Amari error

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Description

This function measures the Amari error between two matrices.

Usage

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Arguments

Q1

First matrix.

Q2

Second matrix.

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)}∑_{j=1}^M≤ft(\frac{∑_{i}|a_{ij}|}{max_{i}|a_{ij}|}-1\right)+\frac{1}{2M(M-1)}∑_{i=1}^M≤ft(\frac{∑_{j}|a_{ij}|}{max_{j}|a_{ij}|}-1\right),

where Q2 is invertible and a_{ij} is the ijth element of Q1Q2^{-1}.

Value

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

Author(s)

Lee, S., Shen, H., Truong, Y. and Zanini, P.

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

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

amari_distance(A,B)