For that, first of all, we need to show a structure and a unique representation for an extended class of frequent itemsets that are restricted by X and contain an item constraint.
One is that it is found by definition, i.e., the class of frequent itemsets (mathrm{FS}(s_0)) with the threshold (s_{0}) needs to be mined by a well-known algorithm, such as Apriori [1, 23] or Declat [37].
If this is your diagnosis (after a careful examination of your symptoms), your doctor may suggest a higher or more frequent dose of a class of medication called a proton pump inhibitor (such as Prilosec, Nexium, or Prevacid).
For each (Ain {mathcal F}{mathcal S}({s_0,s_1})), we denote ([A]buildrel mathrm{def} over = {Bin {mathcal F}{mathcal S}( {s_0,s_1}): h(B =h(A)}) as the equivalence class of all frequent itemsets having the same closure h(A) and for each ({L} in {mathcal F}{mathcal C}{mathcal S}({s_0,s_1})), we have ({[L]}:= {L^{prime } subseteq L: L^{prime } ne varnothing, h(L^{prime })=L}).
If (s_1 = 1), ({mathcal F}{mathcal S}) is the class of all frequent itemsets in the traditional meaning.
In the worst case, the cardinality of the class of all frequent itemsets is of exponent which leads to many difficulties for users.
First, it is easier to store because its cardinality is much smaller than the size of the class of all frequent itemsets, especially for dense databases.
First, it is easier to store because the number of condensed ones is much smaller than the size of the class of all frequent ones, especially on dense datasets.
Two post-processing approaches For the first algorithm, MFS-PP-EDC1, we first find the class of all frequent itemsets ({A} subseteq C_{11} ), ({A} in {mathcal F}{mathcal S}_{subseteq {C_{11}}}(s_0)), by one of the well-known algorithms such as dEclat or FPGrowth with the consideration of only items belonging to (C_{11} ).
