多向度認知空間之分析及視覺化模式之研究

Analysis and Visualization of Multidimensional Perceptual Space

產品設計上常以多向度評量法（Multidimensional Scaling；或MDS） 建構之認知空間進行設計分析。而多維度的資料空間架構在三個維度以上時，於視覺化及設計分析上有其困難性。本研究籍由探討平行座標系統的理論基礎，與目的架構之認知空間的顯示特性會發展以平行座標系統建構MDS 多向度認知空間的視覺化模式，並將自動化系統於全球資訊網（World-Wide-Web 或WWW）環境中實現。其中針對平行座標系統中視覺化的主要盲點一平行軸的排序問題一提出解決建議，就軸間關係藉自認知空筒中各屬性間或屬性與向度間之夾角予以表達，輔以將屬性群集的方式，運用圓形理論（Graph Theory） 和離散最佳化（Discrete Optimization）的計算方法提出較佳解建議，作為自動化系統之預設模式。本研究之目的在提出自動化整合多維認知空間之分析及視覺化的模式，發展之系統將作為MDS自動化系統之一環，以建構具良好直覺性的互動式整合環境，輔助設計師進行設計分析及決策應用。

Product perceptual space, which can be constructed by using Multidimensional Scaling （or MDS）, is often applied at the design analysis stage in product design. One of the problems with applying MDS is the visualization and analysis of a perceptual space that requires more than three dimensions to represent. This research proposes a new model for visualizing multidimensional perceptual space based on Parallel Coordinates. The basics of Parallel Coordinates, including the conversion to and from Cartesian Coordinates and the elegant duality properties between the two kinds of coordinates, are reviewed. By examining the characteristics of a perceptual space generated by MDS, special requirements for integrating multidimensional representations and perceptual spaces are identified. To facilitate analyzing and interpreting a multidimensional perceptual space, an integrated structure combining dimensional axes and attributive axes is developed in a Web-based environment. When using Parallel Coordinates, the parallel axes need to be carefully ordered so that important relationships among the axes can be recognized immediately. Finding an optimal ordering of axes, which minimizes the distances between adjacent axes, is formulated as a Hamiltonian Path problem in Graph Theory. Optimal ordering of parallel axes can then be found by using discrete optimization techniques. In addition, by taking angles among nearby axes into account, the optimal distances between axes can be computed automatically as a default layout, in which strongly correlated axes are placed close together. Finally, this paper demonstrates the analysis and visualization model by using Java programming language to implement a WWW-based system. The goal of this research is to propose an integrated model to visualize and analyze the perceptual space. The developed system will be a subsystem of WebMDS, an integrated, intuitive, and interactive environment to designers for analyzing and visualizing multidimensional perceptual space.