NDLI: A majorization-minimization approach to the sparse generalized eigenvalue problem

Content Provider	Springer Nature Link
Author	Sriperumbudur, Bharath K. Torres, David A. Lanckriet, Gert R. G.
Copyright Year	2010
Abstract	Generalized eigenvalue (GEV) problems have applications in many areas of science and engineering. For example, principal component analysis (PCA), canonical correlation analysis (CCA) and Fisher discriminant analysis (FDA) are specific instances of GEV problems, that are widely used in statistical data analysis. The main contribution of this work is to formulate a general, efficient algorithm to obtain sparse solutions to a GEV problem. Specific instances of sparse GEV problems can then be solved by specific instances of this algorithm. We achieve this by solving the GEV problem while constraining the cardinality of the solution. Instead of relaxing the cardinality constraint using a ℓ $_{1}$-norm approximation, we consider 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 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. Finally, we illustrate the merits of this general sparse GEV algorithm with three specific examples of sparse GEV problems: sparse PCA, sparse CCA and sparse FDA. Empirical evidence for these examples suggests that the proposed sparse GEV algorithm, which offers a general framework to solve any sparse GEV problem, will give rise to competitive algorithms for a variety of applications where specific instances of GEV problems arise.
Starting Page	3
Ending Page	39
Page Count	37
File Format	PDF
ISSN	08856125
Journal	Machine Learning
Volume Number	85
Issue Number	1-2
e-ISSN	15730565
Language	English
Publisher	Springer US
Publisher Date	2010-12-07
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Generalized eigenvalue problem Principal component analysis Canonical correlation analysis Fisher discriminant analysis Sparsity D.c. program Majorization-minimization Zangwill’s theory of global convergence Music annotation Cross-language document retrieval Language Translation and Linguistics Computing Methodologies Artificial Intelligence (incl. Robotics) Simulation and Modeling Control, Robotics, Mechatronics
Content Type	Text
Resource Type	Article
Subject	Artificial Intelligence Software

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1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
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4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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