About whitenlearn(X, qidxs, pidxs)

[michaeltian108]

Hi, I've been carefully reading your paper, your codes and your major references as well, all of which I found to be awesome, clear and systematic. Really enjoyed. However, I'm a bit confused when I came to read the part of the codes doing learnable whitening.

    m = X[:, qidxs].mean(axis=1, keepdims=True)
    df = X[:, qidxs] - X[:, pidxs]
    S = np.dot(df, df.T) / df.shape[1] 
    P = np.linalg.inv(cholesky(S))
    df = np.dot(P, X-m)
    D = np.dot(df, df.T)
    eigval, eigvec = np.linalg.eig(D)
    order = eigval.argsort()[::-1]
    eigval = eigval[order]
    eigvec = eigvec[:, order]
 
   P = np.dot(eigvec.T, P)

First of all, do S and D refer to Cs and Cd as you mentioned in your paper?
Everything makes sense to me until line 4 where a cholesky decomposition function is called. And I started to lose track of what exactly do P and D refer to. And I cannot understand how the P in the last line is the learned projection matrix.

I referred to the original paper and googled cholesky decomp for more details but that didn't help a lot.
Could you please simply explain what each line does from line 4?
Thank you very much for your time!
@filipradenovic

[lr87]

I noticed that filipradenovic post his doctor thesis in this issue #40
You can find the introduction of this whitening method in Page54 of the thesis.

[michaeltian108]

@lr87 Thanks for your infomration. I actually do undertand the whitening process, but what I'm confused is that I cannot link the arugments here in the code with such process. But thanks again for your help!

[lr87]

@michaeltian108 After carefully reading the paper and the code, I understand what confused you, and now it confuses me, too 😓
Looking forward to the explanation from @filipradenovic

[liyongqing-1101]

Hello, this problem also confuses me, I wonder that do you figure out the codes of 'whitenlearn' in 'whiten.py'. If you do, Could you please explain the code, I'll really appreciate it.
@michaeltian108
@lr87