## 2 Related Work
### Improved Loss Function-Assisted Fusion of Commodity Features  
To acquire uniform commodity features, we designed a three-channel parallel neural network to extract the features of keyframe images, features, and comments and integrate them. MobileNetV2 was used to extract the images' features, and MLP was used to extract the attributes' features and the comment's features; that is, the text vector obtained in Section 3.2 was inputted into the MLP. The \(l_{\text{text}}\)-dimensional feature vector of text information was obtained by feature extraction. Because the comments and attributes of the commodity are both word-based descriptions, we hoped to retain the different types of information contained in them to a greater extent. Therefore, the algorithm introduced [PERSON]'s correlation coefficient into the network loss function to measure the correlations between comments and attributes. The features of comments were calculated as \(\mathbf{X}_{rcv}=\left\{\mathbf{x}_{rcv1},\mathbf{x}_{rcv2},\ldots,\mathbf{x}_ {rcv2}\right\}\) and the features of the attribute were calculated as \(\mathbf{X}_{pro}=\left\{\mathbf{x}_{pr01},\mathbf{x}_{pr02},\ldots,\mathbf{x}_ {pr02}\right\}\). Then Pearson's correlation coefficient for the comment features and attribute features could be obtained via Formula (3)  
Figure 2: Keyframe stacking and input. The input dimension of MobileNetV2 is \(3\times(m+n)\). where \(Cov\big{(}\mathbf{X}_{rev},\mathbf{X}_{pro}\big{)}\) represents the covariance of \(\mathbf{X}_{rev}\) and \(\mathbf{X}_{pro}\), and  
\(\sigma_{\mathbf{X}_{rev}}=\sqrt{\frac{\sum\limits_{i=1}^{z}(\mathbf{X}_{rev}-E (\mathbf{X}_{rev}))^{2}}{z}}\) and \(\sigma_{\mathbf{X}_{pro}}=\sqrt{\frac{\sum\limits_{i=1}^{z}(\mathbf{X}_{pro}-E (\mathbf{X}_{pre}))^{2}}{z}}\) are the variances of \(\mathbf{X}_{rev}\) and \(\mathbf{X}_{pro}\), respectively. \[Cov\big{(}\mathbf{X}_{rev},\mathbf{X}_{pro}\big{)}=\frac{\sum\limits_{i=1}^{ z}\big{(}\mathbf{X}_{revi}-E(\mathbf{X}_{rev})\big{)}\big{(}\mathbf{X}_{proi}-E \big{(}\mathbf{X}_{pro}\big{)}\big{)}}{z} \tag{4}\]  
where \(E(\mathbf{X}_{rev})=\frac{\sum\limits_{i=1}^{z}\mathbf{X}_{revi}}{z}\) is the expectation of \(\mathbf{X}_{rev}\) and \(E\big{(}\mathbf{X}_{pro})=\frac{\sum\limits_{i=1}^{z}\mathbf{x}_{pri}}{z}\) is the expectation of \(\mathbf{X}_{pro}\). The loss function combining the cross-entropy and Pearson's correlation coefficient is defined by Formula (5)  
\[L=-\frac{1}{N}\underset{i}{\sum}\sum\limits_{c=1}^{M}y_{ic}\log(p_{ic})+\sqrt{ \rho_{\mathbf{X}_{rev}}{\mathbf{x}_{pro}}^{2}}\]  
\[=-\frac{1}{N}\underset{i}{\sum}\sum\limits_{c=1}^{M}y_{ic}\log(p_{ic})+\sqrt{ \left(\frac{\sum\limits_{i=1}^{z}(\mathbf{X}_{revi}-E(\mathbf{X}_{rev})) \big{(}\mathbf{X}_{proi}-E\big{(}\mathbf{X}_{pro}\big{)}\big{)}}{\sqrt{\sum \limits_{i=1}^{z}(\mathbf{X}_{rev}-E(\mathbf{X}_{rev}))^{2}}\sqrt{\sum \limits_{i=1}^{z}(\mathbf{X}_{pro}-E\big{(}\mathbf{X}_{pro}\big{)})^{2}}} \right)^{2}} \tag{5}\]  
where \(N\) is the total number of samples, \(M\) is the number of categories, and \(y_{ic}\) is the symbolic item, which has a value of 0 or 1. When the true category of sample \(i\) is \(c\), this took 1; otherwise, 0 was taken. \(p_{ic}\) represents the probability that sample \(i\) belongs to category \(c\). When \(L\) decreases gradually, \(\rho_{\mathbf{X}_{rev}}{\mathbf{x}_{pro}}\) also decreases, which means that the attributes and comments become increasingly irrelevant. The purpose of this approach is to preserve more diversified features within them and enrich the features after fusion.