多點群聚現象的跨尺度特性

Abstract

傳統針對點形態分析的空間統計方法主要聚焦於其全域或區域形態的探討，而忽略了點資料的整體分佈趨勢，這整體分佈可透過一個跨尺度過程中被觀察與描述。過去空間統計研究提出，由多點所組成的點分佈則可能呈現出會隨着尺度而改變的空間形態，亦即可調整空間單元問題 (MAUP) 。另一方面，碎形分析研究指出，點形態在跨尺度過程的初期會以固定的速率發生變化，而經過某一尺度後此速率會降低。發生速率轉換的尺度 (即臨界尺度) 是可反映點的整體分佈趨勢 (即巨觀形態) 的最大尺度，亦即從全域形態開始逐漸提高尺度的過程中，其形態因 MAUP 而發生變化的速率是固定的，而在臨界尺度以上的尺度遞增則只對一些區域造成形態上的影響。 本研究提出一個跨尺度分析架構以偵測臨界尺度，並建立一套將原始點分佈加總成巨觀形態的流程架構。本研究進行了三項實驗，包括兩個針對理論分佈的實驗以及一組實證資料的分析。這三項實驗分別以：（1）探討跨尺度過程中的加總效果；（2）探討單核心群聚特性對跨尺度分析的影響；以及（3）探討真實資料中所反映的巨觀形態與原始分佈之間的差異。結果反映在臨界尺度下的整併點分佈已足夠反映原始點資料的空間形態；群聚的大小與組成群聚的點數量對於跨尺度分析結果呈對數變化的關係；整體分佈趨勢可悲臨界尺度下加總點所形成的巨觀形態所捕捉。 在過去常見於瞭解點分佈形態的全域或區域空間統計研究中之外，本研究不但提供了一個新的分析工具，也提供了一種對於檢視點分佈形態上的新視角。這個分析架構，包括臨界尺度的偵測，以及巨觀形態的呈現方式，對於空間點資料的資料探索以及地圖視覺化將有所幫助。

Conventional spatial statistics analysis reveal either the global or local spatial pattern for point distribution but ignore the big picture of the point data, which can be observed through a scaling process. As discussed in spatial statistical studies, point distribution may show a scale-dependent spatial pattern, namely the modifiable areal unit problem (MAUP). On the other hand, as suggested in fractal analysis studies, the point pattern change at a consistent rate at the beginning of the scaling process, and the rate decrease after a scale. This scale of rate shifting (namely critical scale, CS) is the finest scale that can capture the big picture of the point distribution (namely macro pattern), i.e. the changes of pattern due to MAUP have the same effect since the global level, and the higher scales after CS will only affect the pattern of partial area. In this study, a scaling analysis framework was proposed to identify the critical scale, and a set of aggregation procedure was designed to convert the original point dataset into the macro pattern. Three experiments were conducted to test the scaling analysis framework, including two experiments on theoretical distributions and one on empirical point distributions. The three experiments were designed: (1) to test the aggregation effect on scaling process; (2) to test the influences of mono-centric clustering properties to the scaling analysis; and (3) to illustrates the contrast between macro patterns and the original distribution of empirical data. The results suggested that the aggregation point on critical scale could capture most of the spatial properties from original data; the area and number of point formed a logarithm relationship with the critical and final scale; and the big picture of the point distribution could be captured by the macro pattern of the aggregated points on critical scale. Aside from the conventional understanding of point pattern as discussed in the previous global or local spatial statistics methods, this study provides not only a new tool but also a novel perspective of viewing the point distribution. This analysis framework, including the critical scale identification and macro pattern aggregation, can be useful for spatial point data exploration and map visualization.