- how to create a DFT with scalloping/spectal leakage
- correctnes of multi prime RSA algorithm
- Can PRF F with generator P be secure?
- What to expect about the mobile phone usage during a flight to China and based on the CAAC regulations
- At what time of day does US visa expire?
- Travel Issues to Turkey
- Can a US green card holder transiting through China leave the airport? Recommendation for sight-seeing in Shanghai?
- Amtrak Seating NY to DC
- The soul as the form of the body – considering massive changes of the body
- Why can't uniformity of nature (in principle) be proven deductively?
- Need help to understand Kierkegaard's “An Ecstatic Discourse”
- Understanding Herr and its various meanings
- What is the english translation of ,,dagobertinisch"?
- How did they manage to make this song feel speeded?
- Writing a simple 12-tone row
- Hyperlink to a specific place in a document
- How can I create a looping workflow in Sharepoint 2010?
- Tracing Application Server in Use
- SP2013 retrieving localized term Path (term.getPath(lcid))
- How to set form type as 'hierarchical_select' programatically?

# How to obtain covariance matrix eigenvalues from singular values?

I would like to implement closed form of PPCA (Bishop, Tipping, 1999, Appendix A). In this paper they calculate $W$ in formula (15):

$W=U_q(K_q-\sigma^2I)^{1/2}R$

where $K_q$ is a matrix from eigenvalues $\lambda_i$ of covariance matrix as defined in formula (5).

On one hand I read here, that it is possible to calculate eigenvalues with

$\lambda_i = \frac{s_i^2}{n-1}$

Is it true, that principal values depend on number of samples $n$?

On other hand I found python implementation of closed PPCA on github, function __fit_ml, where it is written

mu = np.mean(self.y, 1)[:, np.newaxis]

[u, s, v] = np.linalg.svd(self.y - mu)

...

else:

ss = s[:self.q]

ss = np.sqrt(np.maximum(0, ss**2 - self.prior_sigma))

w = u[:, :self.q].dot(np.diag(ss))

where author is apparently calculating with

$\lambda_i = s_i^2$

which is completely different.

UPDATE

Here $s_i$ is diagonal element of singular values matrix.