Geometric Methods for Mining Large and Possibly Private Datasets Approved by:

To my parents, and my wife iii ACKNOWLEDGEMENTS First of all, I would like to acknowledge the overwhelming contribution and endless hours invested in me by my advisor, Prof. Ling Liu. Without her, I would not even be close to being done. Apart from her research advisory help, I also thank for all the useful life tips I have harvested over the past years from her. I wish to thank the faculty members on my committee- Prof. Elisa Bertino, Prof. Chin-hui Lee, Prof. Shamkant Navathe, and Prof. Edward Omiecinski- for their help in reviewing the final thesis and giving valuable comments. Prof. Elisa Bertino, Prof. Edward Omiecinski, Prof. Calton Pu, and Dr. Gordon Sun also helped me a lot in my job search. I would like to thank them all. I am grateful to many people at Georgia Tech for their guidance and support during my Ph.D. study. My colleagues in the Distributed Data Intensive Systems Lab (DISL) were great friends and often provided valuable advice. I especially want to thank Prof. Calton Pu, who had tried to involve me in proposal writing. The DISL group meetings have been a great source of information, pizza