Semisupervised alignment of manifolds.

TLDR

The authors develop semisupervised algorithms that align datasets sharing a common manifold by optimizing graph‑based approximations, completing partial alignments from prior knowledge or labeled correspondences, and integrating supervised signals with unsupervised manifold learning to mitigate high dimensionality. They demonstrate the approach by learning mappings between image datasets that vary in pose and viewing angle, showing successful alignment. The method is illustrated by mapping between image datasets parameterized by the same underlying modes of variability.

Abstract

In this paper, we study a family of semisupervised learning algorithms for “aligning” different data sets that are characterized by the same underlying manifold. The optimizations of these algorithms are based on graphs that provide a discretized approximation to the manifold. Partial alignments of the data sets—obtained from prior knowledge of their manifold structure or from pairwise correspondences of subsets of labeled examples— are completed by integrating supervised signals with unsupervised frameworks for manifold learning. As an illustration of this semisupervised setting, we show how to learn mappings between different data sets of images that are parameterized by the same underlying modes of variability (e.g., pose and viewing angle). The curse of dimensionality in these problems is overcome by exploiting the low dimensional structure of image manifolds.