Hi,
Can anybody tell me why the eigenvalues of an adaptively updated
covariance matrix are not only shrunk compared to those of the data, but
are spread out? I can see that the filtering processes invovled perhaps
tend to smooth out the non-correlations between variables and hence
reinforce the correlations, but have no idea how to prove this. Update
occurs every nk samples where nk>= number of variables.
Mean update:
mx(k+nk) = mu*mx(k) + (1-mu)*sum(x(k+1:k+nk))/nk
Adaptively scaled data window:
xw = x(k+1:k+nk) - mx(k+nk)
Change in mean:
dmx(k+nk) = mx(k+nk)-mx(k)
Adaptive covariance update:
R(k+nk) = mu*( R(k) + dmx(k+nk)'*dmx(k+nk) ) + (1-mu)*xw'*xw/nk
The eigenvalues of R(k) I thought could be related to those of cov(X)
(assuming now that X is stationary) by a fairly messy equation. When I
try the above on cross-correlated random variables x, the eigenvalues
seem related only on average. The largest eval of Rk is significantly
larger than expected and the smallest, significantly smaller than
expected.
Thanks in advance for any suggestions,
James
--
Mr James Lennox
AWMC, Dept Chemical Engineering
The University of Queensland
St Lucia
QLD 4072
AUSTRALIA
[EMAIL PROTECTED]
Ph: +61 7 33469051
Fax: +61 7 33654726
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