PrincipalComponents

PrincipalComponents[matrix]

transforms elements of matrix into unscaled principal components.

Details and Options

  • PrincipalComponents gives the principal component transform of matrix.
  • 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"Correlation" 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.

Examples

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Basic Examples  (1)

Principal components of two datasets:

Scope  (3)

Principal components computed with arbitrary-precision numbers:

Principal components of exact numbers:

Principal components computation involving symbolic expressions:

Options  (1)

Method  (1)

Principal components using correlation scaling:

Properties & Relations  (2)

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->"Correlation" yields the same results as standardizing the input matrix:

Possible Issues  (1)

For certain symbolic matrices the result may be very large:

Neat Examples  (1)

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

Introduced in 2010
 (8.0)