Discovery of Unconventional Patterns for Sequence Analysis: Theory and Algorithms

The pattern discovery task (or equivalently motif inference) is the knowledge discovery process that, given a dataset and some constrains either on the combinatorial pattern structure or on the occurrence lists, returns all the patterns satisfying the given constraints. In this thesis, we consider the problem of discovering patterns in sequential data, such as texts, biological sequences, access logs, etc. When it comes to defining what is a pattern, several classes have been proposed in literature. For example, rigid patterns like p = c◦tc where the don’t care symbol ◦ matches any single character of the input alphabet Σ, or gapped patterns like p = ctt− 2, 3 − tc where the gap represents either a sequence of 2 or 3 don’t cares (we refer to [154] for a thorough discussion of the above classes of patterns). The adjective “unconventional” in the title of this thesis is referred to the unusual combinatorial structure of the patterns we are going to investigate. In fact, while the classic literature of this field focus on string patterns (maybe with wildcards), our line of research explores three different kind of patterns: mask patterns, where each pattern represents a set of string patterns with wildcards, permutation patterns where each pattern is a multiset of characters, and the order of the contained symbols doesn’t matter, and transposons which, roughly speaking, represent the non-conserved regions of a global alignment.