Iterative-Weighted Thresholding Method for Group-Sparsity-Constrained Optimization With Applications.

Area of Science:

• Data Science
• Optimization Theory
• Machine Learning

Background:

• Group sparse optimization enhances high-dimensional data analysis efficiency and stability.
• Challenges remain in developing effective group sparse-inducing functions and identifying significant groups.

Purpose of the Study:

• To address the group-sparsity-constrained minimization problem.
• To develop a novel weighted framework for improved group feature selection.

Main Methods:

• Converted the problem to an equivalent weighted $\ell _{p,q}$-norm constrained optimization model.
• Applied proximal gradient method for a solution with theoretical convergence analysis.
• Utilized homotopy technique within the Lagrangian dual framework for parameter tuning.

Main Results:

• Developed a robust weighted framework for identifying important groups.
• Demonstrated superior group feature selection accuracy and computational efficiency through simulations and real data.
• Achieved L-stationary points for the original problem using the proposed homotopy algorithm.

Conclusions:

• The proposed weighted group sparse optimization method offers significant improvements in feature selection and efficiency.
• The framework's compatibility with various identification strategies enhances practical robustness.
• The method shows great potential for applications in compressed sensing, image recognition, and classifier design.