Revealing Smooth Structure of Visual Data by Permutation on Manifolds

Advance in technology and commercial media has simplified the process of collecting large-scale visual data, but it also raises new challenges in data organization. In this paper, we propose to characterize data association by recovering an intrinsic order from an unorganized dataset. Our method is motivated by smooth manifold geometry. We advocate that the optimal data order should encode the shape of underlying manifold as well as the latent data association. Following the data order, we find a smooth path to visualize the latent topic of visual data with a perceptually reasonable transition. We develop an efficient algorithm Permutation on Manifolds (PoM) to solve this NP-hard permutation problem. Experiments on synthetic and real-world dataset demonstrate the potential of PoM to serve as a core technique of numerous applications.