pcares
Residuals from principal component analysis
Syntax
residuals = pcares(X,ndim)
[residuals,reconstructed] = pcares(X,ndim)
Description
residuals = pcares(X,ndim)
returns
the residuals
obtained by retaining ndim
principal
components of the n-by-p matrix X
. Rows of X
correspond
to observations, columns to variables. ndim
is
a scalar and must be less than or equal to p. residuals
is
a matrix of the same size as X
. Use
the data matrix, not the covariance matrix, with
this function.
pcares
does not normalize the columns of
X. To perform the principal components analysis based on standardized
variables, that is, based on correlations, use pcares(zscore(X),
ndim)
. You can perform principal components analysis directly
on a covariance or correlation matrix, but without constructing residuals,
by using pcacov
.
[residuals,reconstructed] = pcares(X,ndim)
returns
the reconstructed observations; that is, the approximation to X
obtained
by retaining its first ndim
principal components.
Examples
This example shows the drop in the residuals from the first row of the Hald data as the number of component dimensions increases from one to three.
load hald r1 = pcares(ingredients,1); r2 = pcares(ingredients,2); r3 = pcares(ingredients,3); r11 = r1(1,:) r11 = 2.0350 2.8304 -6.8378 3.0879 r21 = r2(1,:) r21 = -2.4037 2.6930 -1.6482 2.3425 r31 = r3(1,:) r31 = 0.2008 0.1957 0.2045 0.1921
References
[1] Jackson, J. E., A User's Guide to Principal Components, John Wiley and Sons, 1991.
[2] Jolliffe, I. T., Principal Component Analysis, 2nd Edition, Springer, 2002.
[3] Krzanowski, W. J. Principles of Multivariate Analysis: A User's Perspective. New York: Oxford University Press, 1988.
[4] Seber, G. A. F. Multivariate Observations. Hoboken, NJ: John Wiley & Sons, Inc., 1984.
Version History
Introduced before R2006a