Title:  Incorporating Manifold Structure of Natural Variations into Statistical Learning

Committee: 

Dr. Rozell, Advisor       

Dr. Davenport, Chair

Dr. Essa

Abstract:

The objective of the proposed research is to develop methods that exploit the generative manifold structure of identity-preserving transformations in order to improve machine learning performance in cases that lack full information about input structure and variations. The within-class variation in high-dimensional data can be modeled as being low-dimensional due to the constraints of the physical processes producing that variation. We utilize this fact to learn transformations in a source domain which can be used for 3D scene understanding, sample generation, and object classification. For 3D scene understanding, a model of 3D manifold structure is learned from 2D inputs and used for inferring depth from moving 2D inputs. For sample generation, we transfer the manifold transformations that are learned on a subset of data to new classes or examples in order to generate samples that are consistent with the object manifolds. Finally, for classification, the generative manifold structure is used to classify new samples by searching for nearest neighbors in the manifold space.