A Derivation of the Algebraic Curve for Multi-dimensional Data using
the Least-squares Distance
Masahiro Mizuta
Hokkaido UniversityAbstract
We propose a method for finding the algebraic curve that fits multi-dimensional data. An algebraic
curve in n dimensional space is generally defined by n-1 polynomial expressions. The proposed
method finds the n-1 polynomial expressions of the algebraic curve for n dimensional data. The sumof the squares' distances from the data point to the nearest point on the curve is minimum.

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Utilizing MDPREF When the Number of Sources is Large
Akinori Okada and Junko Marumo
Rikkyo (St. Paul's) University, Tokyo
Abstract
The purpose of the present paper is to introduce a procedure to utilize MDPREF(Carroll, 1972, 1980)
when the number of sources is large. The procedure, which is based on the external MDPREF
analysis (Okada & Marumo, 1992), uses cluster analysis and INDSCAL (Arabie, Carroll, &DeSarbo, 1987; Carroll, 1972). When the number of sources becomes large, the difficulty ingraphically representing the result obtained by MDPREF increases. Thus the conventional ways ofutilizing MDPREF when the number of sources is large are (a) to analyze all sources simultaneouslyor (b) to clustering (grouping) homogeneous sources (by cluster analysis or other similar
procedures), to obtain averaged data in each cluster (group), and to analyze average data as if eachcluster is a source. These two conventional ways have shortcomings such that it is practically
impossible to disclose differences among sources, differences among sources within the same cluster(group) or differences among clusters (groups).
The present procedure consists of (a) to find clusters of homogeneous sources by cluster analysis,(b) to compute inner product matrix among objects in each cluster, (c) to analyze inner productmatrices by INDSCAL to obtain a common object configuration and a weight configuration, and (d)to derive a source configuration (vectors) by external MDPREF analysis using the common object
configuration resulted from INDSCAL. The present procedure was applied to the data on eatinghabits.
References[1]Arabie, P., Carroll, J.D., & DeSarbo, W.S. (1987). Three-way scaling and clustering. Newbury
Park, CA: Sage.
[2]Carroll, J. D. (1972). Individual differences and multidimensional scaling. In R. N. Shepard,
A. K. Romney, & S. B. Nerlove (Eds.), Multidimensional scaling: Theory and applications in thebehavioral sciences. Vol. 1 (pp. 105-155). New York: Seminar Press.
[3]Carroll, J. D. (1980). Models and methods for multidimensional analysis of preferential choice (orother dominance) data. In E. D. Lantermann & H. Feger (Eds.), Similarity and choice (pp. 234289), Bern: Hans Huber.
[4]Carroll, J. D., & Chang, J. J. (1970). Analysis of individual differences in multidimensional
scaling via N-way generalization of "Eckart-Young" decomposition. Psychometrika, 35, 283-319.
[5]Okada, A., & Marumo, J. (1992). External MDPREF analysis based on INDSCAL: An
application to the survey data comparing eating habits among Tokyo, Paris, and New York.
Proceedings of the 1992 Fall National Conference of the Operations Research Society of Japan, pp.
252-253.

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6 of 7(eds. Y.Dodge and et al.), COMPSTAT '92, Switzerland, Computational Statistics, Volume 2, PP
43-48, Physica-Verlag Heidelberg.
[11] Ohsumi, N.(1992), An Experimental System for Navigating Statistical Meta-Information -- The
Meta-Stat Navigator, (eds. Y.Dodge and et al.), COMPSTAT '92, Switzerland, Computational
Statistics, Volume 2, PP 375-380, Physica-Verlag Heidelberg.
[12] Nikkei BP Publishing Company(1992), Existing state of Multimedia, Nikkei Byte, No.105, PP
284-289, (in Japanese).
[13] AuthorWare(1992), User's Manual of AuthorWare Star, ASCII, (in Japanese).

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A Consultation System for Statistical Analysis on Multimedia Software
Atsuhiro HAYASHI
Kawasaki Medical SchoolAbstract
The development and popularization of personal computers have had a strong influence on the fieldof statistics during the last ten years. The analysis of data which was once carried out only on main
frame computers can now even at home with a personal computer.
But, many users who have data sets and purposes for analyses are worried about how to selectstatistical methods and combine them, or their possible misuse of methods, because they lackknowledge of and experience with statistical analysis. Furthermore it is difficult that how to selectsoftware which are fit to their purposes, and how to use them.
In the field of Artificial Intelligence(AI), there are some representational models of knowledge. The
semantic network model is an effective model for the hierarchical knowledge, and the knowledge
may be easily modified. The hypertool has the same structure as the semantic network model.
To deal with the above mention problems, we have developed a consultation system for statisticalanalysis based on hypertool. This system advises to the user one appropriate statistical method basedon our knowledge base linking of the knowledge and programs of statistics. And this system utilized
the feature of multimedia for user interface. It offers the representation of consulting things easily
with figures.
The system derives a statistical method to fit the user's purpose by means of a dialogue between theuser and this system. The system is designed for data analysts and students without statisticalknowledge or experience.
In this paper, we describe a statistical consultation system that provides assistance to nonstatisticians. There are many kinds of statistical software programs, but most of them require someknowledge of and experience with statistics. Therefore, the development of a consultation systemthat can provide knowledge of data analyses is eagerly desired by many users.
We developed the consultation system based on hypertool. This system is expandable and has theadvantage of being able to add/modify statistical knowledge. The system derives a statistical method
fitting user's purpose from a dialogue between the user and this system. The system aims at data
analysts and students without statistical knowledge or experience.
Key Words : expert system; consultation system; hypertool; multimedia; semantic network
References[1] Gale, W.A.(1986), Artificial Intelligence and Statistics, Addison Wesley.
[2] Ueno, H. and Ishizuka, M.(1987), Usage of Knowledge and it's Representation, Ohm Inc., (inJapanese).
[3] Tarumi, T. and Hayashi, A.(1988), Statistical Analysis Software --- Seto/B, Kyoritsu Publishing
Company, (in Japanese).
[4] Hayashi, A. and Tarumi, T.(1988), A Consultation System for Method Selection on DataAnalysis, The Proceedings of the 5th Annual JCS Meeting, PP 50-51, (in Japanese).
[5] Christopher F.Chabris(1989), Artificial Intelligence and Turbo C, Multiscience Press, Inc.
[6] MaxThink Inc.(1989), User's Manual of HyperLink, (in Japanese).
[7] Afifi, A.A. and Clark, V.(1990), Computer-aided multivariate analysis 2nd ed., Van NostrandReinhold Company.
[8] Van den Berg G.M. and Visser R.A.(1990), Knowledge Modelling for Statistical Consultation
System; Two Empirical Studies, COMPSTAT '90, Yugoslavia, Physica-Verlag.
[9] Gebhardt F.(1990), An Expert System Strategy for Selecting Interesting Results, COMPSTAT'90, Yugoslavia, Physica-Verlag.
[10] Hayashi,A. and Tarumi,T.(1992), A Consultation System for Statistical Analysis on Hypertool,
JCS Bulletin Vol.6(1992)4 of 7

A Latent Structure in College Entrance Data
Shoichi UEDA
Ryukoku University

Abstract
Due to an excessive preparation for the race to university entrance, students are sliced by 'hensachi'
scores of preliminary achievement tests and guided to a route for entrance with higher passing
possibility. Furthermore, this deduce a hierarchical ranking for high schools and universities
regardless their identical tradition or educational target. This hierarchical structure is clearly found in
high-school-colledge matrix data in Kansai area. Distributions of passing university are comparedand two principal components are derived. These are
1: two dimensional scores reflecting achievement ranking
2: score reflecting commuting distancewith 47% and 16% contribution respectively. Using 1991 and 1992 data, facter scores are computedfor each high school and university, and then two score-maps are compared. Quite stableconfigurations are found and demonstrates that the 'hensachi-slicing' is unchanged in this period.
This suggests a drastic change could follow in comming years when 18-years-old populatin decrease
but university capacity keep unchange. To find any sign of future change, repeated analysis should
be made as soon as 1993 years data become available.

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Contents
A Latent Structure in College Entrance Data
Shoichi UEDARyukoku University
A Consultation System for Statistical Analysis on Multimedia Software
Atsuhiro HAYASHI Kawasaki Medical School
Utilizing MDPREF When the Number of Sources is Large
Akinori Okada and Junko Marumo Rikkyo (St. Paul's) University, TokyoA Derivation of the Algebraic Curve for Multi-dimensional Data using theLeast-squares Distance
Masahiro Mizuta
Hokkaido University

JCS Bulletin Vol.6(1992)

2 of 7BulletinofThe Japanese Classification Society

Volume 6
December 25, 1992
Tokyo, JAPANJCS Bulletin Vol.6(1992)

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