Level 2 Candidate Generation

In regular Apriori candidate itemsets of size two are generated by combining each pair of frequent itemsets of size one. Combining itemsets of size one is a simple matter since each pair results in a valid candidate. The same is true for Apriori Sets And Sequences. The difference is that for each pair of event items there exists thirteen different itemsets that represent the different temporal relationships those two event items can have together. Figure 4 illustrates these relationships.

Figure 4: 13 Temporal Relationships

The resulting relative times for the two events are shown in Table 1. These times correspond to the temporal relationships illustrated in Figure 4 reading left to right.

Table 1: 13 Relative Times

Event 1		Event 2
begin	end	begin	end
0	1	1	2
1	2	0	1
0	1	2	3
2	3	0	1
0	2	1	3
1	3	0	2
0	1	0	1
0	2	0	1
0	1	0	2
0	3	1	2
1	2	0	3
0	2	1	2
1	2	0	2

This is a very important issue when mining for complex temporal relationships. The search space in this problem is much larger than regular Apriori and every effort must be made to make it efficient as possible to obtain results in a reasonable amount of time.