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A Projection free method for Generalized Eigenvalue Problem with a nonsmooth Regularizer.

Seong Jae Hwang1, Maxwell D Collins1, Sathya N Ravi2

  • 1Dept. of Computer Sciences, University of Wisconsin - Madison, Madison, WI.

Proceedings. IEEE International Conference on Computer Vision
|April 16, 2016
PubMed
Summary
This summary is machine-generated.

This study introduces a new optimization method for solving generalized eigenvalue problems (GEP) with complex regularizers. The approach enhances statistical analysis in brain imaging by incorporating diverse data, improving disease pathology insights.

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Area of Science:

  • Computer Vision
  • Linear Algebra
  • Medical Image Analysis

Background:

  • Eigenvalue problems are fundamental in computer vision, yet current solvers are often restrictive 'black boxes'.
  • Incorporating external information like expert supervision or domain knowledge into eigenvalue problem formulations is challenging.
  • Existing methods struggle to regularize generalized eigenvalue problems (GEP) with side information.

Purpose of the Study:

  • To develop a novel optimization scheme for solving generalized eigenvalue problems (GEP) with nonsmooth regularizers.
  • To enable the incorporation of side information and domain knowledge into GEP formulations.
  • To demonstrate the application of the proposed method in improving statistical analysis of brain imaging data.

Main Methods:

  • Reformulated GEP with the Stiefel manifold as the feasibility set.
  • Developed an end-to-end stochastic optimization scheme for the reformulated problem.
  • Applied the method to brain imaging data, using regularizers derived from clinical and image-derived representations.

Main Results:

  • Successfully solved GEP with nonsmooth regularizers using the proposed optimization scheme.
  • Demonstrated improved statistical analysis of brain imaging data.
  • Showcased the ability to integrate multi-view information for enhanced disease pathology insights.

Conclusions:

  • The presented optimization scheme offers a flexible approach to solving regularized GEP.
  • The method effectively integrates diverse data sources for more robust statistical analysis in medical imaging.
  • This work advances the ability to incorporate side information into eigenvalue problems, with significant implications for computer vision and medical data analysis.