# amari: Compute the 'Amari' distance between two matrices In Hanchao-Zhang/ProDenICA: Product Density Estimation for ICA using tilted Gaussian density estimates

## Description

The Amari distance is a measure between two nonsingular matrices. Useful for checking for convergence in ICA algorithms, and for comparing solutions.

## Usage

 `1` ```amari(V, W, orth = FALSE) ```

## Arguments

 `V` first matrix `W` second matrix `orth` are the matrices orthogonal; default is `orth=FALSE`

## Details

Formula is given in second reference below, page 570.

## Value

a numeric distance metween 0 and 1

Trevor Hastie

## References

Bach, F. and Jordan, M. (2002). Kernel independent component analysis, Journal of Machine Learning Research 3: 1-48
Hastie, T., Tibshirani, R. and Friedman, J. (2009) Elements of Statistical Learning (2nd edition), Springer.
http://www-stat.stanford.edu/~hastie/Papers/ESLII.pdf

## See Also

`ProDenICA`

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21``` ```dist="n" N=1024 p=2 A0<-mixmat(p) s<-scale(cbind(rjordan(dist,N),rjordan(dist,N))) x <- s %*% A0 ###Whiten the data x <- scale(x, TRUE, FALSE) sx <- svd(x) ### orthogonalization function x <- sqrt(N) * sx\$u target <- solve(A0) target <- diag(sx\$d) %*% t(sx\$v) %*% target/sqrt(N) W0 <- matrix(rnorm(2*2), 2, 2) W0 <- ICAorthW(W0) W1 <- ProDenICA(x, W0=W0,trace=TRUE,Gfunc=G1)\$W fit=ProDenICA(x, W0=W0,Gfunc=GPois,trace=TRUE, density=TRUE) W2 <- fit\$W #distance of FastICA from target amari(W1,target) #distance of ProDenICA from target amari(W2,target) ```

Hanchao-Zhang/ProDenICA documentation built on Jan. 17, 2022, 12:23 a.m.