Extensions of principal components analysis

To my father iii ACKNOWLEDGEMENTS My journey through the PhD program has been a long one, taking me from robotics, to computer vision, to machine learning, and finally to theory. Making so many transitions slowed my graduation, no doubt, but it also allowed me to work with leaders across several research fields and has given me a better perspective on the The most important man in my PhD career has been my advisor, Santosh Vem-pala, who brought out the best in me. Santosh's deep knowledge of theory and insight into my character allowed him to steer me toward the problems where I would enjoy myself and have success. Working with him closely has taught me how to think about math more intuitively and shown me how a truly great mind thinks. I will never forget his many acts of kindness and sometimes heroic efforts on my behalf. If I can emulate his advisement with my own students, I will consider myself a great success. I also want to thank my two previous faculty advisors Frank Dellaert and Jim Rehg for the opportunity to work with them and for all that I learned under their guidance. Matt Mullin has also been a great resource on all matters mathematical. I am also obliged to some of the great teachers at Georgia Tech. A few that stand out in my memory are committee also deserves thanks for their feedback and thoughtful questions about my work. Among my fellow graduate students, I am grateful to the members of the Theory Group and Wall Lab for their comradery through our shared struggles. I especially enjoyed my conversations with Jie Sun about our efforts at self-improvement and with iv Raffay Hamid about deep questions outside of computer science. These conversations were often the highlight of my day. Lastly, I want to thank my family. My parents more than anyone else cultivated the intellectual curiosity which has enriched my life and been a consolation through hard times. They and my wife Stephanie remained supportive throughout my PhD career. Stephanie has also been an excellent proofreader for all my papers. She and our two children, Charles and Sophie, have been remarkably patient through the late nights I spent in the lab and my bad humors. They mean the world to me. 2 Mapping points to the unit circle and then finding the direction of maximum variance reveals the …