Querying Shapes of Histories

We present a shape de nition language, called SDL, for retrieving objects based on shapes contained in the histories associated with these objects. It is a small, yet powerful, language that allows a rich variety of queries about the shapes found in historical time sequences. An interesting feature of SDL is its ability to perform blurry matching. A \blurry" match is one where the user cares about the overall shape but does not care about speci c details. Another important feature of SDL is its e cient implementability. The SDL operators are designed to be greedy to reduce non-determinism, which in turn substantially reduces the amount of back-tracking in the implementation. We give transformation rules for rewriting an SDL expression into a more e cient form as well as an index structure for speeding up the execution of SDL queries. We used SDL to \mine the mined rules" in a data mining application and found that the capability to query the behavior of the mined rules over a period of time led to the discovery of new and interesting information. Current Address: Politecnico di Milano, Italy. Symbol Description lb ub iv fv up slightly increasing transition .05 .19 anyvalue anyvalue Up highly increasing transition .20 1.0 anyvalue anyvalue down slightly decreasing transition -.19 -.05 anyvalue anyvalue Down highly decreasing transition -1.0 -.19 anyvalue anyvalue appears transition from a zero value to a non-zero value 0 1.0 zero nonzero disappears transition from a non-zero value to a zero value -1.0 0 nonzero zero stable the nal value nearly equal to the initial value -.04 .04 anyvalue anyvalue zero both the initial and nal values are zero 0 0 zero zero Table 1: An Illustrative Alphabet A