Description Usage Arguments Details Value Author(s) References See Also Examples

Computes the Minimum Distance index MD to evaluate the performance of an ICA algorithm.

1 | ```
MD(W.hat, A)
``` |

`W.hat` |
The estimated square unmixing matrix W. |

`A` |
The true square mixing matrix A. |

*MD(W.hat,A) = 1/sqrt(p-1) inf_(P D) ||P D W.hat A - I||,*

where *P* is a permutation matrix and *D* a diagonal matrix with nonzero diagonal entries.

The step that minimizes the index of the set over all permutation matrix can be expressed as a linear sum assignment problem (LSAP)
for which we use as solver the Hungarian method implemented as `solve_LASP`

in the clue package.

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.

The MD index is scaled in such a way, that it takes a value between 0 and 1. And 0 corresponds to an optimal separation.

The value of the MD index.

Klaus Nordhausen

Ilmonen, P., Nordhausen, K., Oja, H. and Ollila, E. (2010), A New Performance Index for ICA: Properties, Computation and Asymptotic Analysis.
In Vigneron, V., Zarzoso, V., Moreau, E., Gribonval, R. and Vincent, E. (editors) *Latent Variable Analysis and Signal Separation*, 229–236, Springer.

Nordhausen, K., Ollila, E. and Oja, H. (2011), On the Performance Indices of ICA and Blind Source Separation. In the Proceedings of *2011 IEEE 12th International Workshop on Signal Processing Advances in Wireless Communications (SPAWC 2011)*, 486–490.

Miettinen, J., Nordhausen, K. and Taskinen, S. (2017), Blind Source Separation Based on Joint Diagonalization in R: The Packages JADE and BSSasymp, *Journal of Statistical Software*, **76**, 1–31, <doi:10.18637/jss.v076.i02>.

`ComonGAP`

, `SIR`

, `amari.error`

, `solve_LSAP`

1 2 3 4 5 6 |

```
[1] 0.07553041
```

Embedding an R snippet on your website

Add the following code to your website.

For more information on customizing the embed code, read Embedding Snippets.