Slow feature Analysis¶
a version of linear factor model that uses information from time signals to learn invariant features
slow feature is motivated by the slowness principle, this principle states that the most important characteristics of a scene change slowly, compared to individual measurements. (pixels change rapidly but the position only slowly)
Problem¶
\[\begin{split}
\min_{\theta} E_l[f(x^{t+1})_i -f(x^{(t)})_i]^2 \\
\text{s.t: } \\
E_t[f(x^{(t)})]_i = 1 \\
E_t[f(x^{(t)})^2]_i = 1 \\
\forall i < j \space E_t[f(x^{(t)})_i f(x^{(t)})_j]=0
\end{split}\]
The last constrain forces the features to be linearly decorelated. If it would not be present then it would capture the same feature.