THIS IS DOCUMENTATION FOR AN OBSOLETE PRODUCT.
SEE THE DOCUMENTATION CENTER FOR THE LATEST INFORMATION.

DOCUMENTATION CENTER SEARCH

BUILT-IN MATHEMATICA SYMBOL

PrincipalComponents

PrincipalComponents[matrix]
transforms elements of matrix into unscaled principal components.

The principal components of matrix are linear transformations of the original columns into uncorrelated columns arranged in order of decreasing variance.

PrincipalComponents supports a Method option. The following explicit settings can be specified:

	"Covariance"	uses covariance method (default)
	"Correlation"	uses correlation method

If principal components of scaled columns (standardized principal components) are required, the option Method should be used.

The dimensions of PrincipalComponents[matrix] are the same as the dimensions of matrix.

If matrix consists of exact numbers or symbols, the result is also exact or symbolic, respectively.

Principal components of two datasets:

Out[1]=

Principal components computed with arbitrary-precision numbers:

Principal components of exact numbers:

Principal components computation involving symbolic expressions:

Principal components using correlation scaling:

The principal component columns are ordered by decreasing variance:

The mean of each principal component column is zero:

The principal component columns are not correlated:

The setting Method

yields the same results as standardizing the input matrix:

For certain symbolic matrices the result may be very large:

Align the principal axis of a two-dimensional shape with the horizontal axis: