## 3 Methods
### Prediction and Recommendation of Job Scores Based on BPTF  
In recent years, some scholars have used tensor decomposition methods for recommendation research [36; 37; 38]. The theoretical basis of three-dimensional tensor decomposition comes from the decomposition of two-dimensional matrices. The matrix factorization (MF) and probabilistic matrix factorization (PMF) utilize users' historical ratings on items to predict unknown and missing user ratings, considering user \(u_{i}\) rating of item \(v_{i}\) as \(R_{i,j}\). The rating matrix \(R\in R_{M\times N}\) is a sparse matrix, which represents the partial ratings of \(M\) users on \(N\) items. At this time, the task of matrix decomposition is to rely on these existing ratings to predict unknown ratings. The PMF model learns by maximizing the posterior probability of the latent matrices \(U\) and \(V\), which is equivalent to minimizing the decomposition error of the sum of squares using a quadratic regularizer [39]. Although PMF is one of the very famous collaborative filtering-based methods, it still has some limitations. For example, PMF assumes that user vectors and item vectors are independent and equally distributed and does not consider users' different browsing habits and implicit factors that are not caused by users but affect the scoring results [40]. This paper focuses on improving the accuracy of the user's prediction of recruitment alternatives and ultimately improving personalized recommendations by extending the PMF model to include the user's different browsing habits and attention characteristics focused on different recruitment items. In order to extend the PMF model to tensor decomposition and consider the effect of the user's attention level when browsing recruitment items, this section introduces the attention-level feature proposed in the previous subsection as an additional factor. The user \(u_{i}\) gives the rating \(R_{ij,k}\) to the recruitment item \(v_{j}\) under the attention level \(a_{k}\). Therefore, the original two-dimensional matrix of ratings can be expanded into a three-dimensional tensor \(R\in\mathbb{R}^{M\times N\times K}\), whose three dimensions correspond to users, recruiting items, and attention-level categories, and the sizes are \(M\), \(N\), and \(K\), respectively. The inner product of these three related factors can be expressed as follows:  
\[R_{ij}^{k}=\sum_{d=1}^{D}U_{di}V_{dj}A_{dk} \tag{9}\]  
where \(D\) is the total number of ratings by users \(U_{i}\) on recruitment items \(V_{j}\), \(R_{i,j}^{k}\) is user \(U_{i}\) rating on recruitment item \(V_{j}\), and \(A_{k}\) is the additional factor of attention level. This matrix decomposition means that users' ratings of items are characterized by three factors, namely, user preferences (matrix \(U\)), item features (matrix \(V\)), and attention levels of users' browsing behavior (matrix \(A\)). This means that the scores in this tensor not only depend on the similarity between user preference habits and recruitment items but also depend on the different attention levels of the same user. Tensor factorization is achieved by using Candecomp/Parafic (CP) to decompose the vector representations (i.e., the rows in the matrix) of job-seeking users, recruiting items, and attention-level matrices to compute the best approximation of the scores. The product of tensors is expressed as Equation (10):  
\[R\approx\sum_{i=1}^{r}u_{i}\otimes v_{i}\otimes a_{i} \tag{10}\]  
where \(R\) is the tensor of user ratings, \(u_{i}\in R^{M},v_{i}\in R^{N}\) and \(a_{i}\in R^{K}\) represent the i row vector of \(U\), \(V\), and \(A\) respectively, and \(\otimes\) is the outer product of the vectors. Under this definition, the following example is used to explain the above calculation: When two A and [PERSON] with similar job selection preferences face a similar job, [PERSON] carefully read the relevant content of the recruitment and carefully thought about his suitability for the job and the possibility of being hired.