Orientation of PCA Initialisation

[MattWenham]

If I wish to set the ratio of the map dimensions to be the ratio of the first two eigenvalues from PCA, should the larger value be n_rows or n_columns? I think this tidbit would be useful to add in to the Python user guide, and perhaps others.

[peterwittek]

Columns, I guess, unless you prefer vertically elongated maps. If you find this important, I would welcome a PR to the Python documentation.

[MattWenham]

More fundamentally, my question boils down to this: is the first principal component projected across the columns or down the rows of the initialised map? In the first case, n_columns should be larger than n_rows, and vice-versa for the second case.

[peterwittek]

The actual 'projection' is this loop:

for j in range(n_columns * n_rows):
    for i in range(eigvec.shape[0]):
        codebook[j, :] = codebook[j, :] + \
            coord[j, i] * eigvec[i, :]

The codebook is initialized with the mean value of each dimension. Then this loop shifts the mean with both eigenvectors, where the scaling factor is given by the coord array, which introduces larger coefficients further away from the centre of the map. So I don't think the shape of the map actually matters.