Matrix of oblique weighted correlations will be computed.
For two series, oblique W-covariation is defined as follows:
$$%
\mathrm{owcov}(F_1, F_2) =
\langle L^\dagger X_1 (R^\dagger)^\mathrm{T},
L^\dagger X_2 (R^\dagger)^\mathrm{T} \rangle_\mathrm{F},
$$
where
\(X_1, X_2\) denotes the trajectory matrices of series \(F_1, F_2\)
correspondingly, \(L = [U_{b_1} : ... : U_{b_r}], R = [V_{b_1}: ... V_{b_r}]\),
where \(\\\{b_1, \dots, b_r\\\}\) is current OSSA component set
(see description of `ossa.set' field of `ossa' object),
`\(\langle \cdot, \cdot
\rangle_\mathrm{F}\)' denotes Frobenius matrix inner product
and `\(\dagger\)' denotes Moore-Penrose pseudo-inverse matrix.
And oblique W-correlation is defined the following way:
$$%
\mathrm{owcor}(F_1, F_2) = \frac{\mathrm{owcov}(F_1, F_2)}
{\sqrt{\mathrm{owcov}(F_1, F_1) \cdot \mathrm{owcov(F_2, F_2)}}}
$$
Oblique W-correlation is an OSSA analogue of W-correlation, that is, a
measure of series separability. If I-OSSA procedure separates series
exactly, their oblique W-correlation will be equal to zero.