Revealing Smooth Structure of Visual Data by Permutation on Manifolds

In this paper, we address the issue of visual data organization by recovering an intrinsic order from an unorganized dataset. The proposed method exploits the inherent nature of manifold. This new perspective, posing no hypothesis on local topology of observed data, is simply built on the smoothness prior of manifold geometry. Under the observation that strong relation exists among visual content, we assume a visual dataset lies on a manifold and thus changes smoothly from point to point. By exploiting the linearity within nearby data points, our goal becomes to visit all of the data points along a manifold-guided order and to characterize the specific manifold’s shape.