# Right-Hand Side Expanding Algorithm for Maximal Frequent Itemset Mining
## 2 Right-Hand Side Expanding Algorithm
### Transaction Set Preprocessing
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**1** & **Name of Transaction Set** & _Accidents_ & _Pumsb\_Star_ & _Pumsb_ & _TUMID100K_ & _Kossrak_ \\ \hline
2 & Dimension of transaction set & 468 & 2088 & 2113 & 942 & 41,270 \\
3 & Number of transactions & 340,183 & 49,046 & 49,046 & 100,000 & 990,002 \\
4 & Average transaction length & 33.807892 & 50.482139 & 74.00000 & 39.665070 & 8.099999 \\
5 & Minimum transaction length & 18 & 49 & 74 & 4 & 1 \\
6 & Maximum transaction length & 51 & 63 & 74 & 77 & 2498 \\
7 & Maximum support of item & 0.999966 & 0.790540 & 0.997920 & 0.287380 & 0.607447 \\
8 & Support threshold & 0.500000 & 0.275000 & 0.800000 & 0.025000 & 0.020400 \\
9 & Dimension of transaction set reduced & 24 & 63 & 25 & 545 & 431 \\
10 & Number of transactions reduced & 340,183 & 49,046 & 49,046 & 100,000 & 93.8324 \\
11 & Average transaction length reduced & 18.632792 & 318.01307 & 23.51786 & 35.122340 & 4.815123 \\
12 & Transaction set reduction rate & 0.55137 & 0.630541 & 0.317809 & 0.886814 & 0.563729 \\
13 & Minimum transaction length reduced & 5 & 19 & 11 & 4 & 1 \\
14 & Maximum transaction length reduced & 24 & 42 & 25 & 67 & 398 \\
15 & Pretreatment time (s) & 281.45 & 60.70 & 847939 & 123.93 & 46.331 \\
16 & Algorithm running time (s) & 8530.40 & 245,644.41 & 46,591.14 & 645,86 & 12.64581 \\
17 & Number of MFIs & 216 & 512 & 3145 & 1061 & 1265 \\
18 & Item list of the top MFI & 12 16 17 18 21 27 29 & 170 180 184 188 442 & & & \\  & & 31 43 & 2297 4933 4937 7072 & 4428 430 432 4434 & & & \\
19 & Support of the top MFI & 0.560634 & 0.344207 & 0.820862 & 0.088950 & 0.005552 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Experimental on large size transaction sets. the optimization. However, fewer MFIs were found, so this was contradictory. However, Table 3 shows that the dimensions of transaction sets reduced from the two largest transaction sets were taken as 545 and 431, respectively, and the algorithm running time was also acceptable. The number of transactions in each reduced transaction set and the average length of overall transactions are given in the 10 th and 11 th rows. If the two figures were reduced, the volume of each transaction set was also shrunk. The shrinkage rate (12 th row) was acquired by dividing two figures, where the divisor was the product between the number of transactions in the original transaction set and the average transaction length, and the dividend was the product between the number of transactions in the reduced transaction set and the average transaction length. Although the shrinkage degree of the transaction set was also decided by the given support threshold, individual transactions in each transaction set had different properties, so the shrinkage rate would differ even under the same threshold. The minimum and maximum transaction lengths of reduced transaction sets are given in the 13 th and 14 th rows. The preprocessing time of transaction (15 th row) was the time spent on acquiring a reduced transaction set from the original one, including the time needed to acquire the parameters of the original transaction set, generate files of the reduced transaction set, and establish a memory data matrix. The time(s) needed to mine all MFIs is presented in the 16 th row. Table 3 shows that the number of transactions in the largest transaction set _kosarak_ reached nearly million class, where its original dimension was 41,270. When the dimension was reduced to 431, it took the algorithm less than 4 h to find all MFIs. The quantity of MFIs found was 1265, which, theoretically, was accurate (i.e., the sets were of integrity and uniqueness). Therefore, the standalone big data association rule mining was feasible. If the transaction sets came from practical production and life, the algorithm would be pragmatic. The 17 th-19 th rows list the number of MFIs found, item details in the MFI with the maximum support, and the corresponding support degree, respectively, aiming to facilitate readers in verifying and comparing this information.