Independent components and principal component analyses

An implementation of the fastICA algorithm

Command	Description
ICA	Fit ICA model to signal data
ADJUST	Adjust original signals given one or more ICs
SVD	Apply time-series PCA to multiple channels

ICA

Independent components analysis

This command implements the fastICA algorithm, providing a C/C++ implementation of R's fastICA package.

We hope that in future vignettes we will be able to provide a more contextualized account of how to apply ICA using Luna to sleep data in practice. For now, this page contains only bare-bones reference material.

By default, ICA adds signals IC_1, IC_2, etc to the internal EDF: these can then be used as signals in other commands (e.g. PSD) to examine the properties of those components. You can also WRITE the EDF containing these ICs.

Currently, this command works on a whole-recording basis, e.g. rather than epoch-by-epoch. This may not be appropriate if the whole recording contains very different types of signals/artifatcs (i.e. if the spatial sources of the components is not relatively stable over time).

Hint

Remember that ICA is not a deterministic algorithm, in that it is randomly seeded. Therefore, IC_4 in one run may not correspond to IC_4 in a second run. It is therefore important to save the results of an ICA run, e.g. if determining which components to remove, etc.

Hint

ICA can be a relatively slow and memory intensive operation for whole-night multi-channel datasets with high sampling rates. It is therefore worth exploring this command starting with smaller and/or down-sampled data, etc.

Warning

Although implementations of ICA are standard, the proper application of ICA to multichannel EEG data is a complex methodological area, with various subtleties. These routines are currently presented 'as is'. In the future we will attempt to outline some best practices for using ICA (primarily for artifact detection) in the context of sleep data.

Parameters

Primary parameters are:

Option	Description
sig	Specify which signals to include
A	Filename for the mixing matrix A
nc	Optionally, the number of components to extract

Secondary parameters include:

Option	Example	Description
no-new-channels		Do not write new channels to EDF
tag	V_	Use V_1, V_2, etc, instead of IC_1, IC_2, etc
file	ica1	Write ICs (S matrix) and other ICA output to files ica1.S, etc

Outputs

As mentioned, one output of ICA is a set of new channels added to the (internal) EDF (unless no-new-channels is specified). These are labelled IC_1, IC_2, etc, by default.

A second key output is the mixing matrix A, which is written to a file. A typical workflow will involve using this matrix/file in a subsequent ADJUST command, in order to remove certain components from the original signals.

Various other outputs are written to the standard output stream:

ICA mixing matrix (also output to a file) (strata: CH x IC)

Variable	Description
A	Element of A matrix

ICA unmixing matrix W (strata: IC1 x IC2)

Variable	Description
W	Element of W matrix

ICA matrix K (strata: KCH x KIC)

Variable	Description
K	Element of K matrix

Example

Running ICA on a single EDF:

luna s.lst k=57 -o out.db -s ' MASK ifnot=N2
                             & RE
                             & ICA sig=${eeg} A=a.mat 
                             & PSD sig=[IC_][1:${k}] spectrum dB
                             & WRITE edf-tag=ic '

Hint

Note that [X][1:4] expands to X1,X2,X3,X4

We can visualize the PSD of the ICs by extracting the information in

destrat out.db +PSD -r F CH > psd.out

combined with the topographics of the ICs, and then use lunaR's ltopo.rb() or similar functions to view these:

Here we see that some components are highly channel-specific (i.e. as indicated by the topoplots, e.g. IC_18). Looking at the PSD, some ICs appear to reflect artifact, e.g. IC_53. We can use the ADJUST command to remove certain components from the original signals, as illustrated below.

ADJUST

Adjusts signals given various ICs and other criteria

This command is designed to work with ICA, and expects as input a) the same signals used to compute the ICs, and b) the A matrix from an ICA run. Based on these, the ADJUST command will remove certain components from the original signals. One can specify the components directly on the command line (e.g. IC_53). Alternatively, it is possible to instruct ADJUST to select components to be removed automatically, based on certain criteria. Currently, only two criteria are supported: topographical outliers and high correlation with one or more other channels (e.g. EOG or EMG).

Parameters

Parameter	Example	Description
sig		Signals to be adjusted
A	a-id1.txt	Filename of A mixing matrix (from ICA)
adj	[IC_][1:57]	Putative set of ICs that may be adjusted for
force	IC_5	Force this component to be removed
spatial	3	Select components with extreme spatial variance
corr-sig	LOC,ROC	Other signals aginst which ICs will be correlated
corr-th	0.8,0.8	Absolute time-domain correlation threshold (matches # of corr-sig channels)
tag	V	If the IC prefix is other than IC_ it can be specified here

Output

This command primarily adjusts the channels in the (internal) EDF, rather than generating summary output. Currently, the one output that is given is the correlation between the original and the adjusted channel:

Channel-level output (strata: CH)

Variable	Description
R	Time-domain correlation between the pre- and post-adjusted signal

Example

Following from the ICA example above, to remove channel IC_57 (and show before and after PSDs) we might write:

luna file-ic.edf -o out.db -s ' TAG ver/pre
                              & PSD sig=${eeg} spectrum dB
                              & ADJUST A=a.mat sig=${eeg} adj=${ic} force=IC_53 
                              & TAG ver/post
                              & PSD sig=${eeg} spectrum dB '

In these example data, the pre- and post-ICA PSD are as follows:

To drop ICs that show time-domain correlations above some threshold with one or more other channels (e.g. EOG), one might use something like:

ADJUST sig=${eeg} adj=${ic} corr-sig=LOC,ROC corr-th=0.5,0.5

Hint

Luna defines channel types as IC components automatically if they start with IC_, and sets an automatic variable ${ic} that corresponds to these.

SVD

Singular value decomposition of time-series data (PCA)

This command performs PCA via SVD of multiple channels, and (optionally) adds new channels to the current in-memory EDF. All input channels must have the same sample rate. A specified number of new channels (with the same sample rate) will be added to the in-memory EDF.

Parameters

Parameter	Example	Description
sig	C3,C4,F3,F4	Signals to be included in the SVD
nc	4	Number of components to extract
tag	C_	Tag to add to new channels (e.g. C_1, C_2, etc)
norm		Normalize channels (to unit variance) prior to SVD
winsor	0.02	Winsorize time series prior to SVD at this percentile (e.g. 2nd, 98th)
no-new-channels		Do not add new channels to the EDF

Outputs

The primary output (unless no-new-channels is set) are the nc new channels added to the EDF.

Primary per-component output (strata: C)

Variable	Description
W	Singular value
INC	Is this componenent included (e.g. given nc)
VE	Variance explainend
CVE	Cumulative variance explained

Component weights (right singular vectors) (strata: C x FTR)

Variable	Description
V	Weight/right singular vector value