Combinatorial QPs via a low-dimensional subspace sampling

Author

Papailiopoulos, Dimitris S. ; Asteris, Megasthenis ; Dimakis, Alexandros G.

Author_Institution

Dept. of Electr. & Comput. Eng., Univ. of Texas at Austin, Austin, TX, USA

fYear

2014

fDate

19-21 March 2014

Firstpage

1

Lastpage

3

Abstract

Several large scale data processing problems can be formulated as quadratic programs subject to combinatorial constraints. We present a novel low-rank approximation framework for problems such as sparse PCA, nonnegative PCA, or finding the k-densest submatrix. Our framework comes with provable approximation guarantees, that dependent on the spectrum of the data-set matrix. Our algorithm operates by solving a number of QP instances, which are randomly sampled from a low-dimensional subspace of the input matrix.

Keywords

combinatorial mathematics; compressed sensing; matrix algebra; principal component analysis; quadratic programming; combinatorial QP; combinatorial constraints; data-set matrix; k-densest submatrix; large scale data processing problems; low-dimensional subspace sampling; low-rank approximation framework; nonnegative PCA; principal component analysis; quadratic programs; sparse PCA; Accuracy; Approximation algorithms; Approximation methods; Eigenvalues and eigenfunctions; Principal component analysis; Sparse matrices; Vectors;

fLanguage

English

Publisher

ieee

Conference_Titel

Information Sciences and Systems (CISS), 2014 48th Annual Conference on

Conference_Location

Princeton, NJ

Type

conf

DOI

10.1109/CISS.2014.6814140

Filename

6814140