JADE (version 2.0-4)

ComonGAP: Comon's Gap

Description

Comon's GAP criterion to evaluate the performance of an ICA algorithm.

Usage

ComonGAP(A, A.hat)

Value

The value of the Comon's GAP.

Arguments

A

The true square mixing matrix.

A.hat

The estimated square mixing matrix.

Author

Klaus Nordhausen

Details

Comon's GAP criterion is permutation and scale invariant. It can take every positive value and 0 corresponds to an optimal separation. If A is however nearly singular the values of the criterion can be huge.

Note that this function assumes the ICA model is $X=S{A}^{\prime }$, as is assumed by JADE and ics. However fastICA and PearsonICA assume $X=SA$. Therefore matrices from those functions have to be transposed first.

References

Comon, P., (1994), Independent Component Analysis, A new concept?, Signal Processing, 36, 287--314.

See Also

amari.error, SIR

Examples

S <- cbind(rt(1000, 4), rnorm(1000), runif(1000))
A <- matrix(rnorm(9), ncol = 3)
X <- S %*% t(A)

A.hat <- JADE(X, 3)$A
ComonGAP(A, A.hat)