Finding Novel Event Relationships in Temporal Data

A path formula of the form "A is followed by B in t time units" – where A and B can themselves be path formulas – is a common syntactical construct in a variety of temporal logic paradigms. We study the problem of mining for such formulas that frequently occur in time-series data in a manner that enables the discovery of complex relationships. This paper introduces a semantics that resembles categorical time series data, a syntax for such formulas that are annotated by the support for which such relationships occur in a time series, and provide algorithms that are capable of mining these relationships. We present several properties of this framework – both exploring worst case scenarios and presenting correct pruning techniques for our mining algorithms. The approach is then demonstrated with an implementation where we mine such relationships from two real-world datasets.