Residuals from principal component analysis
residuals = pcares(X,ndim)
[residuals,reconstructed] = pcares(X,ndim)
residuals = pcares(X,ndim) returns
residuals obtained by retaining
components of the n-by-p matrix
X. Rows of
to observations, columns to variables.
a scalar and must be less than or equal to p.
a matrix of the same size as
the data matrix, not the covariance matrix, with
pcares does not normalize the columns of
X. To perform the principal components analysis based on standardized
variables, that is, based on correlations, use
ndim). You can perform principal components analysis directly
on a covariance or correlation matrix, but without constructing residuals,
[residuals,reconstructed] = pcares(X,ndim) returns
the reconstructed observations; that is, the approximation to
by retaining its first
ndim principal components.
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
 Jackson, J. E., A User's Guide to Principal Components, John Wiley and Sons, 1991.
 Jolliffe, I. T., Principal Component Analysis, 2nd Edition, Springer, 2002.
 Krzanowski, W. J. Principles of Multivariate Analysis: A User's Perspective. New York: Oxford University Press, 1988.
 Seber, G. A. F. Multivariate Observations. Hoboken, NJ: John Wiley & Sons, Inc., 1984.