Incremental methods for simple problems in time series: algorithms and experiments

A time series (or equivalently a data stream) consists of data arriving in time order. Single or multiple data streams arise in fields including physics, finance, medicine, and music, to name a few. Often the data comes from sensors (in physics and medicine for example) whose data rates continue to improve dramatically as sensor technology improves and as the number of sensors increases. So fast algorithms become ever more critical in order to distill knowledge from the data. This paper presents our recent work regarding the incremental computation of various primitives: windowed correlation, matching pursuit, sparse null space discovery and elastic burst detection. The incremental idea reflects the fact that recent data is more important than older data. Our StatStream system contains an implementation of these algorithms, permitting us to do empirical studies on both simulated and real data.