MCDM'08 - paper no. 2


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Optimized star plot as decision aids: applications of maximum resolution topology

Sydney CK Chu, James K. Ho, S.S. Lam


The traditional star plot has been a longstanding means of presenting multi-variate data. Its early-days use can be traced back to "star symbol plot" of automobile data for large rays to represent favorable characteristics. Another pioneering use in clinical data is a graphical way of summarizing patient's evolving responses. Since the early 1970s and with the coined name of Kiviat plot or graph, wide-spread use in visualizing computer and program performance has become industrial standard among software engineers. It is ever more so in the modern advance of computer graphics, transformed into popular evaluation tools such as 2/3-D Kiviat graph and 3-D Kiviat tube. Its importance amidst forward technological strides remains largely in its ease of visualization, qualitatively on the basis of the shape of a star plot.
In recent years we have staged a series of studies, by focusing of its analysis and topology, resulting in usefulness in the following extensions. First, a (canonical) star plot topology for high-dimensional data visualization is applied to data records of, specifically, multi-attribute dichotomies. Our project on data analysis of on-line auction markets provides such generic sample usage for dimensions identified in constructing a multi-attribute dichotomy to help discern relative empirical advantages to buyers and sellers.
The second stage, of data and optimization modeling aspects, bases on the deeper observation that the areas of the plot for the two parts of a dichotomy may be used quantitatively as an aggregate measure of their relative dominance. An optimization GP model is developed to determine a topology the geometry and the arrangement of dimensions that maximizes the resolution of this measure with respect to a given set of reference dichotomies. The outcome of this modeling phase is what we call an MRT (or Maximum Resolution Topology), that in the sense of maximally discriminating its dichotomy of a set of multi-attribute data records, it is an overall best representation (accompanied by an "optimized" visualization).
The third stage is the coding of MRT construction integrated into a spreadsheet-style decision support system (MRT-DSS). Its ease of use has been promising and robust for diverse applications. Samples of these will conclude the paper as illustrations.


Star plot, data visualization, multi-attribute dichotomy, optimization modeling, goal programming, maximum resolution topology (MRT), decision support system, applications for exploratory data analysi

Reference index:

Sydney CK Chu, James K. Ho, S.S. Lam, (2009), Optimized star plot as decision aids: applications of maximum resolution topology, Multiple Criteria Decision Making (4), pp. 41-60

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