환경 데이터를 위한 카운팅 노름 정규화를 이용한 지리 가중 희소 회귀 = Geographically weighted sparse regression using counting norm regularization for environmental data

다국어 초록 (Multilingual Abstract)

Spatial heterogeneity refers to the variation in patterns, relationships, or characteristics across
different spatial locations, and it is a common phenomenon in spatial data. This phenomenon
occurs because environmental factors such as water quality can vary substantially from one
place to another. Geographically weighted regression (GWR) effectively captures such spatial
heterogeneity by allowing coefficients to vary across locations. In GWR, local variable selec
tion is crucial as it helps capture the most relevant spatial relationships and enhances the
interpretation of local features. This study applies geographically weighted sparse regression
with counting norm (L0-GWR) to enhance model sparsity and performance. The method dis
tinguishes between regionally activated and non-activated local features in an adaptive way.
Biochemical oxygen demand (BOD), a key indicator of river water pollution, exhibits distinct
spatial patterns in South Korea, influenced by local environmental factors. However, some
local factors are expected to have minimal impact on BOD in certain regions. This study
aims to demonstrate the effectiveness of applying the L0-GWR method in the spatially vary
ing coefficient model for BOD data. To evaluate its performance, we compare L0-GWR with
GWR and geographically weighted LASSO regression using performance and interpretation
measures. The L0-GWR approach demonstrates competitive performance and provides clear
interpretability

목차 (Table of Contents)

• 1. 서론 1
• 2. L0 노름을 이용한 지리 가중 회귀 3
• 3. 구현 5
• 3.1 알고리즘 5
• 3.2 튜닝 파라미터 선택 7
• 3.3 모형 적합 진단 및 해석 지표 7
• 4. 실증 적용 9
• 5. 결론 14
• 참고문헌 15
• Abstract (in English) 18
• 부록 A. L0-GWR을 위한 적응적 최적 부분집합 선택 알고리즘 19
• 부록 B. 튜닝 파라미터 선택에 대한 민감도 분석 20