Kernel-based extraction of Slow Features: Complex cells learn disparity and translation invariance from natural images

Colloque avec actes et comité de lecture. internationale.; International audience; In Slow Feature Analysis (\cite{Wiskott02}), it has been demonstrated that high-order invariant properties can be extracted by projecting inputs into a nonlinear space and computing the slowest changing features in this space; this has been proposed as a simple general model for learning nonlinear invariances in the visual system. However, this method is highly constrained by the curse of dimensionality which limits it to simple theoretical simulations. This paper demonstrates that by using a different but closely-related objective function for extracting slowly varying features (\cite{Stone95a,Stone01}), and then exploiting the kernel trick, this curse can be avoided. Using this new method we show that both the complex cell properties of translation invariance and disparity coding can be learnt simultaneously from natural images when complex cells are driven by simple cells also learnt from the image.