MULTIDIMENSIONAL SCALING FOR DISSIMILARITY FUNCTIONS WITH CONTINUOUS ARGUMENT(Functional Data Analysis)

In this paper, a method of Multidimensional Scaling (MDS) for dissimilarity functions with continuous argument is discussed. MDS is one of the important methods for data analysis. Most conventional MDS methods suppose that dissimilarities are real values. Nowadays, the types of data set dealt with in data analysis are extended. Ramsay and Silverman proposed the concept of Functional Data Analysis (FDA). FDA deals with functional data or with data as functional data. When dissimilarity data among n objects are given dependent on a variable t, we would like to use methods of MDS of functional version; the aim of the method is to derive functional configuration X(t) that represents the dissimilarity functional data. A method of MDS for dissimilarity functions with discrete argument is also discussed, because most dissimilarity functions are given by discrete values in view of implementation on computer.