The non-negative matrix factorization (NMF) algorithm represents the original image as a linear combination of a set of basis images. This image representation method is in line with the idea of "parts constitute a whole" in human thinking. The existing deep NMF performs deep factorization on the coefficient matrix. In these methods, the basis images used to represent the original image is essentially obtained by factorizing the original images once. To extract features reflecting the deep localization characteristics of images, a novel deep NMF architecture based on underlying basis images learning is proposed for the first time. The architecture learns the underlying basis images by deep factorization on the basis images matrix. The deep factorization architecture proposed in this paper has strong interpretability. To implement this architecture, this paper proposes a deep non-negative basis matrix factorization algorithm to obtain the underlying basis images. Then, the objective function is established with an added regularization term, which directly constrains the basis images matrix to obtain the basis images with good local characteristics, and a regularized deep non-negative basis matrix factorization algorithm is proposed. The regularized deep nonlinear non-negative basis matrix factorization algorithm is also proposed to handle pattern recognition tasks with complex data. This paper also theoretically proves the convergence of the algorithm. Finally, the experimental results show that the deep NMF architecture based on the underlying basis images learning proposed in this paper can obtain better recognition performance than the other state-of-the-art methods.

A simple yet effective semi-supervised method is proposed in this paper based on consistency regularization for crowd counting, and a hybrid perturbation strategy is used to generate strong, diverse perturbations, and enhance unlabeled images information mining. The conventional CNN-based counting methods are sensitive to texture perturbation and imperceptible noises raised by adversarial attack, therefore, the hybrid strategy is proposed to combine a spatial texture transformation and an adversarial perturbation module to perturb the unlabeled data in the semantic and non-semantic spaces, respectively. Moreover, a cross-distribution normalization technique is introduced to address the model optimization failure caused by BN layer in the strong perturbation, and to stabilize the optimization of the learning model. Extensive experiments have been conducted on the datasets of ShanghaiTech, UCF-QNRF, NWPU-Crowd, and JHU-Crowd++. The results demonstrate that the proposed semi-supervised counting method performs better over the state-of-the-art methods, and it has better robustness to various perturbations.

Network pruning can effectively reduce a model's capacity and computational load, thereby making model deployment in mobile devices less difficult than that without pruning. To improve the pruning rate of the model while maintaining the kernel's feature extraction ability, this paper designs a progressive kernel pruning method for CNN model compression based on the proposed information mapping sparsity index. This method first prunes the kernels in the filter and then prunes the kernels in the convolution layer when the model reaches a certain compression ratio. The whole process is called progressive kernel pruning (PKP). For the kernel pruning process, this paper defines the information mapping sparse index (IMSI), which is used to measure the mapping ability of the convolution kernel related to the amount of information transferred by the convolution operation. When pruning the kernels of filters and layers, according to the IMSI, the kernels with the strongest mapping abilities are retained to transfer as much information as possible with the least number of kernels. Progressive kernel pruning can make use of the characteristic that the model is easy to optimize when kernel pruning in the filter, and it avoids having the model easily fall into local optima when kernel pruning in the layer directly. The experimental results on the CIFAR-10/100 and ImageNet datasets show that compared to the existing CNN model compression methods, the IMSI-based progressive kernel pruning method exhibits better compression performance in processing the model compression tasks that are currently popular. In particular, pruning VGG-16 on CIFAR-10 with our model achieves a compression ratio of 80.8x and an acceleration ratio of 14.8×, which are 5.8× and 4.2× higher than the best results at present, respectively, and the classification accuracy decreases by only 0.59% relative to that of the baseline.