Nature vs. Math: Interpreting Independent Component Analysis in Light of Computational Harmonic Analysis

ICA has recently been applied to naturally-occurring data to uncover hidden fundamental components. Harmonic analysis has long been used to uncover hidden fundamental components of mathematically-defined objects. In my talk I will explore some recent parallelisms between ICA and CHA – fascinating similarities in the “hidden components” that the two subjects are uncovering. I will suggest that recent work on the independent components of images can best be interepreted in the light of recent constructions in harmonic analysis – such as ridgelets and curvelets. These mathematical objects exhibit surprising similarities to the results of ICA on certain naturally-occurring data.