then validated with 10-fold cross-validation and a spatially aware checkerboard hold out method against the almost exclusively employed, Euclidean metric. Given a comparison of results for each distance metric, this paper witnesses a goodness of fit (r²) result of 0.6901 ± 0.18 SD for real estate price prediction compared to the traditional (Euclidean) approach obtaining a suboptimal r² value of 0.66 ± 0.21 SD

Distance metric choice can both reduce and induce collinearity in geographically weighted regression

This paper explores the impact of different distance metrics on collinearity in local regression models such as geographically weighted regression. Using a case study of house price data collected in Hà Nội, Vietnam, and by fully varying both power and rotation parameters to create different Minkowski distances, the analysis shows that local collinearity can be both negatively and positively affected by distance metric choice. The Minkowski distance that maximised collinearity in a geographically weighted regression was approximate to a Manhattan distance with (power = 0.70) with a rotation of 30°, and that which minimised collinearity was parameterised with power = 0.05 and a rotation of 70°. The results indicate that distance metric choice can provide a useful extra tuning component to address local collinearity issues in spatially varying coefficient modelling and that understanding the interaction of distance metric and collinearity can provide insight into the nature and structure of the data relationships. The discussion considers first, the exploration and selection of different distance metrics to minimise collinearity as an alternative to localised ridge regression, lasso and elastic net approaches. Second, it discusses the how distance metric choice could extend the methods that additionally optimise local model fit (lasso and elastic net) by selecting a distance metric that further helped minimise local collinearity. Third, it identifies the need to investigate the relationship between kernel bandwidth, distance metrics and collinearity as an area of further work

Geographically weighted regression with parameter-specific distance metrics

Geographically weighted regression (GWR) is an important local technique to model spatially varying relationships. A single distance metric (Euclidean or non-Euclidean) is generally used to calibrate a standard GWR model. However, variations in spatial relationships within a GWR model might also vary in intensity with respect to location and direction. This assertion has led to extensions of the standard GWR model to mixed (or semiparametric)GWR and to flexible bandwidth GWR models. In this article, we present a strongly related extension in fitting a GWR model with parameter-specific distance metrics (PSDM GWR). As with mixed and flexible bandwidth GWR models, a back-fitting algorithm is used for the calibration of the PSDM GWR model. The value of this new GWR model is demonstrated using a London house price data set as a case study. The results indicate that the PSDM GWR model can clearly improve the model calibration in terms of both goodness of fit and prediction accuracy, in contrast to the model fits when only one metric is singly used. Moreover, the PSDM GWR model provides added value in understanding how a regression model’s relationships may vary at different spatial scales, according to the bandwidths and distance metrics selected. PSDM GWR deals with spatial heterogeneities in data relationships in a general way, although questions remain on its model diagnostics, distance metric specification, and computational efficiency, providing options for further research

GWmodel

In GWmodel, we introduce techniques from a particular branch of spatial statistics,termed geographically-weighted (GW) models. GW models suit situations when data are not described well by some global model, but where there are spatial regions where a suitably localised calibration provides a better description. GWmodel includes functions to calibrate: GW summary statistics, GW principal components analysis,GW discriminant analysis and various forms of GW regression; some of which are provided in basic and robust (outlier resistant) forms

GWmodelS: a standalone software to train geographically weighted models

With the recent increase in studies on spatial heterogeneity, geographically weighted (GW) models have become an essential set of local techniques, attracting a wide range of users from different domains. In this study, we demonstrate a newly developed standalone GW software, GWmodelS using a community-level house price data set for Wuhan, China. In detail, a number of fundamental GW models are illustrated, including GW descriptive statistics, basic and multiscale GW regression, and GW principle component analysis. Additionally, functionality in spatial data management and batch mapping are presented as essential supplementary activities for GW modeling. The software provides significant advantages in terms of a user-friendly graphical user interface, operational efficiency, and accessibility, which facilitate its usage for users from a wide range of domains

Examining The Role of Job by Geographically Weighted Poisson Regression in The Post-Migration Adaptation Process: The Case of Van

Migration is a process of social change that involves the geographical relocation of people from one settlement to another, either permanently or temporarily, in order to spend all or part of their future lives. Van province is among the provinces receiving migration due to its geopolitical location and level of development. Migrant individuals need to adapt to that society in order to normalise their relations with the resident population over time. Individuals are in constant contact with the society due to the work done after migration, so it is thought that the work done has an important effect on the adaptation process. In this study, the effect of work on the post-migration adjustment process of individuals migrating from the first and second degree border neighbouring provinces of Van province was analysed using Poisson and Geographically Weighted Poisson Regression methods. The aim of the study is to determine the relationship between the contribution of work in the post-migration adjustment process and independent variables and to analyse which of the models used for the analysis gives stronger results. In the study, a face-to-face survey was conducted with 440 individuals and it was observed that the Geographically Weighted Poisson Regression method gave stronger results according to AIC, AICc and R^2 values. In addition, the effect and significance of the relationship between the dependent variable and independent variables according to provinces and districts are visualised and given with maps

지리 가중 회귀모형 및 섀플리 가법 설명모형에 의한 지역침수 영향요인 분석

학위논문(석사) -- 서울대학교대학원 : 환경대학원 환경조경학과, 2022. 8. 송영근.The landscape is considered as a key component of the ecosystem intervention. Human activities have significantly changed the surface characteristics, such as affected the circulation and flow of natural materials and energy, or weakened the rainwater collection, storage function and runoff drainage capacity of the watershed. These led to waterlogging disasters and increased the risk to the living environment. Therefore, landscape planners and decision-makers need to constantly improve and optimize the landscape pattern to maintain the ecosystem's dynamic balance and reduce waterlogging at the same time. Development of remote sensing technology makes it possible to study large-scale watershed units, meanwhile the experiments on such large-scale sites can be verified by theory. Existing research on verification of theories ignored important interactions within the landscape pattern because the traditional linear regression model (a subfield of supervised learning) such as Geographically Weighted Regression (GWR) could not analyze the relationship between independent variables while analyzing the relationship between independent variables and dependent variables. In recent years, development of interpretable machine learning models in the field of machine learning is making up for this shortcoming. Among them, Shapley Additive Explanations (SHAP) is a representative method which provides an interpretable machine learning model based on game theory. It can not only analyze the relationship between independent variables and dependent variables, but also take into account correlations between multiple independent variables, and produce importance ranking according to the contribution degree. Through our extensive and thorough verification and comparative analysis of the two methods, we first find that in the analysis results of GWR, the Shannon Diversity Index (SHDI, one representative landscape metric) is seriously underestimated, while in the results of SHAP, SHDI shows a great impact on waterlogging in any scale of watershed units. At the same time, according to the prediction result of Prediction Mean Squared Error (MSE), although the error value of GWR is small, SHAP is still far more accurate than GWR. Secondly, the water cycle process has characteristics of producing multi-scale geographical watersheds. In order to taking into account the dynamic balance of hydrology, conducting comparative analysis of multi-level watershed-scale units is necessary. Our results show that the use of finer-scale watersheds as the research scale is not necessarily suitable for waterlogging research. In this study, we find that analysis on waterlogging in the Seoul Capital Area (SCA) based on Large-scale watershed units (LSWU) is the most appropriate and accurate. Finally, it is naturally assumed that a threshold for landscape pattern characteristics exists. When the impact on waterlogging reaches this critical point, its role in promoting or alleviating waterlogging will change. Through estimating threshold values of landscape pattern characteristics, the purpose of waterlogging disaster mitigation can be achieved accurately and at a low cost. In summary, this study explores the new analysis method of interactions between landscape patterns and waterlogging, and provid a reference for methods and results of waterlogging control based on landscape ecology.경관은 생태계 개입의 핵심 요소로 꼽힌다. 인류의 활동은 지표면의 특징을 크게 변화시키고 있으며, 자연 물질과 에너지의 순환과 흐름에 영향을 주어 유역에 빗물을 모으는 기능과 경류배수의 능력을 약화시켜 침수 재해의 발생을 초래하고 생활환경의 위험을 증가시킨다. 따라서 경관계획가와 정책결정자는 생태계의 동적 균형을 유지하기 위해 경관구조의 최적화를 끊임없이 개선하여 침수를 완화하는 목적을 달성할 필요가 있다. 원격 탐사 기술의 발달로 대규모 유역 단위 연구가 가능해졌으며, 이러한 대규모 현장에서의 실험은 이론으로 검증될 수 있 다. 이론 검증에 대한 과거의 연구는 지리 가중 회귀 모델(GWR)와 같은 전통적인 선형 회귀 모델(지도 학습)은 독립변수과 종속변수간의 관계를 분석하면서 독립 변수 간의 관계를 분석할 수 없기 때문에 경관 패턴 내의 상호 작용을 무시했다. 최근 머신러닝 분야에서 해석 가능한 머신러닝 모델의 발전이 이러한 단점을 보완하고 있다. 이 중 섀플리 가법 설명모형(SHAP)은 게임 이론에 기반한 해석 가능한 기계 학습 모델의 대표이다. 독립변수와 종속변수의 관계를 분석할 수 있을 뿐 아니라 여러 독립변수의 상관관계를 고려해 기여도에 따른 중요도 순위를 얻을 수 있다. 두 가지 방법의 검증 및 비교 분석을 통해 GWR의 분석 결과에서 섀넌 다양성 지수(SHDI)가 심각하게 과소평가된 반면, SHAP 결과에서 SHDI는 모든 규모의 유역 단위에서 침수에 큰 영향을 미친다는 것을 알 수 있다. 또한 예측 평균 제곱 오차(MSE)의 예측 결과에 따르면 GWR의 오차 값은 작지만 SHAP가 GWR보다 훨씬 정확하다. 둘째, 물 순환 과정은 다단계 지리적 유역을 생성하는 특성을 가지고 있 다. 수문학의 동적 균형을 실현하기 위해서는 다단계 유역 규모 단위의 비교 분석이 필요하며, 그 결과는 더 미세한 유역을 연구 규모로서 사용하는 것이 반드시 수문 연구에 적합하지 않음을 보여준다. 본 연구에서는 대규모 유역단위(LSWU)를 기반으로 한 수도권(SCA)의 침수 연구가 가장 적절하고 정확하다. 마지막으로 경관패턴 특징은 임계치가 존재한다. 침수에 대한 영향이 임계점에 도달했을 때, 침수를 촉진하거나 완화하는 작용이 변화한다. 경관패턴 특징의 임계치를 통해 정확하고 저비용으로 침수 재해를 완화하는 목적을 달성할 수 있다. 본 연구는 경관패턴와 침수간의 상호작용 분석방법에 대하여 새로운 탐구를 진행하여 경관생태학에 기초한 침수 완화방법과 결과를 참고로 제공한다.Chapter 1. Introduction 01 Section 1.1 Urbanization and Human Intelligence 01 Section 1.2 Landscape and Landscape Ecology 02 Section 1.3 Land Use Land Cover and Landscape Pattern Metrics 03 Section 1.4 Natural Water Cycle and Urban Waterlogging 05 Section 1.5 Comparison with Previous Studies 06 Section 1.6 Workflow and Study Area 10 Chapter 2. Materials and Methods 14 Section 2.1 Land Use Land Cover and Landscape Pattern Metrics 14 Section 2.2 Waterlogging Degree of Watershed Units 26 Section 2.3 Geographically Weighted Regression (GWR) 31 Section 2.4 Shapley Additive Explanations (SHAP) 34 Section 2.5 Prediction Mean Squared Error (MSE) 35 Section 2.6 Piecewise Linear Model 36 Chapter 3. Results 37 Section 3.1 Geographically Weighted Regression (GWR) 38 Section 3.2 Shapley Additive Explanations (SHAP) 52 Section 3.3 Prediction Mean Squared Error (MSE) 69 Section 3.4 Piecewise Linear Model 69 Chapter 4. Discussion 76 Section 4.1 Selection of Data and Tools 76 Section 4.2 Supervised Learning and Interpretive Machine Learning 77 Section 4.3 Landscape Threshold and Hydrological Disaster 84 Section 4.4 Rational Use of Limited Land Resources 84 Section 4.5 Limitation and Future Direction 85 Chapter 5. Conclusion 86 Appendix 89 References 90 Abstract in Korean 9