Natural Image Patch Statistics Conditioned on Activity of an Independent Component

In this paper we offer a relatively comprehensive look at how the activation of one independent component analysis (ICA) feature changes the first and second order statistics in orthogonal directions in whitened image patches. Essential here is normalizing image patch lengths and normalizing the patches by the sign of the active (conditioning) component. First order statistics for high activation are shown to extend the original features even outside the original windows. Changes in second order statistics can be argued to be linked to the ‘errors’ made in describing the actual object in the image patches by the active feature.

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