Mostafa Haghir Chehreghani

Efficiently Mining Unordered Trees

Frequent tree patterns have many applications in different domains such as XML document mining, user web log analysis, network routing and bioinformatics. In this paper, we first introduce three new tree encodings and accordingly present an efficient algorithm for finding frequent patterns from rooted unordered trees with the assumption that children of every node in database trees are identically labeled. Then, we generalize the method and propose the UITree algorithm to find frequent patterns from rooted unordered trees without any restriction. Compared to other algorithms in the literature, UItree manages occurrences of a candidate tree in database trees more efficiently. Our extensive experiments on both real and synthetic datasets show that UITree significantly outperforms the most efficient existing works on mining unordered trees.

An efficient algorithm for approximate betweenness centrality computation

Betweenness centrality is an important centrality measure widely used in social network analysis, route planning etc. However, even for mid-size networks, it is practically intractable to compute exact betweenness scores. In this paper, we propose a generic randomized framework for unbiased approximation of betweenness centrality. The proposed framework can be adapted with different sampling techniques and give diverse methods. We discuss the conditions a promising sampling technique should satisfy to minimize the approximation error and present a sampling method partially satisfying the conditions. We perform extensive experiments and show the high efficiency and accuracy of the proposed method.

Effective co-betweenness centrality computation

Betweenness centrality of vertices is essential in the analysis of social and information networks, and co-betweenness centrality is one of two natural ways to extend it to sets of vertices. Existing algorithms for co-betweenness centrality computation suffer from at least one of the following problems: i) their applicability is limited to special cases like sequences, sets of size two, and ii) they are not efficient in terms of time complexity. In this paper, we present efficient algorithms for co-betweenness centrality computation of any set or sequence of vertices in weighted and unweighted networks. We also develop effective methods for co-betweenness centrality computation of sets and sequences of edges. These results provide a clear and extensive view about the complexity of co-betweenness centrality computation for vertices and edges in weighted and un-weighted networks. Finally, we perform extensive experiments on real-world networks from different domains including social, information and communication networks, to show the empirical efficiency of the proposed methods.

Mining rooted ordered trees under subtree homeomorphism

Mining frequent tree patterns has many applications in different areas such as XML data, bioinformatics and World Wide Web. The crucial step in frequent pattern mining is frequency counting, which involves a matching operator to find occurrences (instances) of a tree pattern in a given collection of trees. A widely used matching operator for tree-structured data is subtree homeomorphism, where an edge in the tree pattern is mapped onto an ancestor-descendant relationship in the given tree. Tree patterns that are frequent under subtree homeomorphism are usually called embedded patterns. In this paper, we present an efficient algorithm for subtree homeomorphism with application to frequent pattern mining. We propose a compact data-structure, called occ, which stores only information about the rightmost paths of occurrences and hence can encode and represent several occurrences of a tree pattern. We then define efficient join operations on the occ data-structure, which help us count occurrences of tree patterns according to occurrences of their proper subtrees. Based on the proposed subtree homeomorphism method, we develop an effective pattern mining algorithm, called TPMiner. We evaluate the efficiency of TPMiner on several real-world and synthetic datasets. Our extensive experiments confirm that TPMiner always outperforms well-known existing algorithms, and in several cases the improvement with respect to existing algorithms is significant.

Transactional Tree Mining

In the transactional setting of finding frequent embedded patterns from a large collection of tree-structured data, the crucial step is to decide whether a tree pattern is subtree homeomorphic to a database tree. Our extensive study on the properties of real-world tree-structured datasets reveals that while many vertices in a database tree may have the same label, no two vertices on the same path are identically labeled. In this paper, we exploit this property and propose a novel and efficient method for deciding whether a tree pattern is subtree homeomorphic to a database tree. Our algorithm is based on a compact data-structure, called EMET, that stores all information required for subtree homeomorphism. We propose an efficient algorithm to generate EMETs of larger patterns using EMETs of the smaller ones. Based on the proposed subtree homeomorphism method, we introduce TTM, an effective algorithm for finding frequent tree patterns from rooted ordered trees. We evaluate the efficiency of TTM on several real-world and synthetic datasets and show that it outperforms well-known existing algorithms by an order of magnitude.