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Title: 主成分選取與因子選取在費雪區別分析上的探討
Discussion of the Fisher's Discriminant Analysis Based on Choices of Principal Components and Factors
Authors: 李婉菁
Contributors: 姜志銘
Keywords: 主成分
Principal Component
Date: 2006
Issue Date: 2009-09-17 13:47:42 (UTC+8)
Abstract: 當我們的資料變數很多時,我們通常會使用主成分
我們將分別利用由Mardia等人 (1979) 和Chang (1983) 所提出的兩種方法
同時我們也證明Mardia等人 (1979) 和Chang (1983)的方法對於
Principal component analysis or factor analysis are often used
to reduce the dimensionality of the original variables.
However, the principal component or factor, which has
larger variance (i.e eigenvalue) explaining larger proportion of total sample
variance, may not retain the most information for other analyses later.
For example, using the first few principal components or factors
having the largest corresponding eigenvalues as
discriminant variables, the discriminant result
may not be good or even appropriate.

\hspace{2.05em}We first discuss two methods, given by Mardia et al. (1979) and Chang (1983)
for choosing discriminant variables when data are randomly obtained from
a mixture of two multivariate normal distributions.
We then use the discriminant result (or classification error rates)
to compare these two methods and the traditional method of using the
principal components, which have the larger corresponding eigenvalues,
as discriminant variables. We also prove that the both the two methods
have the same selection order on principal components and factor (obtained
by the principal component method).
Furthermore, we use the method of
Mardia et al. to select appropriate discriminators when data is from
three populations.
Reference: [1] Mardia K.V., Kent J.T. and Bibby J.M., Multivariate Analysis, Academic
Press, (1979), 322–324.
[2] Chang W.C., On using principal components before separating a mixture of two
multivariate normal distributions, Appl. Statist., 32 (1983), 267–275.
[3] Jolliffe I.T., Morgan B.J.T. and Young P.J., A simulation study of the use of
principal components in linear discriminant analysis, J. Stat. Comput. Simul.,
55 (1996), 353–366.
[4] Jolliffe I.T., Morgan B.J.T. and Young P.J., A note on using principal components
in linear discriminant analysis, (1995). Submitted for publication.
[5] Murry G.D., A cautionary note on selection of variables in discriminant analysis,
Appl. Statist., 3 (1977), 246–250.
[6] Namkoon G., Statistical analysis of introgression, Biomtrics, 22 (1966), 488–
[7] Wolfe J.H., Computational methods for estimating the parameters of multivariate
normal mixtures of distribution, U.S. Naval Personnel Research Activity,
San Diego (1967), SRM 68–2.
[8] Dillon W.R., Mulani N. and Frederick D.G., On the use of component scores
in the presence of group structures, J. Consumer Research, 16 (1989), 106–112.
[9] Kemsley E.K., Discriminant analysis of high-dimensional data: a comparsion
of principal components analysis and least squares data reduction methods,
Journal of Statistical Computitation and Simulation, 55 (1996), 353–366.
[10] Song C.C., Jiang T.J. and Kuo K.L., On the Fisher’s discriminant analysis,
Technical Report # NCCU 701-05-T04-01, Department of Mathematical Sciences,
National Chengchi University.
[11] Jackson J.E., A user’s guide to principal components, Wiley, New York (1991).
[12] Flury B.D., Developments In Principal Component Analysis, (1995), 14–23.
[13] Johnson R.A., Wichern D.W., Alllied Multivariate Statistical Analysis, Prentice
Hall, (2002).
Description: 碩士
Source URI:
Data Type: thesis
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