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In frequent itemset generation of association rule mining, what is the fundamental difference between maximal & closed patterns itemsets. Can someone guide me a resource about them?
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Mining maximal patterns can be viewed as finding a border through the search space tree such that all the nodes below the border are infrequent and all the nodes above the border are frequent.
By definition, An itemset is maximal frequent if none of its immediate supersets is frequent. An itemset is closed if none of its immediate supersets has the same support as the itemset .
Closed frequent itemsets are more widely used than maximal frequent itemset because when efficiency is more important that space, they provide us with the support of the subsets so no additional pass is needed to find this information.
An association rule has two parts: an antecedent (if) and a consequent (then). An antecedent is an item found within the data. A consequent is an item found in combination with the antecedent.
From this original source:
A closed pattern is a frequent pattern. So it meets the minimum support criteria. In addition to that, all super-patterns of a closed pattern are less frequent than the closed pattern.
Let’s see some examples.
Suppose, the minimum support count is 2. For the first example, suppose there are a total of 3 items: a, b, c. Suppose a pattern ab has support count of 2 and a pattern abc has support count of 2. Is the pattern ab is a closed pattern? Pattern ab is a frequent pattern, but it has a super-pattern that is NOT less frequent than ab.
For the second example,
suppose there are a total of 3 items: x, y, z. suppose a pattern xy has support count of 3 and a pattern xyz has support count of 2. Is the pattern xy is a closed pattern? Pattern xy is a frequent pattern and also the only super-pattern xyz is less frequent than xy.
Therefore, xy is a closed pattern.
A max pattern is
a frequent pattern. So it also meets the minimum support criteria like closed pattern In addition, but unlike closed pattern, all super-patterns of a max pattern are NOT frequent patterns.
Let’s see some examples as well.
Suppose, the minimum support count is 2. Like before, for the first example, suppose there are a total of 3 items: a, b, c. Suppose a pattern ab has support count of 3 and a pattern abc has support count of 2. Is the pattern ab is a max pattern? Pattern ab is a frequent pattern, but it has a super-pattern that is a frequent pattern as well. So, pattern ab is NOT a max pattern.
For the second example,
suppose there are a total of 3 items: x, y, z. Suppose a pattern xy has support count of 3 and a pattern xyz has support count of 1. Is the pattern xy is a max pattern? Pattern xy is a frequent pattern and also the only super-pattern xyz is NOT a frequent pattern. Therefore, xy is a max pattern.
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