Abstract-In this paper, we aim at learning compact and discriminative linear regression models. Linear regression has been widely used in different problems. However, most of the existing linear regression methods exploit the conventional zeroone matrix as the regression targets, which greatly narrows the flexibility of the regression model. Another major limitation of theses methods is that the learned projection matrix fails to precisely project the image features to the target space due to their weak discriminative capability. To this end, we present an elastic-net regularized linear regression (ENLR) framework, and develop two robust linear regression models which possess the following special characteristics. First, our methods exploit two particular strategies to enlarge the margins of different classes by relaxing the strict binary targets into a more feasible variable matrix. Second, a robust elastic-net regularization of singular values is introduced to enhance the compactness and effectiveness of the learned projection matrix. Third, the resulting optimization problem of ENLR has a closed-form solution in each iteration, which can be solved efficiently. Finally, rather than directly exploiting the projection matrix for recognition, our methods employ the transformed features as the new discriminate representations to make final image classification. Compared with the traditional linear regression model and some of its variants, our method is much more accurate in image classification. Extensive experiments conducted on publicly available datasets well demonstrate that the proposed framework can outperform the state-of-the-art methods. The MATLAB codes of our methods can be available at http://www.yongxu.org/lunwen.html.

Linear regression (LR) and some of its variants have been widely used for classification problems. Most of these methods assume that during the learning phase, the training samples can be exactly transformed into a strict binary label matrix, which has too little freedom to fit the labels adequately. To address this problem, in this paper, we propose a novel regularized label relaxation LR method, which has the following notable characteristics. First, the proposed method relaxes the strict binary label matrix into a slack variable matrix by introducing a nonnegative label relaxation matrix into LR, which provides more freedom to fit the labels and simultaneously enlarges the margins between different classes as much as possible. Second, the proposed method constructs the class compactness graph based on manifold learning and uses it as the regularization item to avoid the problem of overfitting. The class compactness graph is used to ensure that the samples sharing the same labels can be kept close after they are transformed. Two different algorithms, which are, respectively, based on -norm and -norm loss functions are devised. These two algorithms have compact closed-form solutions in each iteration so that they are easily implemented. Extensive experiments show that these two algorithms outperform the state-of-the-art algorithms in terms of the classification accuracy and running time.

Though widely used in image classification, convolutional neural networks (CNNs) are prone to noise interruptions, i.e. the CNN output can be drastically changed by small image noise. To improve the noise robustness, we try to integrate CNNs with wavelet by replacing the common down-sampling (maxpooling, strided-convolution, and average pooling) with discrete wavelet transform (DWT). We firstly propose general DWT and inverse DWT (IDWT) layers applicable to various orthogonal and biorthogonal discrete wavelets like Haar, Daubechies, and Cohen, etc., and then design wavelet integrated CNNs (WaveCNets) by integrating DWT into the commonly used CNNs (VGG, ResNets, and DenseNet). During the down-sampling, WaveCNets apply DWT to decompose the feature maps into the low-frequency and high-frequency components. Containing the main information including the basic object structures, the low-frequency component is transmitted into the following layers to generate robust high-level features. The high-frequency components are dropped to remove most of the data noises. The experimental results show that WaveCNets achieve higher accuracy on ImageNet than various vanilla CNNs. We have also tested the performance of WaveCNets on the noisy version of ImageNet, ImageNet-C and six adversarial attacks, the results suggest that the proposed DWT/IDWT layers could provide better noise-robustness and adversarial robustness. When applying WaveCNets as backbones, the performance of object detectors (i.e., faster R-CNN and RetinaNet) on COCO detection dataset are consistently improved. We believe that suppression of aliasing effect, i.e. separation of low frequency and high frequency information, is the main advantages of our approach. The code of our DWT/IDWT layer and different WaveCNets are available at https://github.com/CVI-SZU/WaveCNet.

A common intrinsic limitation of the traditional subspace learning methods is the sensitivity to the outliers and the image variations of the object since they use the norm as the metric. In this paper, a series of methods based on the -norm are proposed for linear dimensionality reduction. Since the -norm based objective function is robust to the image variations, the proposed algorithms can perform robust image feature extraction for classification. We use different ideas to design different algorithms and obtain a unified rotational invariant (RI) dimensionality reduction framework, which extends the well-known graph embedding algorithm framework to a more generalized form. We provide the comprehensive analyses to show the essential properties of the proposed algorithm framework. This paper indicates that the optimization problems have global optimal solutions when all the orthogonal projections of the data space are computed and used. Experimental results on popular image datasets indicate that the proposed RI dimensionality reduction algorithms can obtain competitive performance compared with the previous norm based subspace learning algorithms.