Bio-medical Ontologies Maintenance and Change Management

Substructure Analysis of Metabolic Pathways 245
of the input graph after compression is DL(G|S). SUBDUE’s discovery algorithm
tries to minimize DL(S)+DL(G|S) which represents the description
length of the graph G given the substructure S. The compression of the graph
can be calculated as
Compression = DL(S)+DL(G|S)
DL(G)
where description length DL() is calculated as the number of bits in a
minimal encoding of the graph. Cook and Holder describe the detailed computation
of DL(G) in[5].
The discovery algorithm of SUBDUE is computationally expensive as other
graph-related algorithms. SUBDUE uses two heuristic constraints to maintain
polynomial running time: Beam and Limit. Beam constrains the number
of substructures by limiting the length of the Q ′ in figure 2. Limit is a userdefined
bound on the number of substructures considered by the algorithm.
4.3 Unsupervised Learning
Once the best structure is discovered, the graph can be compressed using
the best substructure. The compression procedure replaces all instances of
the best substructure in the input graph with a pointer, a single vertex, to
the discovered best substructure. The discovery algorithm can be repeated
on this compressed graph for multiple iterations until the graph cannot be
compressed any more or on reaching the user-defined number of iterations.
Each iteration generates a node in a hierarchical, conceptual clustering of the
input data. On the ith iteration, the best substructure Si is used to compress
the input graph, introducing a new vertex labeled Si to the next iteration.
Consequently, any subsequently discovered subgraph Sj canbedefinedin
terms of one or more Si, wherei