KarhunenLoeveDecomposition

KarhunenLoeveDecomposition[{a1,a2,}]
gives the KarhunenLoeve transform of the numerical arrays , where .

KarhunenLoeveDecomposition[{b1,b2,},m]
uses the inverse of the matrix m for transforming to .

Details and OptionsDetails and Options

  • KarhunenLoeve decomposition is typically used to reduce the dimensionality of data and capture the most important variation in the first few components.
  • The can be arbitrary rank arrays or images of the same dimensions.
  • The inner product of m and gives .
  • In KarhunenLoeveDecomposition[{a1,}], rows of the transformation matrix m are the eigenvectors of the covariance matrix formed from the arrays .
  • The matrix m is a linear transformation of . The transformed arrays are uncorrelated, are given in order of decreasing variance, and have the same total variance as .
  • 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)
| Updated in 2014
(10.0)