最小化空間異質性損失之分群演算法

Abstract

空間分析中常利用聚合資料的方法來去除資料的不確定性並做後續的分析，然而聚合的結果不同進而導致空間現象在統計解讀的不同，其為Modifiable area unit problem (MAUP) 中分區效果的影響。如何控制MAUP儼然成為重要議題。近年來，研究指出Spatial aggregation entropy (SAE) 可做為衡量MAUP的統計量。然而，目前SAE多用於檢視區域分區受MAUP影響的結果而未應用於最適分群方法，且SAE對於相同變異不同平均的組別，有估計上的差異。因此本研究欲將以SAE進行改善後，做為目標函數並提出新的演算法 Searching Neighbors and Aggregating algorithm (SNA)，目的是在給定分組數下計算最小異質性損失量的空間劃分。為了衡量演算法的表現，本研究模擬12種不同空間型態之資料與臺灣中部鄉鎮區域之收入平均與變異係數，應用於不同演算法中，討論其整體分組與各組組內均質程度以評估演算法的表現。結果顯示，SNA的表現與自相關的程度有關。在高度自相關時，SNA整體表現較其他演算法都來的好，中度自相關時，該演算法在分組數小於6時表現較佳。而低度自相關時該演算法則表現較差。本研究以改良後的SAE作為目標函數控制MAUP的效果，與過往分群方法比較，討論分群結果在統計量上的表現，並提供單變量在特定尺度下，最小異質性損失量的空間劃分結果。

Aggregation is typically used to smooth the noise in data for spatial analysis. Different aggregating methods may lead to various zoning schemes, and the statistical outcome may differ owing to the zoning effect of the modifiable area unit problem (MAUP). The spatial aggregation entropy (SAE) method has been proposed to measure the MAUP effect. However, SAE is used to verify the MAUP effect using aggregated data and has not been applied for optimal zoning. This study aims to correct SAE and takes it as the objective function to propose a new algorithm, Searching Neighbors and Aggregating (SNA). The performance of this algorithm is tested via various aggregating method using 12 types of spatial pattern "single-core" hypothetical data and individual income tax data of middle Taiwan. The results show that SNA's performance is related to spatial autocorrelation (SA). Specifically, SNA's performance is the best when SA is high (0.9), or SA is approximately 0.5 and the number of groups is less than six. Overall, this study corrects the SAE formula and provides a new algorithm that returns the optimal zoning, thereby preserving most spatial heterogeneity at a specific scale.