This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.
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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.
"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.
  • If matrix consists of exact numbers or symbols, the result is also exact or symbolic, respectively.
Principal components of two datasets:
Principal components of two datasets:
In[1]:=
Click for copyable input
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:
New in 8