R 語言在統計領域非常熱門，許多新穎的統計研究方法都會發布成 R 語言的套件。本研究旨在 R 語言中實現廣義相關圖（Generalized Association Plots; GAP）以處理區間資料，能夠被 R 語言龐大的象徵型區間資料庫與演算法套件所支援。GAP 是矩陣視覺化（Matrix Visualization; MV）的擴展。特別著重於象徵型區間資料的探索性分析 (Exploratory data analysis; EDA)，在進行複雜統計方法之前能讓資料自述其故事。對此本研究開發出一款套件名為 iGAP，將 GAP 概念引入 R 中，使區間資料進行排列並視覺化，讓使用者能快速且清晰的了解到資料之間的關係與型樣。我們相信 GAP 作為一個進階的探索性資料分析工具，在 R 中不僅能應用在區間資料上，未來也能對各種資料型態進行推廣。

R language is highly popular in the statistical field, with many innovative statistical methods being released as R packages. This study aims to implement Generalized Association Plots (GAP) for interval data in R, supported by a vast repository of symbolic interval data and algorithmic packages in R. GAP is an extension of Matrix Visualization (MV). Focusing particularly on the Exploratory Data Analysis (EDA) of symbolic interval data, the study facilitates data to narrate its story before applying complex statistical methods. To this end, we have developed a package named iGAP, integrating the GAP concept into R, enabling the arrangement and visualization of interval data for users to quickly and clearly understand the relationships and patterns within the data. We believe that GAP, as an advanced tool for EDA in R, can be applied to interval data and potentially extended to various data types in the future.

目錄
第一章 緒論 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 研究背景與動機 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 研究目的 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 論文架構 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
第二章 文獻探討. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.1 象徵型資料分析 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.2 廣義相關圖 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.3 象徵型區間資料矩陣視覺化 . . . . . . . . . . . . . . . . . . . . . . . . 6
2.3.1 區間資料變量相關性關係矩陣 . . . . . . . . . . . . . . . . . . . 7
2.3.2 區間資料概念距離關係矩陣 . . . . . . . . . . . . . . . . . . . . 9
2.4 排序演算法 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
第三章 套件設計與相關套件 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3.1 iGAP 設計流程 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3.2 資料預處理與建立 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.3 象徵型資料處理 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.4 視覺化技術 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.5 iGAP 函式總結 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
第四章 實例應用. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
4.1 汽車資料 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
4.2 食用油資料 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
第五章 結論與未來工作 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
5.1 研究總結 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
5.2 未來研究方向 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
圖目錄
圖 2.1 一般資料和象徵型區間資料矩陣與其變量之間相關性矩陣及概念之
間距離矩陣圖 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
圖 2.2 區間資料矩陣視覺化漸層上色 . . . . . . . . . . . . . . . . . . . . . 7
圖 3.1 iGAP 套件設計流程圖 . . . . . . . . . . . . . . . . . . . . . . . . . 16
圖 3.2 ex1_db2so 區間資料量化後的關係矩陣視覺化 . . . . . . . . . . . . 23
圖 3.3 區間資料標準化上色 . . . . . . . . . . . . . . . . . . . . . . . . . . 24
圖 3.4 兩個關係矩陣進行 R2E 排序 . . . . . . . . . . . . . . . . . . . . . . 25
圖 3.5 uscrime_int 區間資料矩陣視覺化 . . . . . . . . . . . . . . . . . . . 27
圖 3.6 RColorBrewer 色譜 . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
圖 3.7 ex1_db2so 區間資料廣義相關圖，參數變數為預設 . . . . . . . . . 31
圖 4.1 Cars.int 區間資料廣義相關圖，Concept 間距離採用 Span Normalized Euclidean Hausdorff distance，變數相關性採用 Empirical Correlation Coefficient，並且使用 R2E 進行排序 . . . . . . . . . . . . . . . . 35
圖 4.2 oils 區間資料廣義相關圖，Concept 間距離採用 Span Normalized
Euclidean Hausdorff distance，變數相關性採用 Empirical Correlation
Coefficient，並且使用 Single-linkage agglomerative algorithm 進行排序 37
圖 5.1 iGAP 套件介面化示意圖 . . . . . . . . . . . . . . . . . . . . . . . . 41
表目錄
表 3.1 R 語言 dataSDA 套件內建的區間資料 . . . . . . . . . . . . . . . . 19
表 3.2 R 語言 RSDA 套件內建的區間資料 . . . . . . . . . . . . . . . . . . 20
表 3.3 R 語言 ggESDA 套件內建的區間資料 . . . . . . . . . . . . . . . . . 20
表 3.4 運算環境 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
表 3.5 iGAP 函式總結 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

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