Bio-medical Ontologies Maintenance and Change Management

Mining Clinical, Immunological, and Genetic Data 227
represents a sequence of pages that starts from the root, then after 2 seconds
continues with page ’papers.html’ and finally, after 90 seconds ends with page
’kdd.html’. Notice that in this case all itemsets of the sequence are singletons.
Similarly to traditional sequence pattern mining, it is possible to define a
containment relation between annotated sequences:
Definition 5 (τ-containment (�τ)). Given a n-TAS T1 =(s1, α1) and a
m-TAS T2 =(s2, α2) with n ≤ m, and a time threshold τ, we say that T1 is
τ-contained in T2, denoted as T1 �τ T2, if and only if there exists a sequence
of integers 0 ≤ i0 < ... < in ≤ m such that:
1. ∀0≤k≤n. s1,k ⊆ s2,ik
2. ∀1≤k≤n. | α1,k − α∗,k |≤τ
where ∀1≤k≤n. α∗,k = �
ik−1