Computer-aided study of correspondence analysis

我对对应分析（Hayashi的第三种量化方法）的人工数据进行了一系列研究。对于具有多个线性特征的人工数据，特征值问题的每个解都属于某个线性特征的Guttman级数。我提出了一种识别它们的方法（数学。日本）。, 1994年)。2。为了给Iwatsubo（1984）的圆形数据添加一个表示半径的线性特征，我提出了人工磁盘。我解决了特征值问题（j .日本统计社）。, 1994年)。3。我提出了具有圆形特征和表示长度的线性特征的人工圆柱体数据。特征值问题是可解析解决的（统计学家）。和概率。字母,1994)。4。我提出了具有两个圆形特征的人工环面数据，此外，实体环面数据还具有表示半径的线性特征（Behaviormetrika, 1994）。这四篇论文关注的是每条线连接两点的情况。一条线经过两个以上点的情况可以处理（数学。日本）。, 1995年)。6。远藤先生和我都想知道，除了线性或圆形特征之外，是否还存在一些典型的几何特征。我们发现，五种正多面体中的每一种都导致了三维的球形性状，扩展了一维的线性性状和二维的圆形性状（J.Japan statistics . soc .）。, 1995)。

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).