Is ? monotone, anti-monotone, or non-monotone?
A discriminant rule is a rule of the form {p1, p2,...,pn} ?? {q}, where
the rule consequent contains only a single item. An itemset of size k can
produce up to k discriminant rules. Let ? be the minimum confidence
of all discriminant rules generated from a given itemset:
? is non-monotone. We can show this by comparing ?({A, B}) against
?({A, B, C}).
Since s(A, B, C) ? s(A, B) and max(s(A, B), s(A, C), s(B,C)) ? max(s(A), s(B)),
therefore ?({A, B, C}) can be greater than or less than ?({A, B}).
Hence, the measure is non-monotone.
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