bci2000.org BBS

Hello,

I am currently working on my thesis about motor imagery EEG-based BCI's, and I ran into a bit of a problem trying to understand how the Wadsworth BCI derives the weights for the control signal in cursor control applications.

So in "Emulation of computer mouse control with a noninvasive brain computer interface" they discuss using a linear least-squares criteria and say that feature weights are calculated as b = (X'X)^(-1)X'Y, where X is an m by n matrix formed from the n observations of m predictor variables (i.e., EEG amplitudes at specific frequencies and locations) and Y is the vector of n values (i.e., target predictions) to be predicted.

The actual linear equation controlling (vertical) cursor movement is: delta V = b_V(S_V-a_V) where S_V is just the selected features weighted by the weights obtained from the Least-squares regression, b_V is the gain, and a_V is the mean of the vertical control signal for the user's previous performance.

So my question is whether or not X and Y are augmented with ones to generate an intercept for the regression equation and that value is just tossed out in computing S_V, or if the X and Y are not augmented in which case they force the regression line to pass through the origin of feature space. It just doesn't mathematically make a lot of sense to me if you force the intercept to be 0 when doing regression because your line will not fit the data as well. However, it doesn't make a whole lot of sense to completely throw out the intercept either.

Does anyone have any insight into what I'm not understanding about all of this?

Thank you,
James

We didn't mention this in the article, but there was a column of 1s in the X matrix that would represent the intercept. This doesn't matter though as the signal was normalized in real time with respect to the mean and standard deviation.

One other issue- whether the intercept is 0 or not is not a mathematical issue (i.e., either zero or non-zero make mathematical sense). It is an issue of how one wishes to model the data.

Thank you Dr. McFarland! I just tried it in Matlab, and you do in fact get the same weights whether or not you augment the zero-mean, unit variance matrix X with ones or not.