Apprication of Neural Networks to Discriminant Analysis
Mikinori Tsuiki and others
National Institute of Agro-Environmental Sciences
Abstract(not received)––––––––––––––––––––––––––––––––––
Pasture Production Prediction under Seven Different Patterns of
Meteorological Conditions: Case Study for the Konsen Area(Hokkaido)
Masae Shiyomi, Tsuyoshi Akiyama, Tomoyuki Hakamata, Shinsuke Morinaga, andMichio Shibayama
National Institute of Agro-Environmental Sciences
Abstract(not received)––––––––––––––––––––––––––––––––––An Analysis of Seasonal Changes in Air Temperature forPrediction ofthe Changes in Agro-Ecosystems in Japan Caused by Global Warming
Tomoyuki Hakamata and Masaru Takeya
National Institute of Agro-EnvironmentalSciences
Abstract(not received)––––––––––––––––––––––––––––––––––
Analyzing Survey Data of CIM(Computer IntegratedManufucturing)
Keiji Yajima
Science University of Tokyo
Abstract(not received)

JCS Bulletin Vol.5(1991)

11 of 11

Study of Maturity Indicators of Craniofacial Complex and Staturein Korean Children- Possibilities and problems of their adaptation Sumimasa Ohtsuka, Kim Byung Chan, Yoshinobu ShibasakiandTatsuo Fukuhara
Department of Orthodontics, Showa University Dental School
Kitasenzoku 2-1-1, Ohta-ku,Tokyo JAPANNoboru Ohsumi
The Institute of Statistical Mathematics
4-6-7, Minami-Azabu, Minato-ku
Tokyo 106, JAPANAbstract
In clinical orthodontic practice, many of the patients are in the growing and developing stage,
and most of them are treated at the stage inclusive of puberty. Making diagnosis and decisionof orthodontic treatment for the patient in the pubertal growth, it is necessary to evaluate theindividual growth increment, direction and timing. It has long been recognized that anindividual’s chronologic age does not necessarily correlate well with his maturational age.
Investigators have studied possible correlations between skeletal growth of the craniofacialcomplex and general skeletal growth of the body. Longitudinal or cross-sectional evaluation of
maturity by means of pubertal development and the biological development such as bone age,dental age and menarche age could give reliable informations as to whether or not a certain
period of pubertal growth has been attained.
The purpose of this study is to investigate the comparisons that exist between chronologic andskeletal ages within a Korean population to know strictly the degree of maturity about
craniofacial complex.The subjects for this study consisted of 447 males and 339 females withnormal occlusion on whom cephalograms, right and left wrist-hand radiograph and standingheight were cross-sectionally taken from 6 to18 years. For an evaluation of individual bone
maturation from wrist-hand radiograph,we have newly added one stage to Fishman’sSMI(1982) which was originally applied for over 10 years old child from 1 to 11 stages.
Basic statistics summarized the changes in standing height and the craniofacial complex
parameters from 6 to 18 years. Principle component analysis was done to select fiveparameters of linears to describe the craniofacial complex. For the purpose of quantification ofSMI as qualitative data, the correspondence analysis was used. Then,we affirmed therelationship between craniofacial complex and the newly quantified scores of SMI byregression equation.
The results obtained were as follows.
1 . SMI of females showed early maturation than males by almost 2.2 years, sexual difference
was greatest during the time of maximum growth velocity from 4 to 5 of SMI.
2 . Wide variation is demonstrated in the maturational development of craniofacial complex
based on SMI.
3 . After the quantification of SMI, relationship between the parameters of craniofacial complex, especially in Cd-Gn(mandibular length) and body height showed highly correlation.

JCS Bulletin Vol.5(1991)

10 of 11

On Clustering an Asymmetric Similarity Matrix
Tadashi Imaizumi
Tama Institute of Management and Information SciencesAbstract
We encounter an asymmetric similarity matrix in some situations, such as in analyzing thedegree of the communications from a place to other place. Each elements of this matrix isinterpreted as the degree of similarity from one object to the other object. In this paper, a newmodel is proposed. In this model, the degree of communication between two places isassumed to be proportional to the number of nodes of each places and to value of a decreasing
function of distance between these places.
And it is assumed that the structural relations raises the degree of asymmetric similarity. An
estimator of the symmetric components is estimated as the minimum value of twocorresponding elements. The degree of asymmetry is expressed with a row effect and acolumn effect, which indicate the sensitivity of the sender and the receiver respectively.

JCS Bulletin Vol.5(1991)

9 of 11Sensitivity Analysis in Covariance Structure Analysis with
Equality Constraints
Yutaka Tanaka Okayama University
Shingo Watadani Sanyo Gakuen CollegeAbstract(not received)––––––––––––––––––––––––––––––––––
Evaluating the Adjoint Projection Pursuit Regression throughits Applications
Hideaki Hida, Takenobu Tasaki, and Masashi Goto
Shionogi Kaiseki Center
Abstract(not received)

JCS Bulletin Vol.5(1991)

8 of 11

Table 1.
eigenvalue percentage percentage correl. ratio
cum.
between 2 groups----------------------------------------------1
0.2264421.0
21.0-0.36820.13316
12.4
33.4
0.101
3
0.1087010.1
43.5-0.075
40.09276
8.6
52.1
0.165
5
0.081657.6
59.7-0.382
6
0.07274
6.7
66.4-0.15670.06962
6.5
72.9-0.10880.06325
5.9
78.8
0.136
9
0.06013
5.6
84.4
0.067
100.05315
4.9
89.3
11
0.043924.1
93.4
12
0.029152.7
96.1
130.022832.1
98.2
140.019361.8
100.0----------------------------------------------multiple reg. coeff.(correl.ratio)(with 1,4,5)
0.555
m.r.c. adjusted for deg. of freedom
0.532
Table 2.
independent variables

partial correl.
(item)
item categ. coeff.
-------------------------------------------------------------------ability to understand the questions
A1,A20.250
clarity of response
B1,B20.188
degree of awareness of the necessity of
one's own existence within the family
E1,E20.369
peace of mind within the family
F1,F20.182
degree of satisfaction with financial status
G1,G2,G30.468
Character1:punctilious
L1,L20.271
Character2:ability to make good relationships M1,M20.345
daily routine
S1,S20.254
ADL: hearing abilityT1,T20.314
ADL: ability to look after oneself
X1,X20.198
physical condition (in general)
U1,U20.166
ill or not
W2,W10.230
history of cerebral illness(cerebral haemorrhage etc.)
Z2,Z1
0.199
multiple correlation coefficient (correlation ratio)
0.739
multiple correl. coef. adjusted for the degree of freedom 0.546--------------------------------------------------------------------JCS Bulletin Vol.5(1991)

code7 of 11

1One Method of Classification based on an Analysis of
the Structural Relationship between Independent Variables
Setsuko Takakura
Tokyo-Jogakkan Junior College
1105, Tsuruma, Machida-shi,Tokyo, Japan
Abstract
In this paper we will present one method for the classification ofindividuals concerning
whom a number of independent variables have beenmeasured. In order to classify individuals
the method of discriminant analysis isgenerally used. In this paper, we will limit the number ofgroups to two; inwhich case discriminant analysis derives the same result as multipleregression
analysis. When discriminant analysis or multiple regression analysis are used, it is not clear
what the structural relationship between the independent variables is, and also which variables
are more effective for thediscrimination on the basis of the structure of the variables. Then, wewill try first to understand the structure of independent variables by the method ofcorrespondence analysis; secondly, we will tryto assign individuals to two groups by themethod of multiple regression analysis taking as independent variables the scores derived bythe correspondence analysis. There, we will be able to choose some eigen-vectors which are
more effective in discriminating the two groups. That is, we will calculate the linear equation
model according tothe multiple regression model. Then, we can easily choose someeigenvectors which are more effective for the discrimination, and by looking at the positions(coordinates) of the independent variables on the axes chosen, we can understand which
variables are more effective than others in discriminating the groups withreference to thestructural relationship between the variables. We will present it by one example.
This study is concerned with the discrimination of two groups, one which is normal and one
in which there is considerable evidence of senile dementia. The independent variables are 13
items which relate to physical condition, activity in daily life, the degree of awareness offamily and social life, etc.. Each item contains two or three categories. The result we will
present here is based upon the study of 87 elderly males.
First, we will apply the method of correspondence analysis to this data. The eigenvalues andpercentage of variance (ratio of the contribution are shown in Table 1.
Secondly, we will apply the method of multiple regression analysis taking as independent
variables the sample scores which correspond to each eigenvalue resulting from thecorrespondence analysis.
In Table 1 we will add each correlation ratio (equal to the correlation coefficient) between
these two groups using these sample scores.
From this result we can see that the 1st and 5th eigenvectors are effective in discriminating thetwo groups. Then, we will present the disposition of the independent variables on the 1st and5th axes in Fig. 1 and the sample scores on the same axes in Fig. 2.
And, taking three sample scores which correspond to the 1st, 5th and 4th eigenvalues weobtain 0.555 as the multiple regression coefficient. This coefficient is satisfactory.
Thus, we are able to understand the structural relationship between the independent variables
and to clarify which variable is particulary effective in discriminating the two groups byreferring to the structure of all the variables.
As reference, in Table 2 we will present the partial correlation coefficient of each independent
variable when we only apply multiple regression model with these variables.

1

JCS Bulletin Vol.5(1991)

6 of 11

A Study of Cluster Analysis
Wataru Iwamoto and Masakatsu Murakami
The Institute of Statistical Mathematics
Abstract(not received)

JCS Bulletin Vol.5(1991)

5 of 11

Some Variations of Correspondence Analysis
Mariko Murata
The Graduate University for Advanced Studies
Noboru Ohsumi
Institute of Statistical Mathematics
Abstract
The purpose of this paper is to introduce several variations of correspondence analysis which
are proposed by D'Ambra and Lauro(1989a,b).
We first discuss one of the variations, non-symmetrical correspondence analysis (NSCA) for
two-way contingency tables. NSCA is a method to study association structure between anexplanatory variable and a response variable based on a decomposition of Goodman-Kruskal's
tau coefficient. In NSCA, two variables play non-symmetrical role, though they dosymmetrically in the ordinary CA. (Thus, it seems similar to principal component analysis
rather than CA.)
Second, two extensions of NSCA are developed to analyze three-way tables using a flatteningof the table. It is interesting that these extensions can be applied to multi-way data wherevariables can be distinguish into explanatory or response.
Finally, to compare these variations with the ordinary CA, we apply them to data which isresult of a survey of urban dwellers' attitudes toward their environment. If you need, wepresent a floppy disk which gives detail of the survey and the data tables.
References[1] D'Ambra, L. and N. Lauro. (1989a).
Non symmetrical analysis of three-way contingency tables.
``Secondes Journées Internationales: Analyse Statistique des Grands Tableaux'',
Université des Antilles et de la Guyane, Pointe-à-Pitre, 6-9 Mars 1989.
[2] D'Ambra, L. and N. Lauro. (1989b).
Non symmetrical analysis of three-way contingency tables.
In {\em Multiway Data Analysis.}(eds. R. Coppi and S. Bolasco). North-Holland, Amsterdam.

JCS Bulletin Vol.5(1991)

4 of 11

Yasumasa Baba
The Institute of Statistical Mathematics
Abstract(not received)

JCS Bulletin Vol.5(1991)

3 of 11

Contents
Classification Method based on Rankings
Yasumasa Baba
The Institute of Statistical Mathematics
Some Variations of Correspondence Analysis
Mariko Murata and Noboru Ohsumi
The Institute of Statistical Mathematics
A Study of Cluster Analysis
Wataru Iwamoto and Masakatsu Murakami
The Institute of Statistical Mathematics
A Method of Classification based on an Analysis of the Structural
Relationship between Independent Variables
Setsuko Takakura Tokyo Jyogakukan Junior College
Sensitivity Analysis in Covariance Structure Analysis with Equality
Constraints
Yutaka Tanaka
Okayama University
Shingo Watadani
Sanyo Gakuen CollegeEvaluating the Adjoint Projection Pursuit Regression throughits Applications
Hideaki Hida, Takenobu Tasaki, and Masashi Goto
Shionogi Kaiseki Center
On Clustering an Asymmetric Similarity MatrixTadashi Imaizumi
Tama Institute of Management and Information Sciences
Study of Maturity Indicators of Craniofacial Complex and Stature in
Korean Children - Possibilities and problems of their adaptation Sumimasa Ohtsuka, Kim Byung Chan, Yoshinobu Shibasaki, Tatsuo Fukuhara
Department of Orthodontics, Showa University Dental School
Noboru Ohsumi
The Institute of Statistical Mathematics
Apprication of Neural Networks to Discriminant Analysis
Mikinori Tsuiki and others
National Institute of Agro-Environmental Sciences
Pasture Production Prediction under Seven Different Patterns ofMeteorological Conditions: Case Study for the Konsen Area (Hokkaido)
Masae Shiyomi, Tsuyoshi Akiyama, Tomoyuki Hakamata, Shinsuke Morinaga,and Michio Shibayama
National Institute of Agro-Environmental Sciences
An Analysis of Seasonal Changes in Air Temperature for Prediction ofthe Changes in Agro-Ecosystems in Japan Caused by Global Warming
Tomoyuki Hakamata and Masaru Takeya
National Institute of Agro-Environmental Sciences
Analyzing Survey Data of CIM(Computer Integrated Manufucturing)
Keiji Yajima
Science University of Tokyo

Classification Method based on Rankings
JCS Bulletin Vol.5(1991)

2 of 11

BulletinofThe Japanese Classification Society

Volume 5
November 16, 1991
Tokyo, JAPANJCS Bulletin Vol.5(1991)1 of 11