Learning low-dimensional representations that disentangle the underlying factors of variation in data has been posited as an important step towards interpretable machine learning with good generalization. To address the fact that there is no consensus on what disentanglement entails, Higgins et al. (2018) propose a formal definition for Linear Symmetry-Based Disentanglement, or LSBD, arguing that underlying real-world transformations give exploitable structure to data. Although several works focus on learning LSBD representations, such methods require supervision on the underlying transformations for the entire dataset, and cannot deal with unlabeled data. Moreover, none of these works provide a metric to quantify LSBD. We propose a metric to quantify LSBD representations that is easy to compute under certain well-defined assumptions. Furthermore, we present a method that can leverage unlabeled data, such that LSBD representations can be learned with limited supervision on transformations. Using our LSBD metric, our results show that limited supervision is indeed sufficient to learn LSBD representations.
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