Recently the problem of dimensionality reduction (or, subspace learning) has received a lot of interests in many fields of information processing, including data mining, information retrieval, and pattern recognition. Some popular methods include Principal Component Analysis (PCA), Linear Discriminant Analysis (LDA) and Locality Preserving Projection (LPP). However, a disadvantage of all these approaches is that the learned projective functions are linear combinations of all the original features, thus it is often difficult to interpret the results. In this paper, we propose a novel dimensionality reduction framework, called Unified Sparse Subspace Learning (USSL), for learning sparse projections. USSL casts the problem of learning the projective functions into a regression framework, which facilitates the use of different kinds of regularizers. By using a L1-norm regularizer (lasso), the sparse projections can be efficiently computed. Experimental results on real world classification and clustering problems demonstrate the effectiveness of our method.

I would like to thank my thesis advisor, Sridhar Mahadevan. Sridhar has been such a wonderful advisor, and every aspect of this thesis has benefitted from his guidance and support throughout my graduate studies. I also like to thank Sridhar for giving me the flexibility to explore many different ideas and research topics. I am appreciative of the support offered by my other thesis committee members, Andrew McCallum, Erik Learned-Miller, and Weibo Gong. Andrew helped me on CRF, MALLET and topic modeling. Erik helped me on computer vision. Weibo has many brilliant ideas on how brains work. I got a lot of inspirations from him. I am grateful for many other professors and staff members, who helped me along. Andy Barto offered me many insightful comments and advice on my research. David Kulp and Oliver Brock helped me on bioinformatics. Stephen Scott brought me to this country, taught me machine learning/bioinformatics and offers me constant support. Vadim Gladyshev helped me on biochemistry. Mauro Maggioni helped me on diffusion wavelets. I also thank Gwyn Mitchell and Leanne Leclerc for their help with my questions over the years. I am deeply thankful to my Master thesis advisor, Zhuzhi Yuan and other teachers in Nankai University for guiding my development as

This paper proposes a novel algorithm for manifold alignment preserving global geometry. This approach constructs mapping functions that project data instances from different input domains to a new lower-dimensional space, simultaneously matching the instances in correspondence and preserving global distances between instances within the original domains. In contrast to previous approaches, which are largely based on preserving local geometry, the proposed approach is suited to applications where the global manifold geometry needs to be respected. We evaluate the effectiveness of our algorithm for transfer learning in two real-world cross-lingual information retrieval tasks. 1