# Calibrated Q-Matrix-Enhanced Deep Knowledge Tracing with Relational Attention Mechanism
###### Abstract
According to this calibrated Q-matrix, the corresponding knowledge vectors will replace the text representation in the positional attention layer. The smart educational system, which applies the QRAKT model, can provide more personalized exercises due to the fact that the QRAKT model further improves the ability to track the students' knowledge state by incorporating the Q-matrix in the knowledge tracing process. Our experiments were carried out on two real-world datasets and indicated that RAKT and QRAKT performed better than the four baseline models. The general solutions of QRAKT can be seen in Figure 2. In Figure 2, there exist four parts to our paper. The first part is the input part. The student response data include exercise-related information, the corresponding student's responses, and the corresponding knowledge vectors, which will replace the text representation in the positional attention layer. The second part is relation modeling, including exercise relation modeling, time-order forgetting behavior modeling, and student behavior modeling. Exercise relation modeling is developed according to the contingency table, which is calculated from students'performance data and exercise word embedding vectors. Time-order forgetting behavior modeling is used for estimating the students' forgetting behavior by calculating different time intervals between the previous exercises and the current exercise. All time is required to uniformize the time order, which means t1 < t2 < t3<...<t_n. The last modeling is student behavior modeling, which considers the students' interaction behavior, including the guessing factor and slipping factor to trace the students' knowledge state. The third part is two types of attention mechanisms involving the positional attention and relational attention layers. In the positional attention layer, the relative distance, which combines edge vectors, replaces the absolute distance in the traditional attention mechanism to generate the output of this layer. In the relational attention layer, the results of the positional attention layer are applied as the inputs of the relational attention layer. The relational attention mechanism incorporates the relation modeling coefficient, R, with the traditional attention weights to produce the final relational attention weights. The last part is the output part: three outputs are specified, the next interaction result prediction, a description of knowledge state evolution, and a description of the student mastery level. In the next prediction of the interaction result, the QRAKT model will be applied to predict the performance of the next exercise e\({}_{n+1}\) for each student. To illustrate the significance of the QRAKT model compared with two standard knowledge tracing models, the DKT model and the DKT+ model, the evolution of a student's knowledge state in these three models is introduced. It is indicated that the QRAKT model outperformed the other two models. The last output is an illustration of the student's mastery level. Three heat maps were used to estimate the student's mastery level on Skill 49 and indicate that the QRAKT model also performed better than the other two models. The contributions of our paper are as follows:  
* The positional attention layer was utilized to replace the position encoding part with relative distances to capture the connection of each input vector to acquire better prediction results in the KT task. * This paper designed three types of relation modeling, _exercise relation modeling, time-order forgetting behavior modeling_, and _student behavior modeling_. Compared with traditional exercise relation modeling in the EKT model [10], this paper considered the student behaviors such as the forgetting behavior. When considering the traditional student behavior modeling in the EKPT model [5], the Q-matrix is calibrated and the guessing factor and slipping factor are involved in the student behavior modeling to track the students' knowledge state.