Learning Pattern Transformation Manifolds for Classification

Manifold models provide low-dimensional representations that are useful for analyzing and classifying data in a transformation-invariant way. In this paper we study the problem of jointly building multiple pattern transformation manifolds from a collection of image sets, where each set consists of observations from a class of geometrically transformed signals. We build the manifolds such that each manifold approximates a different signal class. Each manifold is characterized by a representative pattern that consists of a linear combination of analytic atoms selected from a continuous dictionary manifold. We propose an iterative algorithm for jointly building multiple manifolds such that the classification accuracy is promoted in the learning of the representative patterns. We present a DC (Difference-of-Convex) optimization scheme that is applicable to a wide range of transformation and dictionary models, and demonstrate its application to transformation manifolds generated by the rotation, translation and scaling of a reference image. Experimental results suggest that the proposed method yields a high classification accuracy compared to reference methods based on individual manifold building or locally linear manifold approximations.