Abstract
A new method of multidimensional scaling (MDS) based on band function model is described, which is aimed to treat comparison data obtained by the method of triads, and is capable to apply when comparison data has some missing observations. Configurations determined by the method exist in a certain domain called the solution domain. An algorithm employing the method of steepest descent is proposed and a point located in the solution domain is found out by the algorithm.
First, the proposed method is evaluated by computer simulations. It becomes clear that the method can estimate configurations with higher accuracy than the conventional method does, and it is shown that data for this algorithm must be more than 1/3 of the complete data set of triads method.
Next, the proposed method is evaluated by an experiment. Experimental data on dissimilarities between eleven colors that differ in their value and chroma are processed. Configuration derived by the method fairly agrees to JIS color code of Munsell color system, and the configuration also points out that nonorthogonality may exist between value axis and chroma axis in JIS color code.
