Bio-medical Ontologies Maintenance and Change Management

244 C.h. You, L.B. Holder, and D.J. Cook
Subdue(graph G, beam B, limit L)
Q = {v | v is a vertex in G with a unique label}
bestSub = first substructure in Q
repeat
foreach substructure S ∈ Q do
add Extend(S) intoextSubs
foreach newSub ∈ extSubs do
Evaluate(newSub)
add newSub in Q ′ (length L
return bestSub
Extend(S): extend Sub. S by one edge in all possible ways
Evaluate(S): evaluate Sub. S using MDL
Fig. 2. SUBDUE’s discovery algorithm
and limit value. The beam length limits the length of the queue which contains
extended substructures, and the limit value restricts the total number
of substructures considered by the algorithm. The initial state of the search
is the set of substructures representing each uniquely labeled vertex and their
instances. The Extend(S) function extends each instance of a substructure in
the Q in all possible ways by adding a single edge and a vertex, or by adding
a single edge if both vertices are already in the substructure. The substructures
in the Q ′ are ordered base on their ability to compress the input graph
as evaluated by Evaluate(S), using the minimum description length (MDL)
principle. This search (repeat loop) terminates when the number of substructures
considered reaches the limit value, or the algorithm exhausts the search
space. Then it returns the best substructure.
SUBDUE can be given background knowledge in the form of predefined
substructures. SUBDUE finds the instances of these substructures and compresses
them. Using this approach, we can verify whether the patterns learned
from a graph belong to another graph.
4.2 MDL and Heuristic Methods
The discovery algorithm of SUBDUE fundamentally is guided by the
minimum description length principle. The heuristic evaluation by the MDL
principle assumes that the best substructure is the one that minimizes the
description length of the input graph when compressed by the substructure
[5]. The description length of the substructure S is represented by DL(S), the
description length of the input graph is DL(G), and the description length