Slow Feature Analysis (SFA) finds slow signals (see References below). The problem has an
analytic solution and thus can be computed quickly using generalized eigen-value solvers.
For ForeCA it is important to know that SFA is equivalent to
finding a linear combination signal with largest lag \(1\) autocorrelation.
The disadvantage of SFA for forecasting is that, e.g., white noise (WN)
is ranked higher than an AR(1) with negative autocorrelation coefficient
\(\rho_1 < 0\). While it is true that WN is slower, it is not more
forecastable. Thus we are also interested in the fastest signal, i.e.,
the last eigenvector. The so obtained fastest signal corresponds to minimizing
the lag 1 auto-correlation (possibly \(\rho_1 < 0\)).
Note though that maximizing (or minimizing) the lag \(1\) auto-correlation does
not necessarily yield the most forecastable signal (as measured
by Omega
), but it is a good start.