| Research Abstract |
I carried out a series of research on artificial data for correspondence analysis (Hayashi's third method of quantification).
1. For artificial data having several linear traits, each solution of the eigenvalue problem belongs to the Guttman series of some linear trait. I proposed a method to identify them (Math.Japon., 1994).
2. I proposed artificial disk in order to add a linear trait representing the radius to the circular data by Iwatsubo (1984). I solved the eigenvalue problem (J.Japan Statist.Soc., 1994).
3. I presented artificial cylinder data having a circular trait and also a linear trait representing the length. The eigenvalue problem is solvable analytically (Statist.& Prob.Letters, 1994).
4. I presented artificial torus data having two circular traits and furthermore the solid torus data having also a linear trait representing the radius (Behaviormetrika, 1994).
5. These four papers are concerned with the situation where each line connects two points. The situation where some line passes through more than two points can be dealt with (Math.Japon., 1995).
6. Mr.H.Endo and myself wondered whether there exists some typical geometrical trait besides the linear or circular trait. We found that each of five types of regular polyhedrons leads to the spherical trait which has three dimensions, extending one dimension of linear trait and two dimensions of circular trait (J.Japan Statist.Soc., 1995).
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