1,538 research outputs found
A D.C. Programming Approach to the Sparse Generalized Eigenvalue Problem
In this paper, we consider the sparse eigenvalue problem wherein the goal is
to obtain a sparse solution to the generalized eigenvalue problem. We achieve
this by constraining the cardinality of the solution to the generalized
eigenvalue problem and obtain sparse principal component analysis (PCA), sparse
canonical correlation analysis (CCA) and sparse Fisher discriminant analysis
(FDA) as special cases. Unlike the -norm approximation to the
cardinality constraint, which previous methods have used in the context of
sparse PCA, we propose a tighter approximation that is related to the negative
log-likelihood of a Student's t-distribution. The problem is then framed as a
d.c. (difference of convex functions) program and is solved as a sequence of
convex programs by invoking the majorization-minimization method. The resulting
algorithm is proved to exhibit \emph{global convergence} behavior, i.e., for
any random initialization, the sequence (subsequence) of iterates generated by
the algorithm converges to a stationary point of the d.c. program. The
performance of the algorithm is empirically demonstrated on both sparse PCA
(finding few relevant genes that explain as much variance as possible in a
high-dimensional gene dataset) and sparse CCA (cross-language document
retrieval and vocabulary selection for music retrieval) applications.Comment: 40 page
Quadratic Projection Based Feature Extraction with Its Application to Biometric Recognition
This paper presents a novel quadratic projection based feature extraction
framework, where a set of quadratic matrices is learned to distinguish each
class from all other classes. We formulate quadratic matrix learning (QML) as a
standard semidefinite programming (SDP) problem. However, the con- ventional
interior-point SDP solvers do not scale well to the problem of QML for
high-dimensional data. To solve the scalability of QML, we develop an efficient
algorithm, termed DualQML, based on the Lagrange duality theory, to extract
nonlinear features. To evaluate the feasibility and effectiveness of the
proposed framework, we conduct extensive experiments on biometric recognition.
Experimental results on three representative biometric recogni- tion tasks,
including face, palmprint, and ear recognition, demonstrate the superiority of
the DualQML-based feature extraction algorithm compared to the current
state-of-the-art algorithm
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