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The 3D PCP \u003cbr /\u003e proposed in this dissertation can display several characteristics of multiple variables \u003cbr /\u003e simultaneously. First, it can show all the information of each observation at a glance. \u003cbr /\u003e Second, it can make some nonlinear structures in data clear. Finally, it is useful to \u003cbr /\u003e find piecewise linear relationships of variables and their conditions. \u003cbr /\u003e The basic idea of the 3D PCP has already appeared in the parallel coordinate plot. \u003cbr /\u003e The parallel coordinate plot can visualize multi dimensional data on a two dimensional \u003cbr /\u003e plane. Coordinates of all variables are set in parallel. In the standard form of parallel \u003cbr /\u003e coordinate plot the bottom position of each axis corresponds to the minimum value of \u003cbr /\u003e each variable, and the top to the maximum value. One observation corresponds to one \u003cbr /\u003e set of connected lines. Parallel coordinate plot can shows the characteristic between \u003cbr /\u003etwo adjoining axes of variables directly. If two variables have a correlation coefficient \u003cbr /\u003eof 1, lines expressing observations are located horizontally. If two variables have \u003cbr /\u003ecorrelation coefficient l, lines of them cross in one point in the middle between two \u003cbr /\u003eaxes. \u003cbr /\u003e However, relations between two variables whose positions are apart more than two \u003cbr /\u003eaxes are not clearly shown immediately. Another serious problem of static parallel \u003cbr /\u003ecoordinate plot is that it is not easy to distinguish one observation from another when \u003cbr /\u003ethe number of observations is large. To solve these problems, several interactive \u003cbr /\u003etechniques have been developed including highlighting by brushing operations. The \u003cbr /\u003e3D PCP can show the same effect as the highlighting by brushing operation in a \u003cbr /\u003eparallel coordinate plot by extending it into 3dimensional space. We choose one \u003cbr /\u003evariable as a reference variable, usually a response variable. The 3D PCP places \u003cbr /\u003econnected lines expressing observations in 3dimensional spaces by sorting them \u003cbr /\u003eaccording to the values of the reference variable. This observationwise 3D PCP \u003cbr /\u003erepresentation is useful for illustrating the characteristics of observations such as \u003cbr /\u003eoutliers. \u003cbr /\u003e The 3D PCP has another representation in which values of observations on each \u003cbr /\u003evariable are connected by lines. It is called variablewise connection representation \u003cbr /\u003eand is useful to see relations between the reference variable and other variables. For \u003cbr /\u003eexample, the connected lines expressing the variable which has strong linear \u003cbr /\u003erelationships with the reference variable are located around a straight line expressing \u003cbr /\u003ethe reference variable. It is well known that the scatterplot matrix can show \u003cbr /\u003erelationships between variables clearly. However, if the number of variables is large, \u003cbr /\u003ethe single scatterplot elements become too small to be seen properly. The 3D PCP can \u003cbr /\u003eshow more variables than a scatterplot matrix. It is sometimes more suitable to show \u003cbr /\u003echaracteristics of data simultaneously than using a static representation of scatterplot \u003cbr /\u003ematrlx. \u003cbr /\u003e We note that the 3D PCP can detect particular nonlinear relations, i.e. interaction \u003cbr /\u003eby two variables, through observationwise connection representation. This \u003cbr /\u003erelationship is detected by the special pattern of the angles of connected lines \u003cbr /\u003eexpressing observations. As explained earlier, a correlation coefficient near 1 or 1 \u003cbr /\u003ebetween two variables whose axes are adjacent produces parallel or crossing patterns \u003cbr /\u003ein parallel coordinate plots. Similar patterns can be detected in 3D PCP. If we find the \u003cbr /\u003echange of such patterns at specific values of the reference variable, we conclude that \u003cbr /\u003ethe structures of data are different for each region of the reference variables. In such \u003cbr /\u003ecases, it is natural to divide the data into several groups in which the structures have \u003cbr /\u003eno more changes. We propose to draw many 3D PCPs corresponding to the groups \u003cbr /\u003esimultaneously and use a lattice layout, which places many graphs on a grid. We show \u003cbr /\u003ethat they are useful to identify the interaction between two variables by analyzing \u003cbr /\u003esimulation and real data. \u003cbr /\u003e We realize our 3D PCP by using the Java language. Java has several advantages for \u003cbr /\u003eimplementing modern data visualization methods. It is a pure object oriented \u003cbr /\u003eprogramming language and has welldesigned standard graphics libraries which are \u003cbr /\u003euseful to realize 2D and 3D graphics and interactive graphical user interfaces. These \u003cbr /\u003elibraries can work as useful components of statistical graphics and be in incorporated \u003cbr /\u003eby using socalled design patterns. Design patterns are suggested solutions to common \u003cbr /\u003eproblems often appearing in objectoriented software development. Our \u003cbr /\u003eimplementation is based on several design patterns for generality and reusability. Our \u003cbr /\u003esoftware enables us to analyze data by utilizing advanced interactive operations given \u003cbr /\u003eby Java. We show that the 3D PCP and the software are expected to lead to new \u003cbr /\u003eachievements in the field of data visualization. \u003cbr /\u003e This dissertation is set out as following. Chapter 1 surveys issues of information \u003cbr /\u003evisualization and basic statistical graphics used in multivariate data visualization \u003cbr /\u003esuch as scatterplot, scatterplot matrix, 3D scatterplot and parallel coordinate plot. It \u003cbr /\u003ealso discusses dynamic techniques of data visualization and existing software products \u003cbr /\u003efor data visualization such as Mondrian, ParallAX, and GGobi. In Chapter 2, 2D \u003cbr /\u003eparallel coordinate plots are discussed. Important issues at visual data analysis with \u003cbr /\u003eparallel coordinate pIot are considered. We introduce several existing works for \u003cbr /\u003eextending parallel coordinate plot into 3\u0027dimensional spaces. In Chapter 3, we discuss \u003cbr /\u003eour extension of parallel coordinate plot into 3dimensional space, and several of its \u003cbr /\u003echaracteristics. We show usefulness of lattice layout to display several 3D PCP at a \u003cbr /\u003etime in Chapter 4. Chapter 5 analyzes three data sets by using our 3D PCP. In \u003cbr /\u003eChapter 6, we explain details of our software design. Finally, concluding remarks are \u003cbr /\u003egiven in Chapter 7. \u003cbr /\u003e", "subitem_description_type": "Other"}]}, "item_1_description_7": {"attribute_name": "学位記番号", "attribute_value_mlt": [{"subitem_description": "総研大甲第1150号", "subitem_description_type": "Other"}]}, "item_1_select_14": {"attribute_name": "所蔵", "attribute_value_mlt": [{"subitem_select_item": "有"}]}, "item_1_select_8": {"attribute_name": "研究科", "attribute_value_mlt": [{"subitem_select_item": "複合科学研究科"}]}, "item_1_select_9": {"attribute_name": "専攻", "attribute_value_mlt": [{"subitem_select_item": "15 統計科学専攻"}]}, "item_1_text_10": {"attribute_name": "学位授与年度", "attribute_value_mlt": [{"subitem_text_value": "2007"}]}, "item_creator": {"attribute_name": "著者", "attribute_type": "creator", "attribute_value_mlt": [{"creatorNames": [{"creatorName": "HONDA, Keisuke", "creatorNameLang": "en"}], "nameIdentifiers": [{"nameIdentifier": "0", "nameIdentifierScheme": "WEKO"}]}]}, "item_files": {"attribute_name": "ファイル情報", "attribute_type": "file", "attribute_value_mlt": [{"accessrole": "open_date", "date": [{"dateType": "Available", "dateValue": "20160217"}], "displaytype": "simple", "download_preview_message": "", "file_order": 0, "filename": "甲1150_要旨.pdf", "filesize": [{"value": "321.7 kB"}], "format": "application/pdf", "future_date_message": "", "is_thumbnail": false, "licensetype": "license_11", "mimetype": "application/pdf", "size": 321700.0, "url": {"label": "要旨・審査要旨", "url": "https://ir.soken.ac.jp/record/789/files/甲1150_要旨.pdf"}, "version_id": "57279c47633f4607abc407e87fc600d0"}]}, "item_language": {"attribute_name": "言語", "attribute_value_mlt": [{"subitem_language": "eng"}]}, "item_resource_type": {"attribute_name": "資源タイプ", "attribute_value_mlt": [{"resourcetype": "thesis", "resourceuri": "http://purl.org/coar/resource_type/c_46ec"}]}, "item_title": "A 3Dimensional Extension of Parallel Coordinate Plot", "item_titles": {"attribute_name": "タイトル", "attribute_value_mlt": [{"subitem_title": "A 3Dimensional Extension of Parallel Coordinate Plot"}, {"subitem_title": "A 3Dimensional Extension of Parallel Coordinate Plot", "subitem_title_language": "en"}]}, "item_type_id": "1", "owner": "1", "path": ["17"], "permalink_uri": "https://ir.soken.ac.jp/records/789", "pubdate": {"attribute_name": "公開日", "attribute_value": "20100222"}, "publish_date": "20100222", "publish_status": "0", "recid": "789", "relation": {}, "relation_version_is_last": true, "title": ["A 3Dimensional Extension of Parallel Coordinate Plot"], "weko_shared_id": 1}
A 3Dimensional Extension of Parallel Coordinate Plot
https://ir.soken.ac.jp/records/789
https://ir.soken.ac.jp/records/7899502162baff8419b8f5d79413284918e
名前 / ファイル  ライセンス  アクション 

要旨・審査要旨 (321.7 kB)

Item type  学位論文 / Thesis or Dissertation(1)  

公開日  20100222  
タイトル  
タイトル  A 3Dimensional Extension of Parallel Coordinate Plot  
タイトル  
言語  en  
タイトル  A 3Dimensional Extension of Parallel Coordinate Plot  
言語  
言語  eng  
資源タイプ  
資源タイプ識別子  http://purl.org/coar/resource_type/c_46ec  
資源タイプ  thesis  
著者名 
本多, 啓介
× 本多, 啓介 

フリガナ 
ホンダ, ケイスケ
× ホンダ, ケイスケ 

著者 
HONDA, Keisuke
× HONDA, Keisuke 

学位授与機関  
学位授与機関名  総合研究大学院大学  
学位名  
学位名  博士（学術）  
学位記番号  
内容記述タイプ  Other  
内容記述  総研大甲第1150号  
研究科  
値  複合科学研究科  
専攻  
値  15 統計科学専攻  
学位授与年月日  
学位授与年月日  20080319  
学位授与年度  
2007  
要旨  
内容記述タイプ  Other  
内容記述  The three dimensional parallel coordinate plot (3D PCP) is a visualization method <br /> to detect hidden information in data by using human spatial perception. The 3D PCP <br /> proposed in this dissertation can display several characteristics of multiple variables <br /> simultaneously. First, it can show all the information of each observation at a glance. <br /> Second, it can make some nonlinear structures in data clear. Finally, it is useful to <br /> find piecewise linear relationships of variables and their conditions. <br /> The basic idea of the 3D PCP has already appeared in the parallel coordinate plot. <br /> The parallel coordinate plot can visualize multi dimensional data on a two dimensional <br /> plane. Coordinates of all variables are set in parallel. In the standard form of parallel <br /> coordinate plot the bottom position of each axis corresponds to the minimum value of <br /> each variable, and the top to the maximum value. One observation corresponds to one <br /> set of connected lines. Parallel coordinate plot can shows the characteristic between <br />two adjoining axes of variables directly. If two variables have a correlation coefficient <br />of 1, lines expressing observations are located horizontally. If two variables have <br />correlation coefficient l, lines of them cross in one point in the middle between two <br />axes. <br /> However, relations between two variables whose positions are apart more than two <br />axes are not clearly shown immediately. Another serious problem of static parallel <br />coordinate plot is that it is not easy to distinguish one observation from another when <br />the number of observations is large. To solve these problems, several interactive <br />techniques have been developed including highlighting by brushing operations. The <br />3D PCP can show the same effect as the highlighting by brushing operation in a <br />parallel coordinate plot by extending it into 3dimensional space. We choose one <br />variable as a reference variable, usually a response variable. The 3D PCP places <br />connected lines expressing observations in 3dimensional spaces by sorting them <br />according to the values of the reference variable. This observationwise 3D PCP <br />representation is useful for illustrating the characteristics of observations such as <br />outliers. <br /> The 3D PCP has another representation in which values of observations on each <br />variable are connected by lines. It is called variablewise connection representation <br />and is useful to see relations between the reference variable and other variables. For <br />example, the connected lines expressing the variable which has strong linear <br />relationships with the reference variable are located around a straight line expressing <br />the reference variable. It is well known that the scatterplot matrix can show <br />relationships between variables clearly. However, if the number of variables is large, <br />the single scatterplot elements become too small to be seen properly. The 3D PCP can <br />show more variables than a scatterplot matrix. It is sometimes more suitable to show <br />characteristics of data simultaneously than using a static representation of scatterplot <br />matrlx. <br /> We note that the 3D PCP can detect particular nonlinear relations, i.e. interaction <br />by two variables, through observationwise connection representation. This <br />relationship is detected by the special pattern of the angles of connected lines <br />expressing observations. As explained earlier, a correlation coefficient near 1 or 1 <br />between two variables whose axes are adjacent produces parallel or crossing patterns <br />in parallel coordinate plots. Similar patterns can be detected in 3D PCP. If we find the <br />change of such patterns at specific values of the reference variable, we conclude that <br />the structures of data are different for each region of the reference variables. In such <br />cases, it is natural to divide the data into several groups in which the structures have <br />no more changes. We propose to draw many 3D PCPs corresponding to the groups <br />simultaneously and use a lattice layout, which places many graphs on a grid. We show <br />that they are useful to identify the interaction between two variables by analyzing <br />simulation and real data. <br /> We realize our 3D PCP by using the Java language. Java has several advantages for <br />implementing modern data visualization methods. It is a pure object oriented <br />programming language and has welldesigned standard graphics libraries which are <br />useful to realize 2D and 3D graphics and interactive graphical user interfaces. These <br />libraries can work as useful components of statistical graphics and be in incorporated <br />by using socalled design patterns. Design patterns are suggested solutions to common <br />problems often appearing in objectoriented software development. Our <br />implementation is based on several design patterns for generality and reusability. Our <br />software enables us to analyze data by utilizing advanced interactive operations given <br />by Java. We show that the 3D PCP and the software are expected to lead to new <br />achievements in the field of data visualization. <br /> This dissertation is set out as following. Chapter 1 surveys issues of information <br />visualization and basic statistical graphics used in multivariate data visualization <br />such as scatterplot, scatterplot matrix, 3D scatterplot and parallel coordinate plot. It <br />also discusses dynamic techniques of data visualization and existing software products <br />for data visualization such as Mondrian, ParallAX, and GGobi. In Chapter 2, 2D <br />parallel coordinate plots are discussed. Important issues at visual data analysis with <br />parallel coordinate pIot are considered. We introduce several existing works for <br />extending parallel coordinate plot into 3'dimensional spaces. In Chapter 3, we discuss <br />our extension of parallel coordinate plot into 3dimensional space, and several of its <br />characteristics. We show usefulness of lattice layout to display several 3D PCP at a <br />time in Chapter 4. Chapter 5 analyzes three data sets by using our 3D PCP. In <br />Chapter 6, we explain details of our software design. Finally, concluding remarks are <br />given in Chapter 7. <br />  
所蔵  
値  有 