For a course in my Computer Science studies, I have to come up with a set of constraints and a score-definition to find a tiling for frequent itemset mining. The matrix with the data consists of ones and zeroes.
My task is to come up with a set of constraints for the tiling (having a fixed amount of tiles), and a score-function that needs to be maximized. Since I started working out a solution that allows overlapping tiles, I tried to find a score-function to calculate the total "area" of all tiles. Bear in mind that the score function has to be evaluated for every possible solution, so I can't simply go over the total matrix (which contains about 100k elements) and see if it is part of a tile. However, I only took into account overlap between only 2 tiles, and came up with the following:
TotalArea = Sum_a_in_Tiles(Area(a)) - Sum_a/b_in_tiles(Overlap(a,b))
Silly me, I didn't consider a possible overlap between 3 tiles. My question is the following: Is it possible to come up with a generic score-function for n tiles, considering only area per tile and area per overlap between 2 (or more) tiles, and if so, how would I program it?
I could provide some code, but then again it has to be programmed in some obscure language called Comet :(
