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BUILT-IN MATHEMATICA SYMBOL
KarhunenLoeveDecomposition
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 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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