## 4 Data Mining Analysis and Experimental Simulation
### Data Mining (Correlation Analysis)
#### 4.1.1 Modified Jaccard Analysis (MJA)  
As mentioned before, Jaccard analysis measures the similarity between two sets of data. It determines the similarity percentage of the elements of the sets. A and B are two sets, and Jaccard analysis measures the similarity between A and B using the following formula [13]:  
\[\text{J(A,B)}=\left\lvert\text{A}\cap\text{B}\right\rvert/\left\lvert\text{A} \text{UB}\right\rvert\]  
Since our datasets consisted of many features, such GPAU, GPAH, GAT, AT, WS, and QS, we considered each feature as a set, and we measured the similarity. We measured the similarities between GPAU from one side and GPAH, GAT, AT, WS, and QS from the other side. However, our dataset consisted of students' records, so we proposed the concept of MJA, which measures the similarities between the elements of two sets and the same records. For example, it checks the similarity of GPAU and GPAH for the same student. Figure 1 shows the difference between Jaccard analysis and the proposed MJA. For four students, GPAU = {99, 91, 86, 66} and GPAH = {91, 86, 85, 80}. It is clear that the first elements of the two sets belong to one student (one record), the second elements of the two sets belong to another student (one record), and so on.  
Therefore, the result of the traditional Jaccard analysis was approximately 33.34%, as it found two similarities [91, 86] out of six elements [99, 91, 86, 66, 85, 80]. It compared the elements of the two sets regardless of their records. The result of the MJA was 0%, as it checked the similarity of the first elements in the two sets, then the second elements, and so on. In other words, it considered the similarity only if the student's GPAU matched his/her GPAH. Then, we separated the investigation results into two groups, which were scientific colleges, as shown in Table 4, and theoretical colleges, as shown in Table 5. Clearly, Table 4 shows the number of students and the MJA calculation between the GPAU and other scores (which are GPAH, GAT, AT, and QS), and Table 5 also shows the MJA calculation between the GPAU and GPAH, GAT, and WS. The general results of the MJA for scientific colleges  
Figure 1: Illustrates a comparison between Jaccard analysis and MJA.  
in Table 4 show very low similarities, as they do not exceed 9%, and the most similar percentages lay between 3% and 5%. In addition, the MJA results differ from one college to another. The MJA results between GPAU and QS are the highest for 45% of scientific majors such as dentistry, public health and tropical medicine, pharmacy, design and architecture, and business administration. The table also shows that for 27% of majors, such as medicine, nursing, and applied medical sciences, GPAU to GPAH is the best indicator, while GPAU to AT is the best indicator for engineering, computer science and information technology, and science colleges and GPAU to GAT is the best indicator for some other colleges. However, there are some colleges that have the same MJA results for two or more indicators. For instance, the nursing college has the same result for GPAU to GPAH and GPAU to GAT. Moreover, most of the findings also apply to the MJA results for theoretical colleges that appear in Table 5.  
To summarize, the MJA does not show strong relations between student performance at university (GPAU) and the other features. Thus, this study proposes further investigating feature relations using scores behind these features.