Deep Fourier Ranking Quantization for Semi-Supervised Image Retrieval.

To reduce the extreme label dependence of supervised product quantization methods, the semi-supervised paradigm usually employs massive unlabeled data to assist in regularizing deep networks, thereby improving model performance. However, the existing method focuses on the overall distribution consistency between unlabeled data and class prototypes, while ignoring subtle individual variances between unlabeled instances. Therefore, the local neighborhood structure is not fully explored, which will cause the model to easily overfit in the training set. In this paper, we introduce a new Fourier perspective to alleviate this issue by exploring the semantic relations between unlabeled instances in a self-supervised manner. Specifically, based on Fourier Transform, we first design a Phase Mixing (PM) strategy, which can manipulate the mixing area and values of the phase component between two images to control the proportion of semantic information. In this way, we can construct multi-level similarity neighbors naturally for unlabeled data. Then, a ranking quantization loss is formulated to perceive multi-level semantic variances in neighbor instances, which improves the robustness and generalization of the model. Extensive experiments in three different semi-supervised settings show that our method outperforms existing state-of-the-art methods by averaged 3.95% improvement on four datasets.

Multi-Objective Matrix Normalization for Fine-grained Visual Recognition.

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.