Statistics Toolbox

princomp

Principal Components Analysis (PCA)

Syntax

• PC = princomp(X)
  [PC,SCORE,latent,tsquare] = princomp(X)
  

Description

[PC,SCORE,latent,tsquare] = princomp(X) takes a data matrix X and returns the principal components in PC, the so-called Z-scores in SCORE, the eigenvalues of the covariance matrix of X in latent, and Hotelling's T² statistic for each data point in tsquare.

The Z-scores are the data formed by transforming the original data into the space of the principal components. The values of the vector, latent, are the variance of the columns of SCORE. Hotelling's T² is a measure of the multivariate distance of each observation from the center of the data set.

Example

Compute principal components for the ingredients data in the Hald dataset, and the variance accounted for by each component.

• load hald;
  [pc,score,latent,tsquare] = princomp(ingredients);
  pc,latent
  pc =
      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
  

Reference

[1]  Jackson, J. E., A User's Guide to Principal Components, John Wiley and Sons, Inc. 1991. pp. 1-25.

See Also
barttest, canoncorr, factoran, pcacov, pcares

prctile

procrustes