Inferring relevant features: from QFT to PCA

Understand

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".