UserReference:P300ClassifierMethods

Signals are obtained either for each training or testing data file and are arranged in a matrix form as:

${𝐗}_{\mathbf{𝐢}}^{\mathbf{𝐤}}\mathbf{(}\mathbf{𝐧}\mathbf{)}=\left[\begin{array}{ccccccccc}{x}_1^1(1)& x_1^1(2)& \cdots & x_1^1(p)& \cdots & x_1^l(1)& x_1^l(2)& \cdots & x_1^l(p)\\ x_2^1(1)& x_2^1(2)& \cdots & x_2^1(p)& \cdots & x_2^l(1)& x_2^l(2)& \cdots & x_2^l(p)\\ ⋮& ⋮& \cdots & ⋮& \cdots & ⋮& ⋮& \cdots & ⋮\\ x_m^1(1)& x_m^1(2)& \cdots & x_m^1(p)& \cdots & x_m^l(1)& x_m^l(2)& \cdots & x_m^l(p)\\ \end{array}\right]$

for

$i=1,2,\dots ,m;$

$k=1,2,\dots ,l;$

$n=1,2,\dots ,p;$

being $m$ the total number of observations (stimuli), $l$ the total number of channels, and $p=t*Fs$ the total number of samples recorded for each channel. $t$ is the recording stimulus time, and $Fs$ is the sampling frequency.

Let us consider the following example to help you understand the previous mathematical notation. A BCI data set is recorded during a P300 Speller task using a 6 by 6 matrix of characters. Each row and column of the matrix is randomly intensified resulting in 12 different stimuli. The sets of 12 intensification are repeated 15 times for each intended character to spell. For this example, the subject pretend to spell only two characters. The data set is recorded from 8 channels at 256 Hz, and the elapsed time from the start to the end of each intensification is 800 ms. For this example, $m=12x15x2=360$, $l=8$, and $p=256x0.800=205$. The total number of columns of the above matrix is $8x256=2048$.