Computer-aided study of correspondence analysis

我对人工数据进行了一系列的研究，用于对应分析（Hayashi的第三种量化方法）。1.对于具有多个线性特征的人工数据，特征值问题的每一个解都属于某个线性特征的Guttman级数。我提出了一种方法来识别它们（Math.Japon.，1994年）。我提出了人工圆盘，以便在岩坪（1984）的圆形数据中添加代表半径的线性特征。我解决了特征值问题（日本统计学会，1994年）。我提出了人工圆柱体数据具有圆形性状，也是线性性状代表的长度。特征值问题是可解的解析（统计学。Prob.Letters，1994）。我提出了具有两个圆形特征的人工环面数据，并且还提出了具有代表半径的线性特征的实心环面数据（Behaviormetrika，1994）。这四篇论文是关于每条线连接两点的情况。可以处理某条直线通过两个以上点的情况（Math.Japon.，1995年）。远藤健二先生和我都想知道，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。我们发现五种类型的正多面体中的每一种都导致具有三维的球形特征，扩展了线性特征的一维和圆形特征的二维（J.Japan Statist.Soc.，1995年）。

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).