以自組織映射網路整合群集分析及識別分析

Abstract

對於水文學者來說，區域化(regionalization)是用來推估未設測站地區某些水文資訊的有效工具。其中，水文均一區的劃分是區域化中極為重要的工作。過去，水文均一區的劃分是透過三種複雜的統計技術（包含主成分分析、群集分析及識別分析）的結合而完成。在這三種統計技術中，主成分分析並非劃分水文均一區必要的步驟；大部份關於水文均一區的劃分的問題則存在於傳統的群集分析方法中；而識別分析在水文均一區劃分中的用法則並不直覺。因此傳統水文均一區的劃分方法並不是一個良好的方法。水文學家強烈需要簡單且直觀的方法來劃分水文均一區。 本文的目的在於發展一整合群集分析及識別分析的方法，以改進水文均一區劃分的方法。本論文首先說明劃分水文均一區的本質。由於大部分水文均一區劃分的問題發生於傳統群集分析方法中，所以接著以實例說明傳統群集分析方法的缺失。本論文所提出的方法以自組織映射網路(self-organizing map, SOM)為基礎。因此，本論文首先簡單的介紹自組織映射網路的理論。接著說明本論文基於自組織映射網路而發展的方法的理論及使用方法。本文所提出的方法，可簡稱為SOMCD(SOM-based cluster and discrimination analysis)。為測試SOMCD的性能，本論文將數個人為產生的資料集以SOMCD加以分析。從分析結果中可發現，利用SOMCD，可同時展現出資料點間的相對拓璞關係、決定適當的群集數目並將未知的資料點恰當的配置到已知的群集中，且不會漏失任何原始資料中的重要資訊。由可決定適當的群集數目這個優點來說，SOMCD確實較傳統群集分析法優越。而將未知的資料點配置到已知的群集中的結果顯示與真實情況相符。 接下來，本論文利用SOMCD分析影響台灣南部地區低流量延時曲線的水文因子。結果顯示SOMCD的表現確實相當傑出，而分析結果可做為進行台灣南部地區低流量延時曲線的區域化之用。由上述SOMCD的應用中，發現SOMCD不同的參數設定可使用者以不同的觀點檢視所分析的資料。關於SOMCD參數設定的資訊，亦整理並呈現於本論文中。

Regionalization is a useful tool for hydrologists to extrapolate certain hydrological information at ungauged sites. The delineation of hydrologically homogeneous regions is the major task. The conventional method for the delineation of hydrologically homogeneous regions consists of three complicated statistical techniques (principal component analysis, cluster analysis, and discrimination analysis). Among these three methods, principal component analysis is not necessary; a large amount of severe problems (such as the determination of the number of clusters) encountered in the delineation of hydrologically homogeneous regions arise in conventional clustering methods and the employ of discrimination analysis is not intuitional. Thus the conventional method for the delineation of hydrologically homogeneous regions is not an excellent method. An easy and intuitional method for the delineation of hydrologically homogeneous regions is of great demand. For facilitating the delineation of hydrologically homogeneous regions, the purpose of this thesis is to develop a method that combines cluster analysis and discrimination analysis. Therefore, the substance of the conventional method for the delineation of hydrologically homogeneous regions is first described. Since most of problems arise in conventional clustering methods, the shortcomings of the conventional clustering methods are then indicated through several examples. The basis of the proposed method is self-organizing map (SOM). Hence, the simple introduction of self-organizing map is given and then the theory of the proposed method is presented. The proposed method is based on self-organizing map, and combines cluster analysis and discrimination analysis. Thus, the proposed method is named SOMCD (SOM-based cluster and discrimination analysis). Artificial data sets are employed to examine the capabilities of SOMCD. By the results of the applications, it is shown that using SOMCD one can view the relative topological relationships of input patterns, determine the proper number of clusters, and assign unknown patterns to known clusters without losing any information of input patterns. Regarding the capability of determining the proper number of clusters, SOMCD is superior to conventional cluster analysis. The discrimination results also show that the assignments of unknown patterns to known clusters are reasonable using SOMCD. SOMCD is also applied to analyze the hydrological factors affecting low-flow duration curves in southern Taiwan. The results of SOMCD to the actual data set also show that SOMCD is an outstanding method. It can be derived from the results that different parameters settings of SOMCD make SOMCD inspect the data set in different views. Suggestions of the parameters setting of SOMCD are extracted from the applications and are presented in this thesis.