Alternating direction method of multipliers for penalized zero-variance discriminant analysis Ames, Brendan Hong, Mingyi Hong, Mingyi
dc.contributor.department Industrial and Manufacturing Systems Engineering 2018-02-18T04:41:01.000 2020-06-30T04:49:16Z 2020-06-30T04:49:16Z Fri Jan 01 00:00:00 UTC 2016 2017-02-12 2016-02-12
dc.description.abstract <p>We consider the task of classification in the high dimensional setting where the number of features of the given data is significantly greater than the number of observations. To accomplish this task, we propose a heuristic, called sparse zero-variance discriminant analysis, for simultaneously performing linear discriminant analysis and feature selection on high dimensional data. This method combines classical zero-variance discriminant analysis, where discriminant vectors are identified in the null space of the sample within-class covariance matrix, with penalization applied to induce sparse structures in the resulting vectors. To approximately solve the resulting nonconvex problem, we develop a simple algorithm based on the alternating direction method of multipliers. Further, we show that this algorithm is applicable to a larger class of penalized generalized eigenvalue problems, including a particular relaxation of the sparse principal component analysis problem. Finally, we establish theoretical guarantees for convergence of our algorithm to stationary points of the original nonconvex problem, and empirically demonstrate the effectiveness of our heuristic for classifying simulated data and data drawn from applications in time-series classification.</p>
dc.description.comments <p>This is a manuscript of an article Computational Optimzation and Applications 64 (2016): 725. The final publication is available at Springer via <a href="" target="_blank"></a>.</p>
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dc.identifier archive/
dc.identifier.articleid 1089
dc.identifier.contextkey 9702839
dc.identifier.s3bucket isulib-bepress-aws-west
dc.identifier.submissionpath imse_pubs/91
dc.language.iso en
dc.source.bitstream archive/|||Sat Jan 15 02:28:23 UTC 2022
dc.source.uri 10.1007/s10589-016-9828-y
dc.subject.disciplines Industrial Engineering
dc.subject.disciplines Systems Architecture
dc.subject.disciplines Systems Engineering
dc.subject.disciplines Theory and Algorithms
dc.subject.keywords Linear discriminant analysis
dc.subject.keywords Alternating direction method of multipliers
dc.subject.keywords Nonconvex optimization
dc.subject.keywords Dimension reduction
dc.subject.keywords Feature selection
dc.subject.keywords Classification
dc.title Alternating direction method of multipliers for penalized zero-variance discriminant analysis
dc.type article
dc.type.genre article
dspace.entity.type Publication
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relation.isOrgUnitOfPublication 51d8b1a0-5b93-4ee8-990a-a0e04d3501b1
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