Abstract
A concept that is closely related to linear regression (preceding chapter) is principal components [15.1]. Linear regression addressed the question of how to fit a curve to one set of data, using a minimum number of factors. By contrast, the principal components problem asks how to fit many sets of data with a minimum number of curves. The problem is now of higher dimensionality. Specifically, can each of the data sets be represented as a weighted sum of a “best” set of curves? Each curve is called a “principal component” of the data sets.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
H. Hotelling: J. Educ. Psych. 24, 417, 498 (1933)
J.L. Simonds: J. Phot. Sci. Eng. 2, 205 (1958)
R.C. Gonzalez, P. Wintz: Digital Image Processing (Addison-Wesley, Reading, MA 1977) pp. 310–314
M.G. Kendall, A. Stuart: The Advanced Theory of Statistics, Vol. 3 (Charles Griffin, London 1968)
M.A. Girshick: Ann. Math. Statist. 10, 203 (1939)
Additional Reading
Wilkinson, J. H.: The Algebraic Eigenvalue Problem (Clarendon, Oxford 1965)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Frieden, B.R. (2001). Principal Components Analysis. In: Probability, Statistical Optics, and Data Testing. Springer Series in Information Sciences, vol 10. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-56699-8_15
Download citation
DOI: https://doi.org/10.1007/978-3-642-56699-8_15
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-41708-8
Online ISBN: 978-3-642-56699-8
eBook Packages: Springer Book Archive