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Han, Jiawei Huang, Thomas S. Zhai, ChengXiang Chang, Kevin C-C. Cai, Deng 2009-05-05T20:26:47Z 2009-05-05T20:26:47Z 2009 Spectral methods have recently emerged as a powerful tool for dimensionality reduction and manifold learning. These methods use information contained in the eigenvectors of a data affinity (\ie, item-item similarity) matrix to reveal the low dimensional structure in the high dimensional data. The most popular manifold learning algorithms include Locally Linear Embedding, ISOMAP, and Laplacian Eigenmap. However, these algorithms only provide the embedding results of training samples. There are many extensions of these approaches which try to solve the out-of-sample extension problem by seeking an embedding function in reproducing kernel Hilbert space. However, a disadvantage of all these approaches is that their computations usually involve eigen-decomposition of dense matrices which is expensive in both time and memory. In this thesis, we introduce a novel dimensionality reduction framework, called {\bf Spectral Regression} (SR). SR casts the problem of learning an embedding function into a regression framework, which avoids eigen-decomposition of dense matrices. Also, with the regression as a building block, different kinds of regularizers can be naturally incorporated into our framework which makes it more flexible. SR can be performed in supervised, unsupervised and semi-supervised situation. It can make efficient use of both labeled and unlabeled points to discover the intrinsic discriminant structure in the data. We have applied our algorithms to several real world applications, e.g. face analysis, document representation and content-based image retrieval. not peer reviewed Submitted by Deng Cai (dengcai2@illinois.edu) on 2009-05-05T20:26:47Z No. of bitstreams: 1 Thesis_Deng.pdf: 775217 bytes, checksum: ee663d0102658d3a842e23fe836bb0f2 (MD5) Made available in DSpace on 2009-05-05T20:26:47Z (GMT). No. of bitstreams: 1 Thesis_Deng.pdf: 775217 bytes, checksum: ee663d0102658d3a842e23fe836bb0f2 (MD5) Previous issue date: 2009 published or submitted for publication Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Computer Science in the Graduate College of the University of Illinois at Urbana-Champaign, 2009 http://hdl.handle.net/2142/11702 en Copyright 2009 Deng Cai Machine Learning Spectral Regression: A Regression Framework for Efficient Regularized Subspace Learning Dissertation / Thesis text Computer Science Computer Science University of Illinois at Urbana-Champaign Dissertation Ph.D.