From: stewart@cs.umd.edu (G. W. Stewart)
Newsgroups: sci.math.num-analysis
Subject: Re: Principle Components Analysis
Date: 3 Oct 92 05:58:50 GMT
Distribution: na
Organization: U of Maryland, Dept. of Computer Science, Coll. Pk., MD 20742

In article <BvIqF0.9IF@csn.org> sullivan@teal.csn.org (Steve Sullivan) writes:
>
>I'm interested in learning about principle components
>analysis, but none of the profs I've talked to have
>any references.
>
>Can anyone recommend some good introductory books or
>articles?
>
>Many thanks in advance -
>
>Steve Sullivan
>sullivan@csn.org

Here is a dump from my bibliography.  Keep in mind that it represents
a numerical analysts view.  A statistician could give you many
more references.

Pete Stewart

\begin{thebibliography}{10}

\bibitem{cham:72}
J.~M. Chambers.
\newblock Stabilizing linear regression against observational error in
  independent variats.
\newblock Manuscript, Bell Laboratories, Murray Hill, New Jersey., 1972.

\bibitem{ecyo:36}
C.~Eckart and G.~Young.
\newblock The approximation of one matrix by another of lower rank.
\newblock {\em Psychometrika}, 1:211--218, 1936.

\bibitem{gaza:79}
K.~R. Gabriel and S.~Zamir.
\newblock Lower rank approximation of matrices by least squares with any choice
  of weights.
\newblock {\em Technometrics}, 21:489--498, 1979.

\bibitem{golu:69}
G.~H. Golub.
\newblock Matrix decompositions and statistical calculations.
\newblock Technical Report 124, Computer Science Department, Stanford
  University, 1969.

\bibitem{golu:69a}
G.~H. Golub.
\newblock Matrix decompositions and statistical computation.
\newblock In R.C. Milton and J.~A. Nelder, editors, {\em Statistical
  Computation}, pages 365--397, New York, 1969. Academic Press.
\newblock Cited in {\AA ke Bj\"orck's} bibliography on least squares, which is
  available by anonymous ftp from {\tt math.liu.se} in {\tt pub/references}.

\bibitem{good:69}
I.~J. Good.
\newblock Some applications of the singular decomposition of a matrix.
\newblock {\em Technometrics}, 11:823--831, 1969.

\bibitem{guns:78}
R.~F. Gunst.
\newblock Similarities among least squares, principal component, and latent
  root regression estimators.
\newblock Manuscript. Department of Statistics, Southern Methodist University,
  1978?

\bibitem{guwm:76}
R.~F. Gunst, J.~T. Webster, and R.~L. Mason.
\newblock A comparison of least squares and latent root regression estimators.
\newblock {\em Technometrics}, 18:75--83, 1976.
\newblock Cited in \cite{govl:89}.

\bibitem{hamm:85}
S.~J. Hammarling.
\newblock The singular value decomposition in multivariate statistics.
\newblock {\em {ACM} {SIGNUM} Newsletter}, 20:2--25, 1985.
\newblock Cited in \cite{govl:89}.

\bibitem{hano:81}
R.~J. Hanson and M.~J. Norris.
\newblock Analysis of measurements based on the singular value decomposition.
\newblock {\em {SIAM} Journal on Scientific and Statistical Computing},
  2:363--374, 1981.
\newblock Cited in \cite{govl:89}.

\bibitem{hawk:73}
D.~M. Hawkins.
\newblock On the investigation of alternative regressions by principal
  component analysis.
\newblock {\em Appl.\ Statist.}, 22:275--286, 1973.

\bibitem{hote:33}
H.~Hotelling.
\newblock Analysis of a complex of statistical variables into principal
  components.
\newblock {\em Journal of Educational Psychology}, 24:417--441 and 498--520,
  1933.

\bibitem{hote:57}
H.~Hotelling.
\newblock Relation of the newer multivariate statistical methods to factor
  analysis.
\newblock {\em Br. J. Static. Psychol.}, 10:69--79, 1957.

\bibitem{hucu:62}
J.~R. Hurley and R.~B. Cattell.
\newblock The {Procrustes} program: {Direct} rotation to test a hypothesized
  factor structure.
\newblock {\em Behavioral Science}, 7:258--262, 1962.

\bibitem{paig:85}
C.~C. Paige.
\newblock The general linear model and the generalized singular value
  decomposition.
\newblock {\em Linear Algebra and its Applications}, 70:269--284, 1985.
\newblock Cited in \cite{govl:89}.

\bibitem{pear:01}
K.~Pearson.
\newblock On lines and planes of closest fit to points in space.
\newblock {\em Philosophical Magazine}, 2:559--572, 1901.
\newblock Cited in \cite{govl:89}.

\bibitem{rao:80}
C.~R. Rao.
\newblock Matrix approximations and reduction of dimensionality in multivariate
  statistical analysis.
\newblock In P.~R. Krishnaiah, editor, {\em Multivariate Analysis--V}.
  North-Holland, Amsterdam, 1980.

\bibitem{vhva:91}
S.~Van~Huffel and J.~Vandewalle.
\newblock {\em The Total Least Squares Problem: Computational Aspects and
  Analysis}.
\newblock SIAM, Philadelphia, 1991.

\bibitem{wegm:74}
J.~Webster, R.~Gunst, and R.~Mason.
\newblock Latent root regression analysis.
\newblock {\em Technometrics}, 16:513--522, 1974.

\bibitem{wegm:76}
J.~Webster, R.~Gunst, and R.~Mason.
\newblock A comparison of least squares and latent root regression estimators.
\newblock {\em Technometrics}, 18:75--83, 1976.

\end{thebibliography}
Newsgroups: sci.math.num-analysis