xii 3.6 Unwrapped mnist-0 digits with a selection of images of the actual digits on top. Orientation and thickness of digits smoothly vary across horizontal and vertical directions, respectively. . 34 3.7 Unfolding mnist-0 digits using two benchmark manifold learning methods. Unlike the proposed method, no smooth variation of structure is preserved using these methods. . . . . 35 3.8 Unfolding mnist-2 digits using the proposed method and t-SNE. Similar to Figure 3.7(b) for mnist-0, no smooth variation of structure is preserved using t-SNE, while proposed method shows smooth change of thickness and shape in horizontal and vertical coordinates, respectively. 36 3.9 Unfolding mnist-9 digits using the proposed method, which shows smooth change of thickness Sylvain Bouix, who were also my mentors, for all of their guidance through this process; your discussion, ideas, and feedback have been absolutely invaluable.