Time-decaying Representations of Streaming Time Series

During the last years we have witnessed a wealth of research on approximate representations for time series. The vast majority of the proposed approaches represent each value with approximately equal fidelity, which may not be always desirable. For example, mobile devices and real time sensors have brought home the need for representations that can approximate the data with fidelity proportional to its age. We call such time-decaying representations amnesic. In this work, we introduce a novel representation of time series that can represent arbitrary, user-specified time-decaying functions. We propose online algorithms for our representation, and discuss their properties. The algorithms we describe are designed to work on both the entire stream of data, or on a sliding window of the data stream. Finally, we perform an extensive empirical evaluation on £¥¤ datasets, and show that our approach can efficiently maintain a high quality amnesic approximation