Spectral Regression: A Regression Framework for Efficient Regularized Subspace Learning
Cai, Deng
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https://hdl.handle.net/2142/11702
Description
Title
Spectral Regression: A Regression Framework for Efficient Regularized Subspace Learning
Author(s)
Cai, Deng
Issue Date
2009
Doctoral Committee Chair(s)
Han, Jiawei
Committee Member(s)
Huang, Thomas S.
Zhai, ChengXiang
Chang, Kevin C-C.
Department of Study
Computer Science
Discipline
Computer Science
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Date of Ingest
2009-05-05T20:26:47Z
Keyword(s)
Machine Learning
Language
en
Abstract
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.
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