What would the target matrix to train Neural Network?
Example with the following numbers (I use random numbers):


There are 6 possible classes (face expressions in your case).
You have 2000 examples (lets say 2000 photos of faces from which you know the correct face expression).
There are 30 features. From each example you have extracted the 30 features and know the correct class.


With these numbers, the input matrix would be a matrix of $30 \times 2000$, where each column $j$ is an example, and it has the 30 features of it. Hence, the position $(i,j)$ contains the feature $i$ of the example $j$.

The target matrix would be a matrix of $6\times 2000$. Where each column $j$ represents the correct class of the example $j$. The column is formed by zeros, and it has a $1$ at the row that indicates the class. If we have 6 classes, and the first example corresponds to class 3, the first column of the target matrix will be $[0 \ 0 \ 1\  0\  0\  0]$. If the second example corresponds to class 5, the second column of the target matrix will be: $[0 \ 0 \ 0 \ 0 \ 1\  0]$, and so on.

More info here.