Polynomial Time Algorithms for Learning Graph Structured Pattern Languages and its Applications

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During the research period, we focused on several classes of graph-structured patterns which represent structural features common to graph-structured data in real-world databases.The followings are main results of this research.1.In order to represent tree structured patterns such as HTML/XML files, we proposed a new type of tree-structured patterns, called a linear ordered term tree, which consists of ordered tree structures and internal structured variables with distinct variable labels. We showed that several classes of linear ordered term tree languages are polynomial time inductively inferable from positive data.2.A graph is an interval graph if and only if each vertex in the graph can be associated with an interval on the real line such that any two vertices are adjacent in the graph exactly when the corresponding intervals have a nonempty intersection. A number of interesting applications for interval graphs have been found in the literature. We introduced a new interval graph structured pattern, called a linear interval graph pattern, and showed that the class of linear interval graph pattern languages is polynomial time inductively inferable from positive data.3.An outerplanar graph is a planar graph which can be embedded in the plane in such a way that all of vertices lie on the outer boundary. Many chemical compounds are known to be represented by outerplanar graphs. In order to solve a data mining problem of extracting structural features from semi-structured data whose data can be expressed by outerplanar graphs, we introduced a block preserving outerplanar graph pattern (bpo-graph pattern for short) as a new graph pattern having an outerplanar graph structure and structured variables. We presented an incremental polynomial time Apriori-like algorithm for enumerating all frequent bpo-graph patterns with respect to a given finite set of outerplanar graphs.