MOMN

MOMN normalizes bilinear features by jointly applying square-root, low-rank, and sparsity regularizers to stabilize second-order information and improve generalization for fine-grained visual categorization.

Key Features:

• Simultaneous Normalization: Integrates square-root, low-rank, and sparsity regularizers to normalize bilinear features and compact second-order representations.
• Augmented Lagrange Formulation: Employs an augmented Lagrange formulation with approximated constraints to manage joint optimization of non-smooth regularizers with different convex properties.
• Auxiliary Variables and Alternating Solutions: Introduces auxiliary variables to relax constraints and enables alternating optimization for each regularizer.
• Gradient Descent Updating Strategies: Applies gradient-descent-based updating strategies to promote consistent convergence and obtain stable, discriminative normalized bilinear features.
• Efficient Implementation: Implements computations using matrix multiplication to enable GPU acceleration.

Scientific Applications:

• Fine-Grained Visual Categorization (FGVC): Evaluated on five public FGVC benchmarks, demonstrating improved performance over existing normalization-based methods by stabilizing bilinear features and promoting model generalization.

Methodology:

MOMN integrates square-root, low-rank, and sparsity regularizers; formulates the joint optimization via an augmented Lagrange approach with approximated constraints; introduces auxiliary variables for alternating optimization; applies gradient-descent-based updates; and implements operations as matrix multiplications for GPU acceleration.