A Metric for Linear Symmetry-Based Disentanglement
This work addresses the problem of quantitatively measuring disentanglement for researchers working on symmetric data representations, providing a tool to assess how well a representation captures data symmetries.
This paper proposes a metric to quantify the degree of Linear Symmetry-Based Disentanglement (LSBD) in data representations, a concept previously defined by Higgins et al. (2018). The authors demonstrate the practical application of this metric by evaluating disentanglement in representations for three datasets exhibiting underlying SO(2) symmetries.
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.