## 2 Related Work  
CORrelation ALignment (CORAL) [7] works well by aligning the distribution of the source and target features in an unsupervised manner. However, it only relies on a linear transformation to minimize the squared Frobenius norm distance of the covariances of the source and target features, which will limit flexibility and adaptability. Furthermore, CORAL needs to calculate the second-order statistics (covariances) at first between the source and target data and, after that, transform the source domain to the target domain to align their distributions. Training an extra classifier, such as Support Vector Machine (SVM), is necessary with transformed source domain data and, finally, classifying the target domain dataset. In this slightly tedious process, an external classifier must be involved to obtain the final category, which we call \"not-end-to-end\".  
Deep CORAL [8] has been proposed using Deep Neural Networks (DNNs), which is a kind of nonlinear transformation to extend CORAL. Deep CORAL adds the objective function of basic CORAL to be a part of the total loss function, making full use of the characteristics of DNNs, which can minimize the loss function to align covariances between the source and target domain. Hence, Deep CORAL essentially overcomes the linear transformation dependence of CORAL attributed to the nonlinear characteristics of DNNs. Meanwhile, in order to address the not-end-to-end dilemma, Deep CORAL introduces joint training into neural network to reduce the influence of degenerated features induced by minimizing the CORAL loss alone. Nevertheless, we can still point out several problems existing in Deep CORAL.  
First of all, Deep CORAL is not concerned with the quality of data, which will influence the accuracy. Deep CORAL extracts features of the source and target datasets using AlexNet only. AlexNet [9], designed primarily by [PERSON], is a Convolutional Neural Network (CNN), which became famous in 2012 since the championship with an error rate of 15.3% in the ImageNet Large Scale Visual Recognition Challenge (ILSVRC-2012). However, not all features extracted from convolutional layers can perfectly represent the original data. Our experiments illustrated this point (see Section 4).  
Secondly, according to [8], the AlexNet used by Deep CORAL could project the source and target domain to a single point because Deep CORAL relies on the CORAL loss only. Therefore, joint training with both the classification loss and CORAL loss has been chosen by Deep CORAL to reduce this situation, but the classification loss could result in an offset when Deep CORAL tries to align the distributions of the source and target domain with minimizing CORAL loss.  
Basically, minimizing CORAL loss only may align the second-order statistics of the source and target domain properly. However, if classification loss is added to the CORAL loss, then it will be a redundant term for CORAL, so the alignment will be disturbed because of it. To overcome this problem, we imported the p-norm [10] to further align the distributions and improve the generalization accuracy.  
In this paper, we introduced P-norm Attention Deep CORAL (P-ADC) to address the above challenges. The key insight underlying P-ADC is that we added attention into DNN of Deep CORAL, which not only retained the advantages of AlexNet, but also considered the use of attention to highlight image features, which had the effect of image preprocessing. Meanwhile, our experimental results show that Attention Deep CORAL provided an effective improvement when compared with traditional Deep CORAL. Furthermore, we extended the loss function of Deep CORAL, which included two parts into \(n\in[1,\infty)\) parts, to ease the second challenge mentioned above. The first part of the extended loss function still maintained the original classification loss function, and the rest we introduced contained the p-norm to balance the offset caused by the classification loss.