Given that I have a 'pile' of items that need to be split in groups, and given that I can express how much these items differ, relative to eachother, in a number, a score if you will, how would I separate this input into meaningful groups?
I recognise that this is a bit of an abstract question, so to try and make it clearer here is what I have tried so far:
I have tried representing the input as a weighted graph in which every vertex is connected to every other vertex, with the 'strength' of the edge being their relative score. Then I'd take the longest edge of the graph, and separate every other vertex by 'closeness' to the vertices at the end of that longest edge. This works reasonably well, but has the disadvantage of always yielding two groups for a result, which might not necessarily be logical.
For example: say I can express the differentness of fruits in a number. Then given a pile of apples, the different brand of apples would form different categories, like Elstar, Jonagold, what have you... But when I'd have a pile consisting of apples, pears, and oranges, then the apples would be relatively similar and should fall into the same category.
I'm guessing I'd have to remove every edge of the graph bigger than the mean plus the standard deviation or something like that, and then see how many disjointed subgraphs appear, but I'd like to hear the approach of someone with more mathematical knowledge than me.