Generalized weighted tree similarity algorithms for taxonomy trees

Taxonomy trees are used in machine learning, information retrieval, bioinformatics, and multi-agent systems for matching as well as matchmaking in e-business, e-marketplaces, and e-learning. A weighted tree similarity algorithm has been developed earlier which combines matching and missing values between two taxonomy trees. It is shown in this paper that this algorithm has some limitations when the same sub-tree appears at different positions in a pair of trees. In this paper, we introduce a generalized formula to combine matching and missing values. Subsequently, two generalized weighted tree similarity algorithms are proposed. The first algorithm calculates matching and missing values between two taxonomy trees separately and combines them globally. The second algorithm calculates matching and missing values at each level of the two trees and combines them at every level recursively which preserves the structural information between the two trees. The proposed algorithms efficiently use the missing value in similarity computation in order to distinguish among taxonomy trees that have the same matching value but with different miss trees at different positions. A set of synthetic weighted binary trees is generated and computational experiments are carried out that demonstrate the effects of arc weights, matching as well as missing values in a pair