The ideally disentangled latent space in GAN involves the global
representation of latent space with semantic attribute coordinates. In other
words, considering that this disentangled latent space is a vector space, there
exists the global semantic basis where each basis component describes one
attribute of generated images. In this paper, we propose an unsupervised method
for finding this global semantic basis in the intermediate latent space in
GANs. This semantic basis represents sample-independent meaningful
perturbations that change the same semantic attribute of an image on the entire
latent space. The proposed global basis, called Fr\'echet basis, is derived by
introducing Fr\'echet mean to the local semantic perturbations in a latent
space. Fr\'echet basis is discovered in two stages. First, the global semantic
subspace is discovered by the Fr\'echet mean in the Grassmannian manifold of
the local semantic subspaces. Second, Fr\'echet basis is found by optimizing a
basis of the semantic subspace via the Fr\'echet mean in the Special Orthogonal
Group. Experimental results demonstrate that Fr\'echet basis provides better
semantic factorization and robustness compared to the previous methods.
Moreover, we suggest the basis refinement scheme for the previous methods. The
quantitative experiments show that the refined basis achieves better semantic
factorization while constrained on the same semantic subspace given by the
previous method.Comment: 25 pages, 21 figure