  In many-body physics, renormalization techniques are used to extract aspects
of a statistical or quantum state that are relevant at large scale, or for low
energy experiments. Recent works have proposed that these features can be
formally identified as those perturbations of the states whose
distinguishability most resist coarse-graining. Here, we examine whether this
same strategy can be used to identify important features of an unlabeled
dataset. This approach indeed results in a technique very similar to kernel PCA
(principal component analysis), but with a kernel function that is
automatically adapted to the data, or "learned". We test this approach on
handwritten digits, and find that the most relevant features are significantly
better for classification than those obtained from a simple gaussian kernel.
