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研究生:謝宜璋
論文名稱:相似性指標之性質研究
論文名稱(外文):Property Analysis of Similarity Indices
指導教授:潘宏裕潘宏裕引用關係
指導教授(外文):Hung-Yu, Pan
學位類別:碩士
校院名稱:國立嘉義大學
系所名稱:應用數學系研究所
學門:數學及統計學門
學類:數學學類
論文種類:學術論文
論文出版年:2011
畢業學年度:99
語文別:中文
中文關鍵詞:出現性指標豐富度指標多元尺度分析群集分析metric propertiesEuclidean properties
外文關鍵詞:incidence indexabundance indexmultidimensional scaling analysiscluster analysismetric propertiesEuclidean properties
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在生態學上,常用相似性指標來衡量群落之間物種的相似程度,其中出現性指標僅考量物種出現與否;然而豐富度指標除考慮物種的出現與否外,又將物種相對豐富度加入,更能描繪生態系之間的物種分佈相關性。
本研究主要探討十七個豐富度指標,透過不同的準則尋找出具有代表性的豐富度指標。首先,以多變量分析中的多元尺度分析(MDS)與群集分析(Cluster Analysis)作為判定的準則,將資料建構於平面空間上,並觀察物種是否隨季節變動遷徙的情況,但研究發現此兩種方式均無法有效的區分出具有代表性的豐富度指標。因此進一步使用Hessian matrix及3D立體圖來判定各豐富度指標的凹性性質,如果指標凹性呈現上凹或下凹的情況,建議使用時需修正其偏誤。此外亦將此一概念應用於出現性指標上,因為線性、不變性等性質及其大小關係亦無法找出具代表性的出現性指標,所以本文考慮Metric與Euclidean性質加以討論。

In Ecology, it often uses similarity index to measure the correlation coefficient between two communities of species. The incidence index just considered these species which present or not. However, abundance indices not only considered the presence of species, but also include the information of the relative abundance of species. It can be more explicit to depict the appearance of the entire ecosystems.
This study investigated seventeen abundance indices. We try to find out the representative abundance indices through different criteria. First, multidimensional scaling analysis(MDS) and cluster analysis are used to be the criteria for constructing the data structure in the plane space, and observed that whether the migration of species by seasons or not. However, we find that these methods can’t distinguish a valid representative from these indices. Therefore, Hessian matrix and the 3D graph are further used to determine the plane curve of those abundance indices. If the concavity of those indices present convex or concave, suggested to modify their bias. In addition, the concept also applied into incidence indices. Because the properties of linear, invariance and the order of these indices can’t distinguish a representation from these indices, so we give more consideration such as Metric and Euclidean property.

目錄
中文摘要 …………………………………………………………… I
英文摘要 …………………………………………………………… II
致謝辭 ………………………………………………………………III
目錄 …………………………………………………………………IV
表目錄 ………………………………………………………………VI
圖目錄 …………………………………………………………… VII
第一章 緒論 ………………………………………………………1
第二章 符號介紹與文獻回顧 ……………………………………3
2.1 符號介紹 …………………………………………………… 3
2.2 相關文獻回顧 ……………………………………………… 4
2.2.1 出現性指標 …………………………………………… 5
2.2.2 豐富度指標 …………………………………………… 6
2.2.3 豐富度指標的估計量..………………………………… 10
2.2.4 多元尺度分析與群集分析 …………………………… 13
2.2.5 Hessian matrix方法判斷凹性 ...………………… 15
第三章 豐富度指標的性質 ……………………………………… 17
3.1 豐富度指標的相關性 ………………………………… 17
3.1.1 多元尺度分析之應用 …………………………… 21
3.1.2 群集分析之應用 ………………………………… 24
3.2 豐富度指標之凹性性質 ……………………………… 26
3.3 出現性指標之性質研究 ……………………………… 28
3.3.1 1-S與(1-S)^1/2 是否滿足Metric形式 …… 29
3.3.2 1-S與 (1-S)^1/2是否滿足Euclidean形式 …32
第四章 實例分析 …………………………………………………… 35
第五章 結論與未來研究 …………………………………………… 45
附錄2.1 ………………………………………………………… 47
附錄3.2 ………………………………………………………………49
附錄3.3.1…………………………………………………………… 57
附錄3.3.2…………………………………………………………… 66
參考文獻 ………………………………………………………………68

中文文獻

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英文文獻

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