My question is about the question below. How do you figure out how many overlapp
ID: 3196499 • Letter: M
Question
My question is about the question below.
How do you figure out how many overlapping aggregate cells there are?
The solution says, “In particular, any cell that aggregates over the dimensions 6 to 100 will be counted twice”, why is this? How exactly was this derived.
How will the minimum support affect the number aggregate cells?
Suppose that there are only two base cells, namely (a1, a2, a3, a4, a5, a6, . . . , a100) and (a1, a2, a3, a4, a5, b6, . . . , b100), in a 100-dimensional base cuboid, each with a cell count of 100. Compute the number of nonempty aggregate cells (note that, for example, (a1, a2, a3, . . . , a100) is not considered an aggregate cell).
Solution:
Each base cell generates 2^100 1 aggregate cells. We subtract 1 because (a1, a2, a3, . . . , a100), for example, is not an aggregate cell. Thus, the two base cells generate 2×(2100 1) = 2^101 2 aggregate cells. However, several of these cells are counted twice. In particular, any cell that aggregates over the dimensions 6 to 100 will be counted twice. There is a total of 2^5 = 32 such cells. Therefore, the total number of cells generated is 2^101 34.
Explanation / Answer
Each base cell generates 2^100 1 aggregate cells. We subtract 1 because (a1, a2, a3, . . . , a100), for example, is not an aggregate cell. Thus, the two base cells generate 2×(2100 1) = 2^101 2 aggregate cells. However, several of these cells are counted twice. In particular, any cell that aggregates over the dimensions 6 to 100 will be counted twice. There is a total of 2^5 = 32 such cells. Therefore, the total number of cells generated is 2^101 34.
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