A dichotomic search algorithm for mining and learning in domain-specific logics

Many application domains make use of specific data structures such as sequences and graphs to represent knowledge. These data structures are ill-fitted to the standard representations used in machine learning and data-mining algorithms: propositional representations are not expressive enough, and first order ones are not efficient enough. In order to efficiently represent and reason on these data structures, and the complex patterns that are related to them, we use domain-specific logics. We show these logics can be built by the composition of logical components that model elementary data structures. The standard strategies of top-down and bottom-up search are ill-suited to some of these logics, and lack flexibility. We therefore introduce a dichotomic search strategy, that is analogous to a dichotomic search in an ordered array. We prove this provides more flexibility in the search, while retaining completeness and non-redundancy. We present a novel algorithm for learning using domain specific logics and dichotomic search, and analyse its complexity. We also describe two applications which illustrates the search for motifs in sequences; where these motifs have arbitrary length and length-constrained gaps. In the first application sequences represent the trains of the East-West challenge; in the second application they represent the secondary structure of Yeast proteins for the discrimination of their biological functions.