Manifold Topology Divergence: a Framework for Evaluating Data Manifolds
Authors: Serguei Barannikov, Ilya Trofimov, Grigorii Sotnikov, Ekaterina Trimbach, Alexander Korotin, Alexander Filippov, Evgeny Burnaev
Abstract: We develop a framework for evaluating information manifolds, aimed, particularly, in route of the evaluation of deep generative fashions. We describe a novel machine, Cross-Barcode(P,Q), that, given a pair of distributions in a high-dimensional home, tracks multiscale topology spacial discrepancies between manifolds on which the distributions are concentrated. Based mostly totally on the Cross-Barcode, we introduce the Manifold Topology Divergence score (MTop-Divergence) and apply it to guage the effectivity of deep generative fashions in quite a few domains: pictures, 3D-shapes, time-series, and on fully completely different datasets: MNIST, Development MNIST, SVHN, CIFAR10, FFHQ, chest X-ray pictures, market stock information, ShapeNet. We present that the MTop-Divergence exactly detects quite a few ranges of mode-dropping, intra-mode collapse, mode invention, and movie disturbance. Our algorithm scales properly (primarily linearly) with the rise of the dimension of the ambient high-dimensional home. It’s doubtless one of many first TDA-based wise methodologies which may be utilized universally to datasets of varied sizes and dimensions, along with these on which the most recent GANs throughout the seen space are expert. The proposed methodology is space agnostic and would not depend upon pre-trained networks.
