- Allow login with multiple passwords
- Sizing Resistors for Voltage Divider Circuit Feeding Solid-State Relay
- Preferable pattern for differential length matching
- NIMH volt recovery
- Energies of the fields in a plane wave, attenuated and unattenuated
- Why doesn't it matter if a resistor is before or behind an LED wrt voltage drop?
- tracking error state space, linear control example
- Indicator LED directly to AC mains. Which method would you use?
- DC Motor - Ke and Kt are different…?
- Large drift (temperature could be a culprit) in this circuit. Anyone can help?
- Sending audio data in chunks using visible light communication
- Should client ideas about the UI turn into User Stories?
- How to use separated methods?
- Are “technical user stories” allowed in Scrum?
- Cyclomatic Complexity Question
- Rear derailleur speed number interchangability
- mismatched chain and chainring
- Can a character without caster levels learn a metamagic feat?
- Does Flaw (Endurance) reduce health?
- Cached login for Mobile Accounts not working in High Sierra

# 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.