the original terminology of Srikant et al, but rather exploit the vocabulary of Formal Concept Analysis(FCA)(Wille(1982)), as it better fits with the formal folksonomy model introduced in Definition 1.14 Definition 2. A formal contert is a dataset K: =(G, M, I) consisting of a set G of objects, a set M of attributes, and a binary relation ICGxM, where (9,m)∈ i is read as“ object g has attribute m In the usual basket analysis scenario, M is the set of items sold by a supermar- ket, G is the set of all transactions, and, for a given transaction g E G, the set g:=mE MI(g, m)E] contains all items bought in that transaction Definition 3. For a set X of attributes, we define A': =I9 EG Vm E X: (9, m)EI. The support of A is calculated by supp(A) Definition 4(Association Rule Mining Problem(Agrawal et al (1993). Let K be a formal context, and minsupp, minconf E [0, 1, called minimum support and minimum confidence thresholds, resp. The association rule mining problem consists now of determining all pairs A - B of subsets of M whose support supp(A -B): supp(A U B) is above the thresh- old minsupp, and whose confidence conf(A-B): =sspp is above the threshold minc As the rules A-B and A-B A carry the same information, and in particular have same support and same confidence, we will consider in this paper the additional constraint prevalent in the data mining community, that premise A and conclusion B are to be disjoint When comparing Definitions 1 and 2, we observe that association rules annot be mined directly on folksonomies, because of their triadic nature. One either has to define some kind of triadic association rules, or to transform the triadic folksonomy into a dyadic formal context. In this paper, we follow the latter approach 4 Projecting the Folksonomy onto two Dimensions As discussed in the previous section, we have to reduce the three-dimensional folksonomy to a two-dimensional formal context before we can apply any as sociation rule mining technique. Several such projections have already been introduced in Lehmann and Wille(1995 ). In Stumme(2005), we provide a more complete approach, which we will slightly adapt to the association rule For a detailed discussion about the role of FCa for association rule mining see In contrast, in FCA, one often requires A to be a subset of B, as this fits better with the notion of closed itemsets which arose of applying FCa to the association mining problem(Pasquier et al.(1999), Zaki and Hsiao(1999), Stumme(1999)) 5the original terminology of Srikant et al, but rather exploit the vocabulary of Formal Concept Analysis (FCA) (Wille (1982)), as it better fits with the formal folksonomy model introduced in Definition 1.14 Definition 2. A formal context is a dataset K := (G, M, I) consisting of a set G of objects, a set M of attributes, and a binary relation I ⊆ G × M, where (g, m) ∈ I is read as “object g has attribute m”. In the usual basket analysis scenario, M is the set of items sold by a supermar￾ket, G is the set of all transactions, and, for a given transaction g ∈ G, the set g I := {m ∈ M|(g, m) ∈ I} contains all items bought in that transaction. Definition 3. For a set X of attributes, we define A′ := {g ∈ G | ∀m ∈ X: (g, m) ∈ I}. The support of A is calculated by supp(A) := |A ′ | |G| . Definition 4 (Association Rule Mining Problem (Agrawal et al. (1993))). Let K be a formal context, and minsupp, minconf ∈ [0, 1], called minimum support and minimum confidence thresholds, resp. The association rule mining problem consists now of determining all pairs A → B of subsets of M whose support supp(A → B) := supp(A ∪ B) is above the thresh￾old minsupp, and whose confidence conf(A → B) := supp(A∪B) supp(A) is above the threshold minconf. As the rules A → B and A → B \ A carry the same information, and in particular have same support and same confidence, we will consider in this paper the additional constraint prevalent in the data mining community, that premise A and conclusion B are to be disjoint.15 When comparing Definitions 1 and 2, we observe that association rules cannot be mined directly on folksonomies, because of their triadic nature. One either has to define some kind of triadic association rules, or to transform the triadic folksonomy into a dyadic formal context. In this paper, we follow the latter approach. 4 Projecting the Folksonomy onto two Dimensions As discussed in the previous section, we have to reduce the three-dimensional folksonomy to a two-dimensional formal context before we can apply any as￾sociation rule mining technique. Several such projections have already been introduced in Lehmann and Wille (1995). In Stumme (2005), we provide a more complete approach, which we will slightly adapt to the association rule mining scenario. 14 For a detailed discussion about the role of FCA for association rule mining see (Stumme (2002)). 15 In contrast, in FCA, one often requires A to be a subset of B, as this fits better with the notion of closed itemsets which arose of applying FCA to the association mining problem (Pasquier et al. (1999), Zaki and Hsiao (1999), Stumme (1999)). 5