Masaya Iizuka

Acceleration of the alternating least squares algorithm for principal components analysis

Principal components analysis (PCA) is a popular descriptive multivariate method for handling quantitative data and it can be extended to deal with qualitative data and mixed measurement level data. The existing algorithms for extended PCA are PRINCIPALS of Young et al. (1978) and PRINCALS of Gifi (1989) in which the alternating least squares algorithm is utilized. These algorithms based on the least squares estimation may require many iterations in their application to very large data sets and variable selection problems and may take a long time to converge. In this paper, we derive a new iterative algorithm for accelerating the convergence of PRINCIPALS and PRINCALS by using the vector @e algorithm of Wynn (1962). The proposed acceleration algorithm speeds up the convergence of the sequence of the parameter estimates obtained from PRINCIPALS or PRINCALS. Numerical experiments illustrate the potential of the proposed acceleration algorithm.

Variable Selection in Principal Component Analysis

While there exist several criteria by which to select a reasonable subset of variables in the context of PCA, we introduce herein variable selection using criteria in Tanaka and Mori (1997)’s modified PCA (M.PCA) among others.

Statistical Software VASMM for Variable Selection in Multivariate Methods

A statistical software package VASMM (VAriable Selection in Multivariate Methods) has been developed for selecting a subset of variables in multivariate methods without external variables. The current version is fully implemented for variable selection in principal component analysis and factor analysis. The system has been constructed with interactive architecture on Internet. The users can not only use the system via a web browser but can also obtain information related to variable selection in multivariate techniques of their choice. It allows for us to perform variable selection easily in a variety of practical applications.

Web-Based Statistical Graphics using XML Technologies

Most statistical graphics on theWeb are static, noninteractive and undynamic, even though other statistical analysis systems usually provide various interactive statistical graphics. Interactive and dynamic graphics, see Symanzik (2004), can be implemented using Internet technologies such as Java or Flash (Adobe, 2007). Scalable Vector Graphics (SVG) and Extensible 3D (X3D) offer alternative means of realizing an XML-based graphics format. One advantage of using XML is that data from a wide range of research topics are easy to deal with, because they are all presented in the XML format. Another advantage is that XML is a text-based graphics format, i.e., it is scriptable, meaning that it can be generated dynamically by a statistical analysis system or web application. Before introducing XML-based graphics, we introduce the relationship between theWeb, XML, and statistical graphics.

A Generalized Modification of Scheffé’s Paired Comparisons: A theoretical approach to decrease the number of experiments

In the sensory evaluation, Scheffe’s paired comparisons are theoretically interesting and also practically used many times. However, the number of its experiments is so large that there are a few cases in which its experiments can not be carried out. On those occasions, Scheffe’s method can not be used. The current study proposes a generalized modification of Scheffe’s method and demonstrates the parameter estimation and testing, with a manageable number of experiments by keeping the minimum structure of Scheffe’s model. To do this, we suppose the following assumption for all experiments. (1) The scores do not have order effects. (2) Combination effect may exists in a few combination, and the value is constant γ. (3) The observation is considered a random sample drawn from the same population. It is of interest to see if the number of experiments can be reduced without sacrificing the estimation process.