coroICA {coroICA} | R Documentation |

## coroICA

### Description

Estimates the unmixing matrix V=A^-1 of a confounded ICA model of the form X=AS+H, where H is confounding noise which is group-wise stationary and S are non-stationary signal sources. The function can also be used without a group-structure (i.e., using a single group) in which it corresponds to a noisy ICA that allows for arbitrary stationary noise H.

### Usage

```
coroICA(X, group_index = NA, partition_index = NA, n_components = NA,
n_components_uwedge = NA, rank_components = FALSE,
pairing = "complement", max_matrices = 1, groupsize = 1,
partitionsize = NA, timelags = NA, instantcov = TRUE,
max_iter = 1000, tol = 1e-12, minimize_loss = FALSE,
condition_threshold = NA, silent = TRUE)
```

### Arguments

`X` |
data matrix. Each column corresponds to one predictor variable. |

`group_index` |
vector coding to which group each sample
belongs, with length( |

`partition_index` |
vector coding to which partition each
sample belongs, with
length( |

`n_components` |
number of components to extract. If NA is passed, the same number of components as the input has dimensions is used. |

`n_components_uwedge` |
number of components to extract during uwedge approximate joint diagonalization of the matrices. If NA is passed, the same number of components as the input has dimensions is used. |

`rank_components` |
boolean, optional. When TRUE, the components will be ordered in decreasing stability. |

`pairing` |
either 'complement', 'neighbouring' or 'allpairs'. If 'allpairs' the difference matrices are computed for all pairs of partition covariance matrices, if 'complement' a one-vs-complement scheme is used and if 'neighbouring' differences with the right neighbour parition are used. |

`max_matrices` |
float or 'no_partitions', optional (default=1). The fraction of (lagged) covariance matrices to use during training or, if 'no_partitions', at most as many covariance matrices are used as there are partitions. |

`groupsize` |
int, optional. Approximate number of samples in each group when using a rigid grid as groups. If NA is passed, all samples will be in one group unless group_index is passed during fitting in which case the provided group index is used (the latter is the advised and preferred way). |

`partitionsize` |
int or vector of ints, optional. Approximate number of samples in each partition when using a rigid grid as partition. If NA is passed, a (hopefully sane) default is used, again, unless partition_index is passed during fitting in which case the provided partition index is used. If a vector is passed, each element is used to construct a grid and all resulting partitions are used. |

`timelags` |
vector of ints, optional. Specifies which timelags should be included. 0 correpsonds to covariance matrix. |

`instantcov` |
boolean, default TRUE. Specifies whether to include covariance matrix when timelags are used. |

`max_iter` |
int, optional. Maximum number of iterations for the uwedge approximate joint diagonalisation during fitting. |

`tol` |
float, optional. Tolerance for terminating the uwedge approximate joint diagonalisation during fitting. |

`minimize_loss` |
boolean, optional. Parameter is passed to uwedge and specifies whether to compute loss function in each iteration step of uwedge. |

`condition_threshold` |
float, optional. Parameter is passed to uwedge and specifies whether and at which threshold to terminate uwedge iteration depending on the condition number of the unmixing matrix. |

`silent` |
boolean whether to supress status outputs. |

### Details

For further details see the references.

### Value

object of class 'CoroICA' consisting of the following elements

`V` |
the unmixing matrix. |

`coverged` |
boolean indicating whether the approximate joint diagonalisation converged due to tol. |

`n_iter` |
number of iterations of the approximate joint diagonalisation. |

`meanoffdiag` |
mean absolute value of the off-diagonal values of the to be jointly diagonalised matrices, i.e., a proxy of the approximate joint diagonalisation objective function. |

### Author(s)

Niklas Pfister and Sebastian Weichwald

### References

Pfister, N., S. Weichwald, P. Bühlmann and B. Schölkopf (2018). Robustifying Independent Component Analysis by Adjusting for Group-Wise Stationary Noise ArXiv e-prints (arXiv:1806.01094).

Project website (https://sweichwald.de/coroICA/)

### See Also

The function `uwedge`

allows to perform to
perform an approximate joint matrix diagonalization.

### Examples

```
## Example
set.seed(1)
# Generate data from a block-wise variance model
d <- 2
m <- 10
n <- 5000
group_index <- rep(c(1,2), each=n)
partition_index <- rep(rep(1:m, each=n/m), 2)
S <- matrix(NA, 2*n, d)
H <- matrix(NA, 2*n, d)
for(i in unique(group_index)){
varH <- abs(rnorm(d))/4
H[group_index==i, ] <- matrix(rnorm(d*n)*rep(varH, each=n), n, d)
for(j in unique(partition_index[group_index==i])){
varS <- abs(rnorm(d))
index <- partition_index==j & group_index==i
S[index,] <- matrix(rnorm(d*n/m)*rep(varS, each=n/m),
n/m, d)
}
}
A <- matrix(rnorm(d^2), d, d)
A <- A%*%t(A)
X <- t(A%*%t(S+H))
# Apply coroICA
res <- coroICA(X, group_index, partition_index, pairing="allpairs", rank_components=TRUE)
# Compare results
par(mfrow=c(2,2))
plot((S+H)[,1], type="l", main="true source 1", ylab="S+H")
plot(res$Shat[,1], type="l", main="estimated source 1", ylab="Shat")
plot((S+H)[,2], type="l", main="true source 2", ylab="S+H")
plot(res$Shat[,2], type="l", main="estimated source 2", ylab="Shat")
cor(res$Shat, S+H)
```

*coroICA*version 1.0.2 Index]