KarhunenLoeveDecomposition

KarhunenLoeveDecomposition[{a1,a2,}]
gives the KarhunenLoeve transform of the numerical arrays and the transformation matrix m, returning the result in the form .

KarhunenLoeveDecomposition[{a1,a2,},m]
uses the inverse of the matrix m for transforming the .

Details and OptionsDetails and Options

  • The can be arrays of any dimensions, but must all be equal.
  • KarhunenLoeveDecomposition also works with arbitrary images.
  • The inner product of m and gives .
  • The total variance of the is the same as the total variance of the .
  • The are given in order of decreasing variance.
  • The rows of the transformation matrix m returned by KarhunenLoeveDecomposition are the eigenvectors of the covariance matrix formed from the arrays .
  • KarhunenLoeveDecomposition[{b1,b2,},m] effectively computes the inverse KarhunenLoeve transformation. If the length of is less than the size of m, missing components are assumed to be zero.
  • With an option setting "Centered"->True, KarhunenLoeveDecomposition[{a1,a2,}] shifts the datasets so that their means are zero.
Introduced in 2010
(8.0)