Temporal similarity by measuring possibilistic uncertainty in CBR

Similarity is an essential concept in case-based reasoning (CBR). In domains in which time plays a relevant role, CBR systems require good temporal similarity measures to compare cases. Temporal cases are traditionally represented by a set of temporal features, defining time series and temporal event sequences. In the particular situation where these features are not homogeneous (i.e. combination of qualitative and quantitative information), systems find difficulties in performing the CBR cycle. Furthermore, temporal similarity measures cannot directly apply the efficient time series techniques, requiring new approaches to deal with these heterogeneous sequences. To this end, recent proposals are focused on direct matching between pairs of features within sequences, mainly based on classical distances. However, three limitations to the traditional approaches have been identified: (1) they do not consider the implicit temporal relations amongst all features of the sequence (ignoring a large amount of temporal information); (2) they ignore the uncertainty produced in any process of analogy; (3) they are designed to compare pairs of sequences, limiting their use to basic aspects of the Retrieval step of CBR (no benefits on other CBR steps). Temporal constraint networks have proved to be useful tools for temporal representation and reasoning, and can be easily extended to manage imprecision and uncertainty. An approach to solve similarity problems could be the transformation of these heterogeneous sequences into uncertain temporal relations, obtaining a temporal constraint network. The overall uncertainty of this network can be considered as an effective indicator of the sequences similarity. Therefore, this paper proposes a non-classical approach to measure temporal similarity of cases which are heterogeneous temporal event sequences. Given two or more sequences, the temporal similarity is measured by describing a unique temporal scenario of possibilistic temporal relations and calculating the uncertainty produced.