@@ -49,24 +49,24 @@ for (Pattern closed : closedPatterns) {
The following constraints are available in Choco-Mining:
-$CoverSize_{D}(x,f)$ [SchausAG17]: Given an integer variable $f$ that represents the frequency (noted $freq$) of an itemset $x$, the constraint ensures that $f = freq(x)$.
-$CoverClosure_{D}(x)$ [SchausAG17]: The constraint ensures that $x$ is closed w.r.t. the frequency, i.e. $\nexists y \supset x: freq(x) = freq(y)$.
-$AdequateClosure_{D,M}(x)$ [VernereyLAL22]: Given a set of measures $M$, the constraint ensures that $x$ is closed w.r.t. $M$, i.e. $\nexists y \supset x$ such that for all $m \in M : m(x) = m(y)$.
-$FrequentSubs_{D,s}(x)$ [Belaid2BL19]: Given a frequency threshold $s$, the constraint ensures that all the subsets of $x$ are frequent, i.e. $\forall y \subset x : freq(y) \ge s$.
-$InfrequentSupers_{D,s}(x)$ [Belaid2BL19]: Given a frequency threshold $s$, the constraint ensures that all the supersets of $x$ are infrequent, i.e. $\forall y \supset x : freq(y) \lt s$.
-$Generator_{D}(x)$ [BelaidBL19]: The constraint ensures that $x$ is a generator, i.e. $\nexists y \subset x : freq(y) = freq(x)$.
-$ClosedDiversity_{D,\mathcal{H},j,s}(x)$ [HienLALLOZ20]: Given a history of itemsets $\mathcal{H}$, a diversity threshold $j$ and a minimum frequency threshold $s$, the constraint ensures that $x$ is a diverse itemset (i.e. $\nexists y \in \mathcal{H} : jaccard(x,y) \ge j$), $x$ is closed w.r.t. the frequency and $freq(x) \ge s$.
-`CoverSize(x,f)` [SchausAG17]: Given an integer variable `f` that represents the frequency (noted `freq`) of an itemset `x`, the constraint ensures that `f = freq(x)`.
-`CoverClosure(x)` [SchausAG17]: The constraint ensures that `x` is closed w.r.t. the frequency, i.e. there exists no superset `y` of `x` such that `freq(x) = freq(y)`.
-`AdequateClosure(M,x)` [VernereyLAL22]: Given a set of measures `M`, the constraint ensures that `x` is closed w.r.t. `M`, i.e. there exists no superset `y` of `x` such that for each measure `m` in `M`, we have `m(x) = m(y)`.
-`FrequentSubs(s,x)` [Belaid2BL19]: Given a frequency threshold `s`, the constraint ensures that each subset `y` of `x` is frequent, i.e. `freq(y) >= s`.
-`InfrequentSupers(s,x)` [Belaid2BL19]: Given a frequency threshold `s`, the constraint ensures that each superset`y` of `x` is infrequent, i.e. `freq(y) <= s`.
-`Generator(x)` [BelaidBL19]: The constraint ensures that `x` is a generator, i.e. there exists no subset `y` of `x` such that `freq(y) = freq(x)`.
-`ClosedDiversity(H,j,s,x)` [HienLALLOZ20]: Given a history of itemsets `H`, a diversity threshold `j` and a minimum frequency threshold `s`, the constraint ensures that `x` is a diverse itemset (i.e. there exists no itemset `y` in `H` such that `jaccard(x,y) >= j`), `x` is closed w.r.t. the frequency and `freq(x) >= s`.
We can model different problems using these constraints. The above figure shows examples of mining tasks (in blue) with the constraints (in red) involved in their modelling:
- Frequent Itemset Mining: Given a threshold $s$, find all the itemsets $x$ such that $freq(x) \ge s$.
- Closed Itemset Mining: Given a threshold $s$, find all the itemsets $x$ such that $freq(x) \ge s$ and $\nexists y \supset x : freq(x) = freq(y)$.
- Skypattern Mining: Given a set of measures $M$, find all the itemsets $x$ such that there exists no other itemset $y$ that dominates $x$. We say that $y$ dominates $x$ iff $\forall m \in M : m(y) \ge m(x)$ and $\exists m \in M : m(y) \gt m(x)$.
- Maximal Frequent Itemset Mining: Given a threshold $s$, find all the itemsets $x$ such that $freq(x) \ge s$ and $\forall y \supset x : freq(y) \lt s$.
- Minimal Infrequent Itemset Mining: Given a threshold $s$, find all the itemsets $x$ such that $freq(x) \lt s$ and $\forall y \subset x : freq(y) \ge s$.
- Generator Mining: Find all the itemsets $x$ such that $\nexists y \subset x : freq(y) = freq(x)$.
- Association Rule Mining: Find all the association rules $x \Rightarrow y$ that respect the constraints specified by the user.
- Diverse Itemset Mining: Given a diversity threshold $j$ and a minimum frequency threshold $s$, find all the diverse itemsets that are closed w.r.t. the frequency and such that $freq(x) \ge s$.
- Frequent Itemset Mining: Given a threshold `s`, find all the itemsets `x` such that `freq(x) >= s`.
- Closed Itemset Mining: Given a threshold `s`, find all the itemsets `x` such that `freq(x) >= s` and that are closed w.r.t. the frequency.
- Skypattern Mining: Given a set of measures `M`, find all the itemsets `x` such that there exists no other itemset `y` that dominates `x`. We say that `y` dominates `x` iff for each measure `m` in `M` we have `m(y) >= m(y)` and there exists at least one measure `m` in `M` such that `m(y) > m(x)`.
- Maximal Frequent Itemset Mining: Given a threshold `s`, find all the itemsets `x` such that `freq(x) >= s` and for each superset `y` of `x` we have `freq(y) < s`.
- Minimal Infrequent Itemset Mining: Given a threshold `s`, find all the itemsets `x` such that `freq(x) < s` and for each subset `y` of `x` we have `freq(y) >= s`.
- Generator Mining: Find all the itemsets `x` that are generators.
- Association Rule Mining: Find all the association rules `x => y` that respect the constraints specified by the user.
- Diverse Itemset Mining: Given a diversity threshold `j` and a minimum frequency threshold `s`, find all the diverse itemsets that are closed w.r.t. the frequency and such that `freq(x) >= s`.