A Metric for Linear Symmetry-Based Disentanglement

The definition of Linear Symmetry-Based Disentanglement (LSBD) proposed by Higgins et al. 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. In this work, 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 for the data representation obtained for three datasets with underlying SO(2) symmetries.