About translation matrix creation

[neosyon]

Dear josemanuelgp

I found your code really useful. However I have a question about the part where you calculate the translation matrix:

Instead of doing WX=Z -> W=transpose(pinv(X)Z)

DoubleMatrix pinverse_matrix = Solve.pinv(matrix_train_source);
DoubleMatrix translationMatrix = pinverse_matrix.mmul(matrix_train_target).transpose();

Why not directly do this: WX=Z -> W=Z pinv(X)

DoubleMatrix pinverse_matrix = Solve.pinv(matrix_train_source);
DoubleMatrix translationMatrix = matrix_train_target.mmul(pinverse_matrix);

I'm sure that I'm missing something, for that reason I ask you.

Cheers

[josemanuelgp]

As discussed in [1], you need to treat it as the transpose of a linear regression setup. You can also check this empirically by running the code: for example, in your approach the dimensions of the matrices will not fit for multiplication.

[1] http://stackoverflow.com/questions/27980159/fit-a-linear-transformation-in-python