Pattern discovery in structural databases with applications to bioinformatics

Frequent structure mining (FSM) aims to discover and extract patterns frequently occurring in structural data such as trees and graphs. FSM finds many applications in bioinformatics, XML processing, Web log analysis, and so on. In this thesis, two new FSM techniques are proposed for finding patterns in unordered labeled trees. Such trees can be used to model evolutionary histories of different species, among others. The first FSM technique finds cousin pairs in the trees. A cousin pair is a pair of nodes sharing the same parent, the same grandparent, or the same great-grandparent, etc. Given a tree T, our algorithm finds all interesting cousin pairs of T in O(|T|2) time where |T| is the number of nodes in T. Experimental results on synthetic data and phylogenies show the scalability and effectiveness of the proposed technique. This technique has been applied to locating co-occurring patterns in multiple evolutionary trees, evaluating the consensus of equally parsimonious trees, and finding kernel trees of groups of phylogenies. The technique is also extended to undirected acyclic graphs (or free trees). The second FSM technique extends traditional MAST (maximum agreement subtree) algorithms by employing the Apriori data mining technique to find frequent agreement subtrees in multiple phylogenies. The correctness and completeness of the new mining algorithm are presented. The method is also extended to unrooted phylogenetic trees. Both FSM techniques studied in the thesis have been implemented into a toolkit, which is fully operational and accessible on the World Wide Web

Enumerating All Maximal Frequent Subtrees

Given a collection of leaf-labeled trees on a common leafset and a fraction f in (1/2,1], a frequent subtree (FST) is a subtree isomorphically included in at least fraction f of the input trees. The well-known maximum agreement subtree (MAST) problem identifies FST with f = 1 and having the largest number of leaves. Apart from its intrinsic interest from the algorithmic perspective, MAST has practical applications as a metric for tree similarity, for computing tree congruence, in detection horizontal gene transfer events and as a consensus approach. Enumerating FSTs extend the MAST problem by denition and reveal additional subtrees not displayed by MAST. This can happen in tow ways - such a subtree is included in majority but not all of the input trees or such a subtree though included in all the input trees, does not have the maximum number of leaves. Further, FSTs can be enumerated on collection o ftrees having partially overlapping leafsets. MAST may not be useful here especially if the common overlap among leafsets is very low. Though very useful, the number of FSTs suffer from combinatorial explosion - just a single enumeration of maximal frequent subtrees (MFSTs). A MFST is a FST that is not a subtree to any othe rFST. the set of MFSTs is a compact non-redundant summary of all FSTs and is much smaller in size. Here we tackle the novel problem of enumerating all MFSTs in collections of phylogenetic trees. We demonstrate its utility in returning larger consensus trees in comparison to MAST. The current implementation is available on the web