KarhunenLoeveDecomposition[{a1, a2, ...}]
gives the Karhunen-Loeve 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

  • KarhunenLoeveDecomposition works with lists of arbitrary numerical commensurate arrays.
  • 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[{a1, a2, ...}, m] effectively computes the inverse Karhunen-Loeve 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.
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