  Symmetry detection has been shown to improve various machine learning tasks.
In the context of continuous symmetry detection, current state of the art
experiments are limited to the detection of affine transformations. Under the
manifold assumption, we outline a framework for discovering continuous symmetry
in data beyond the affine transformation group. We also provide a similar
framework for discovering discrete symmetry. We experimentally compare our
method to an existing method known as LieGAN and show that our method is
competitive at detecting affine symmetries for large sample sizes and superior
than LieGAN for small sample sizes. We also show our method is able to detect
continuous symmetries beyond the affine group and is generally more
computationally efficient than LieGAN.
