Quantifying sequential subsumption

Abstract Subsumption is used in knowledge representation and ontology to describe the relationship between concepts. Concept A is subsumed by concept B if the extension of A is always a subset of the extension of B, irrespective of the interpretation. The subsumption relation is also useful in other data analysis tasks such as pattern recognition – for example in image analysis to detect objects in an image, and in spectral data analysis to detect the presence of a reference pattern in a given spectrum. Sometimes the subsumption relation may not be 100% true, so it is useful to quantify this relationship. In this paper we study how to quantify subsumption for sequential patterns. We review existing work on subsumption, give an axiomatic characterisation of subsumption, and present one general approach to quantification in terms of set intersection operation over concept extension. Constructing the concept extension set explicitly is impossible without specifying the domain of discourse and the interpretation. Instead, we focus on concept intension for sequences as patterns and propose to represent concept intension of a sequence by its subsequences. We further consider different types of concept intension set – subsequence set, subsequence multiset, embedding set and embedding set with constraints such as warping and selection. We then present a general algorithmic framework for computing set intersections, and specific algorithms for computing different concept intension sets. We also present an experimental evaluation of these algorithms with regard to their runtime performance.