  Bilinear pooling achieves great success in fine-grained visual recognition
(FGVC). Recent methods have shown that the matrix power normalization can
stabilize the second-order information in bilinear features, but some problems,
e.g., redundant information and over-fitting, remain to be resolved. In this
paper, we propose an efficient Multi-Objective Matrix Normalization (MOMN)
method that can simultaneously normalize a bilinear representation in terms of
square-root, low-rank, and sparsity. These three regularizers can not only
stabilize the second-order information, but also compact the bilinear features
and promote model generalization. In MOMN, a core challenge is how to jointly
optimize three non-smooth regularizers of different convex properties. To this
end, MOMN first formulates them into an augmented Lagrange formula with
approximated regularizer constraints. Then, auxiliary variables are introduced
to relax different constraints, which allow each regularizer to be solved
alternately. Finally, several updating strategies based on gradient descent are
designed to obtain consistent convergence and efficient implementation.
Consequently, MOMN is implemented with only matrix multiplication, which is
well-compatible with GPU acceleration, and the normalized bilinear features are
stabilized and discriminative. Experiments on five public benchmarks for FGVC
demonstrate that the proposed MOMN is superior to existing normalization-based
methods in terms of both accuracy and efficiency. The code is available:
https://github.com/mboboGO/MOMN.
