Principal component analysis on covariance matrix
COEFF = pcacov(V)
[COEFF,latent] = pcacov(V)
[COEFF,latent,explained] = pcacov(V)
COEFF = pcacov(V) performs principal components analysis on the p-by-p covariance matrix V and returns the principal component coefficients, also known as loadings. COEFF is a p-by-p matrix, with each column containing coefficients for one principal component. The columns are in order of decreasing component variance.
pcacov does not standardize V to have unit variances. To perform principal components analysis on standardized variables, use the correlation matrix R = V./(SD*SD'), where SD = sqrt(diag(V)), in place of V. To perform principal components analysis directly on the data matrix, use pca.
[COEFF,latent] = pcacov(V) returns latent, a vector containing the principal component variances, that is, the eigenvalues of V.
[COEFF,latent,explained] = pcacov(V) returns explained, a vector containing the percentage of the total variance explained by each principal component.
load hald covx = cov(ingredients); [COEFF,latent,explained] = pcacov(covx) COEFF = 0.0678 -0.6460 0.5673 -0.5062 0.6785 -0.0200 -0.5440 -0.4933 -0.0290 0.7553 0.4036 -0.5156 -0.7309 -0.1085 -0.4684 -0.4844 latent = 517.7969 67.4964 12.4054 0.2372 explained = 86.5974 11.2882 2.0747 0.0397
 Jackson, J. E. A User's Guide to Principal Components. Hoboken, NJ: John Wiley and Sons, 1991.
 Jolliffe, I. T. Principal Component Analysis. 2nd ed., New York: Springer-Verlag, 2002.
 Krzanowski, W. J. Principles of Multivariate Analysis: A User's Perspective. New York: Oxford University Press, 1988.
 Seber, G. A. F., Multivariate Observations, Wiley, 1984.