## 3 Recommended Architecture for Industrial Software Service Components
### FM-Based Models for Service Recommendation
#### 4.2.3 Explicit and Implicit Higher-Order Feature Interactions  
DNNs are good at learning higher-order interactions between features; however, a DNN is a kind of implicit feature interaction which is learned at a bit-wise level, and its interpretability is not high. Thus, we designed a higher-order explicit cross-feature Compressed Interaction Network (CIN) and combined it with the DNN to form a combination of explicit and implicit higher-order interactions. These mainly consists of two components, namely, the CIN component and the DNN component; the computation of each layer of the CIN network based on the fixed formulas is defined as follows:  
\[\mathbf{X}_{h,*}^{  
where \(i\in[1,H_{k}]\), the pooling vector is \(\mathbf{p}^{k}=\left[p_{1}^{k},p_{2}^{k},\ldots,p_{H_{k}}^{k}\right]\), the length of the \(k\)th hidden layer is \(H_{k}\), and the pooled vectors from each layer are spliced to obtain the output of the final CIN: \(\mathbf{p}^{+}=\left[\mathbf{p}^{1},\mathbf{p}^{2},\ldots,\mathbf{p}^{T} \right]\in\mathbb{R}^{\sum_{i=1}^{T}H_{i}}\).  
As mentioned earlier, xDeepFM complements both CIN and DNN, including both explicit and implicit higher-order interactions while adding linear components; the final model output equation is  
\[\hat{y}=sigmoid\left(\mathbf{w}_{\text{linear}}^{T}\ \mathbf{a}+\mathbf{w}_{ dnn}^{T}\mathbf{x}_{dnn}^{k}+\mathbf{w}_{\text{cin}}^{T}\ \mathbf{p}^{+}+b\right), \tag{8}\]  
where \(\mathbf{a}\) represents the original features \(\mathbf{x}_{dnn}^{k}\), \(\mathbf{p}^{+}\) denotes the respective results yielded by the DNN and CIN, respectively, and \(\mathbf{w}_{*}\) and \(b\) are the learnable parameters. Explicit and Implicit Higher-Order Feature Interactions and Attention Factorization Machine for Service Component Recommendation  
In order to simultaneously learn nonlinear explicit and implicit high-order feature interactions and measure the varying importance of feature interactions, we propose a novel model structure, EIAFM, which employs a compressed interaction network to capture explicit higher-order feature interactions, a deep neural network to extract valuable information from implicit higher-order feature interactions, and attention weights to measure the contributions of cross-features to prediction results, thereby enhancing model interpretability. From a mathematical perspective, the EIAFM model formula is derived by incorporating two additional nonlinear functions onto the foundational Formula (5):  
\[\hat{y}_{EIAFM}(\mathbf{x})=w_{0}+\sum_{i=1}^{n}w_{i}x_{i}+g(\mathbf{x})+f( \mathbf{x}) \tag{9}\]  
Here, the first and second terms are nonlinear components similar to the FM, the third captures the explicit higher-order component, the fourth captures the implicit higher-order component, and the fifth is the interaction of different attention scores for second-order features. In this paper, these four components are referred to as the linear component, implicit component, explicit component, and attention component. Equation (9) can be interpreted as follows:  
\[\hat{y}_{EIAFM}(\mathbf{x})=\hat{y}_{LC}(\mathbf{x})+\hat{y}_{EC}(\mathbf{x}) +\hat{y}_{IC}(\mathbf{x})+\hat{y}_{AC}(\mathbf{x}) \tag{10}\]  
\[where\left\{ \begin{aligned} \hat{y}_{LC}(\mathbf{x})&=w_{0}+ \sum_{i=1}^{n}w_{i}x_{i}\\ \hat{y}_{EC}(\mathbf{x})&=g(\mathbf{x})\\ \hat{y}_{IC}(\mathbf{x})&=f(\mathbf{x})\\ \hat{y}_{AC}(\mathbf{x})&=\mathbf{p}^{T}\sum_{i=1}^{ n}\sum_{j=i+1}^{n}a_{ij}(\mathbf{v}_{i}\odot\mathbf{v}_{j})x_{i}x_{j}\end{aligned} \right. \tag{11}\]  
Figure 1 presents a visual depiction of the EIAFM model proposed in this article. The input and embedding layers are identical to those in the FM model, with sparse vector representations of the input features which are then mapped and embedded into dense vectors, and the model parameters of the linear components are \(\Theta_{LC}=\left\{w_{0},\left\{w_{i}\right\}_{i=1}^{n}\right\}\).