A Metric for Linear Symmetry-Based Disentanglement

TL;DR

This paper introduces a new metric to quantify how well data representations capture linear symmetries, specifically $SO(2)$, providing a practical evaluation method for LSBD in various datasets.

Contribution

The paper proposes a novel metric and practical evaluation method for measuring Linear Symmetry-Based Disentanglement in data representations.

Findings

The metric effectively quantifies LSBD in data representations.

Application to three datasets demonstrates the metric's utility.

Results show varying degrees of LSBD achievement across datasets.

Abstract

The definition of Linear Symmetry-Based Disentanglement (LSBD) proposed by (Higgins et al., 2018) outlines the properties that should characterize a disentangled representation that captures the symmetries of data. However, it is not clear how to measure the degree to which a data representation fulfills these properties. We propose a metric for the evaluation of the level of LSBD that a data representation achieves. We provide a practical method to evaluate this metric and use it to evaluate the disentanglement of the data representations obtained for three datasets with underlying $SO(2)$ symmetries.