Abstract
This paper presents an algorithm for block identification of Origin Destination data matrix based on Multi Dimensional Scaling method. The purpose of this identification consists of two phases: one of them is to identify the boundary of an area which has an homogeneous character from the view point of mathematical similarity, the other is to identify the nuclei of the area which has a centered function.
Both the Theory of Quantification 4 (Eij type) and cluster analysis are used. OD data is translated into a 3-D Euclidean distance, next then, the coordinates are clustered to generate a hierarchical tree graph.
The features of algorithm are described as follows;
(1) The normalization of OD data matrix by using the geometric mean.
(2) The identification of boundary of the areas.
i) The Analysis of normalized OD data matrix with the Theory of Quantification 4 presents us some useful eigenvalues.
ii) The hierarchical structure is shown by clulster analysis with the use of three largest eigenvalues. By these processes, the boundary of the areas are identified.
(3) The identification of nuclei of the areas.
i) The sign of geometric mean is reversed.
ii) Theory of Quantification 4 is applied to the reversed data.
iii) The eigenvalues by the Theory of Quantification 4 show the nuclei of the areas which was found by the (2) process.
This method is applied to Telecommunication OD data matrix to ascertain the effectiveness. The results are clear and useful to the analysis of ‘information block’ of Japan.
