Dependent component extraction

Task

The task is to find two interacting components out of 19 components with all other components being mutually statistically independent. There is only one data set.

Test data

Supplied Files

The data are contained in challenge_data.mat [modified: Mar. 15]. modification announcement, Mar. 15
The file showpatterns.zip contains Matlab-code to make figures of spatial patterns and also to visualize e.g. correlation matrices across all channel pairs.

Data description

The data are real EEG data measured in rest under eyes closed condition. They consist of a mixture of 19 sources into 19 channels. Out of the 19 sources 17 come from different subjects (and are hence independent) and 2 come from a single subject and are known to be statistically dependent. The data consist of 150 continuous trials each of 4 seconds durations. The sampling rate is 256Hz.

The data were constructed as follows. Data from a single subject were decomposed using ICA. Two components which are not
independent and cannot be demixed into independent components were kept. For all other 17 components the respective time series (but not the spatial pattern) was replaced by a time series found from an ICA decomposition of a different subject, using here data from 17 different subjects. Here, the i.th time series of the original subject was replaced by the i.th time series of the respective substitute subject and the components were ordered according to magnitude.

Evaluation Criteria

A submission is a 19x2 matrix either as a Matlab-file or as ascii text. Results will be evaluated as follows. Let X be the 19x2 matrix containing in each column the true pattern of one of the dependent sources, and let Y be the respective estimate of these patterns. Then let further PX be the projector on the subspace defined by X, i.e. PX=X*inv(X'*X)*X', and likewise for Y: PY=Y*inv(Y'*Y)*Y'. Then the performance measure is the second largest eigenvalue of the matrix PX*PY*PX. This eigenvalue is 1 if the subspaces are identical and it is zero if a combination of the columns in Y exist which is orthogonal to both columns in X.
Note, that this performance measure only depends on the subspaces spanned by the columns of X and Y and not on the columns themselves.

The above criterion will be used to rank contributions. However, it is conceivable that also other kinds of results can be considered
as a satisfactory analysis of the data. E.g., one could find the 2D-subspace of the respective filters, i.e. the respective rows
of the inverse mixing matrix, or one could find only one of the patterns, or one could find two candidate systems but it is not exactly clear which one is right. Contributions of this kind will be read carefully and will be evaluated on quality.

Submissions

[SUBMISSION CLOSED on Apr.21]
Submit results simply by email to "guido.nolte (at) first.fraunhofer.de".
Please, put 'Dependent component extraction' in the subject.

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