Homogeneity analysis which includes principal component analysis as a special case is a useful method for describing data structure on a low dimensional space. In the method the homogeneity defined by a loss function based on distance between vectors is used as a measure of homogeneity of variables. Introducing a measure based on distance between a vector and a higher dimensional space, we can extend a concept of homogeneity more broadly, that is, the loss function which defines homogeneity is based on distance between a variable vector and a low dimensional space.
In this paper a new method for describing data structure on a low dimensional space is proposed by a natural extension of the concept of homogeneity. The method describes data structure on a low dimensional space by minimizing the loss function based on distances between vectors and a space.
In this paper, we examine a fast computing method of the continuous wavelet transform. That is, we propose ways to improve accuracy and to compute phase infornation which arise when attempting to the fast algorithm in the frequency domain. For improving accuracy, it is effective to use mother wavelets whose frequency is lower by 2 octaves than the Nyquist frequency. This technique doesn't have an influence on the computation speed regardless of improving in the computation accuracy. Moreover, to get a high degree of accuracy in the high frequency area, to use up-sampling by the L-Spline interpolation it is effective. In addition, the effectivity of our method for phase infomation was confirmed by model signal.
Key words: Fast algorithm, Computation speed, Phase, Accuracy, Mother waveletVarimax rotation is often used in factor analysis in order to make the factors easy to interpret. In this paper the author applies the rotation to Hayashi's second method of quantification, and tries to make the category scores easy to interpret. The rotation is applied to the category scores standardized in terms of both the frequency-weighted mean and the within-group variance. A set of simple artificial data is presented to illustrate the method. Then the method is applied to two data sets: medical data on the aged with 9 groups, 62 individuals and 16 variables, and then Fisher's iris data. Finally two results, those obtained by applying varimax rotation to canonical discriminant analysis and those obtained by applying the rotation to Hayashi's second method of quantification, are compared with each other.
Key words: Factor analysis, Canonical discriminant analysis, Category score
In this paper, we discuss properties of uniqueness of principal
points of symmetric univariate distributions.
Li \& Flury(1995) have proposed a sufficient condition that
k principal points of symmetric univariate distributions are
symmetry with respect to the expectations.
We point out some mistakes in the deriving process of
the sufficient condition by Li \& Flury(1995), and
derive the sufficient condition of uniqueness of k
principal points of symmetric univariate distributions using
a sufficient condition for the uniqueness of best L_2 approximation by
piecewise polynomials with variable breakpoints by Chow(1982).
We also derive another sufficient condition of uniqueness of k
principal points of symmetric univariate distributions using
a sufficient condition for the uniqueness of optimum quantizing of
univariate random variables with mean-square error criterion
by Trushkin(1982).