Group Forward–Backward Orthogonal Matching Pursuit for General Convex Smooth Functions

Abstract

This paper introduces the Group Forward–Backward Orthogonal Matching Pursuit (Group-FoBa-OMP) algorithm, a novel approach for sparse feature selection. The core innovations of this algorithm include (1) an integrated backward elimination process to correct earlier misidentified groups; (2) a versatile convex smooth model that generalizes previous research; (3) the strategic use of gradient information to expedite the group selection phase; and (4) a theoretical validation of its performance in terms of support set recovery, variable estimation accuracy, and objective function optimization. These advancements are supported by experimental evidence from both synthetic and real-world data, demonstrating the algorithm’s effectiveness.

Keywords

• compressed sensing
• group orthogonal matching pursuit
• group sparse
• group restricted isometry property
• instance optimality