ComonGAP: Comon's Gap

In JADE: Blind Source Separation Methods Based on Joint Diagonalization and Some BSS Performance Criteria

Comon's Gap

Description

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

Usage

ComonGAP(A, A.hat)

Arguments

A	The true square mixing matrix.
A.hat	The estimated square mixing matrix.

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', as is assumed by JADE and ics. However fastICA and PearsonICA assume X = S A. Therefore matrices from those functions have to be transposed first.

Value

The value of the Comon's GAP.

Author(s)

Klaus Nordhausen

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)

JADE documentation built on Sept. 18, 2023, 1:06 a.m.