Question with Trace Ratio

[crixus5678]

Based on the code implemented in the calculation of trace ratio, if we set s_within and s_between to have a length of n_selected_features. Then the variables "I" and "idx" will just have a length of n_selected_features. In this case, arent we just restricting the selected features to be the first n_selected_features in fs_idx and the loop is essentially updating/optimizing nothing?

# preprocessing
fs_idx = np.argsort(np.divide(s_between, s_within), 0)[::-1]
k = np.sum(s_between[0:n_selected_features])/np.sum(s_within[0:n_selected_features])
s_within = s_within[fs_idx[0:n_selected_features]]
s_between = s_between[fs_idx[0:n_selected_features]]

# iterate util converge
count = 0
while True:
    score = np.sort(s_between-k*s_within)[::-1]
    I = np.argsort(s_between-k*s_within)[::-1]
    idx = I[0:n_selected_features]
    old_k = k
    k = np.sum(s_between[idx])/np.sum(s_within[idx])
    if verbose:
        print('obj at iter {0}: {1}'.format(count+1, k))
    count += 1
    if abs(k - old_k) < 1e-3:
        break