Examples of renormalization group transformations for image sets

TL;DR

This paper introduces RG transformations for image sets inspired by tensor RG, relating criticality to principal component divergence, and compares their effectiveness near fixed points using the 2D Ising model.

Contribution

It proposes a novel RG approach for image data inspired by tensor RG, linking critical phenomena to principal component analysis.

Findings

Criticality correlates with the divergence of the largest principal component.

The proposed RG transformations can produce data collapse.

Comparison with tensor RG shows similar behavior near fixed points.

Abstract

Using the example of configurations generated with the worm algorithm for the two-dimensional Ising model, we propose renormalization group (RG) transformations, inspired by the tensor RG, that can be applied to sets of images. We relate criticality to the logarithmic divergence of the largest principal component. We discuss the changes in link occupation under the RG transformation, suggest ways to obtain data collapse, and compare with the two state tensor RG approximation near the fixed point.