coloredICA (version 1.0.0)

amari_distance: Amari error

Description

This function measures the Amari error between two matrices.

Usage

amari_distance(Q1, Q2)

Arguments

Q1

First matrix.

Q2

Second matrix.

Value

• It returns the Amari error between two matrices $Q1$ and $Q2$.

Details

The Amari error $D(Q1|Q2)$ between two M x M matrices $Q1$ and $Q2$ is evaluated through $$D(Q1|Q2)=\frac{1}{2M(M-1)}\sum_{j=1}^M\left(\frac{\sum_{i}|a_{ij}|}{max_{i}|a_{ij}|}-1\right)+\frac{1}{2M(M-1)}\sum_{i=1}^M\left(\frac{\sum_{j}|a_{ij}|}{max_{j}|a_{ij}|}-1\right),$$ where $Q2$ is invertible and $a_{ij}$ is the $ij$th element of $Q1Q2^{-1}$.

References

Amari, S., Cichocki, A., Yang, H. et al. (1996). A New Learning Algorithm for Blind Signal Separation. Advances in Neural Information Processing Systems, 8, 757--763 Bach, F., Jordan, M. (2003). Kernel Independent Component Analysis. Journal of Machine Learning Research, 3, 1--48

See Also

cICA, scICA

Examples

M <- 4
A <- matrix(rnorm(M*M),M,M)
B <- matrix(rnorm(M*M),M,M)

amari_distance(A,B)