NDLI: Robust Computation of Linear Models by Convex Relaxation

Content Provider	Springer Nature Link
Author	McCoy, Michael B. Lerman, Gilad Zhang, Teng Tropp, Joel A.
Copyright Year	2014
Abstract	Consider a data set of vector-valued observations that consists of noisy inliers, which are explained well by a low-dimensional subspace, along with some number of outliers. This work describes a convex optimization problem, called reaper, that can reliably fit a low-dimensional model to this type of data. This approach parameterizes linear subspaces using orthogonal projectors and uses a relaxation of the set of orthogonal projectors to reach the convex formulation. The paper provides an efficient algorithm for solving the reaper problem, and it documents numerical experiments that confirm that reaper can dependably find linear structure in synthetic and natural data. In addition, when the inliers lie near a low-dimensional subspace, there is a rigorous theory that describes when reaper can approximate this subspace.
Ending Page	410
Page Count	48
Starting Page	363
File Format	PDF
ISSN	16153375
e-ISSN	16153383
Journal	Foundations of Computational Mathematics
Issue Number	2
Volume Number	15
Language	English
Publisher	Springer US
Publisher Date	2014-09-23
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Robust linear models Semidefinite programming Economics general Numerical Analysis Mathematical programming methods Computer Science Convex relaxation Factor analysis and principal components; correspondence analysis Linear and Multilinear Algebras, Matrix Theory Applications of Mathematics Math Applications in Computer Science Iteratively reweighted least squares
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Analysis Computational Theory and Mathematics Computational Mathematics

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