Backward-forward least angle shrinkage for sparse quadratic optimization

Authors:
Tianyi Zhou;Dacheng Tao
Affiliations:
Centre for Quantum computation & Intelligent Systems, Faculty of Engineering and Information Technology, University of Technology Sydney;Centre for Quantum computation & Intelligent Systems, Faculty of Engineering and Information Technology, University of Technology Sydney
Venue:
ICONIP'10 Proceedings of the 17th international conference on Neural information processing: theory and algorithms - Volume Part I
Year:
2010

Citing 5
Cited 0

The FERET Evaluation Methodology for Face-Recognition Algorithms

IEEE Transactions on Pattern Analysis and Machine Intelligence
Discriminative Locality Alignment

ECCV '08 Proceedings of the 10th European Conference on Computer Vision: Part I
Geometric Mean for Subspace Selection

IEEE Transactions on Pattern Analysis and Machine Intelligence
Bregman Divergence-Based Regularization for Transfer Subspace Learning

IEEE Transactions on Knowledge and Data Engineering
Manifold elastic net: a unified framework for sparse dimension reduction

Data Mining and Knowledge Discovery

Quantified Score

Hi-index	0.00

Visualization

Abstract

In compressed sensing and statistical society, dozens of algorithms have been developed to solve l1 penalized least square regression, but constrained sparse quadratic optimization (SQO) is still an open problem. In this paper, we propose backward-forward least angle shrinkage (BF-LAS), which provides a scheme to solve general SQO including sparse eigenvalue minimization. BF-LAS starts from the dense solution, iteratively shrinks unimportant variables' magnitudes to zeros in the backward step for minimizing the l1 norm, decreases important variables' gradients in the forward step for optimizing the objective, and projects the solution on the feasible set defined by the constraints. The importance of a variable is measured by its correlation w.r.t the objective and is updated via least angle shrinkage (LAS). We show promising performance of BF-LAS on sparse dimension reduction.