In many emerging applications, data streams are monitored in a network environment. Due to limited communication bandwidth and other resource constraints, a critical and practical demand is to online compress data streams continuously with quality guarantee. Although many data compression and digital signal processing methods have been developed to reduce data volume, their super-linear time and more-than-constant space complexity prevents them from being applied directly on data streams, particularly over resource-constrained sensor networks. In this paper, we tackle the problem of online quality guaranteed compression of data streams using fast linear approximation (i.e., using line segments to approximate a time series). Technically, we address two versions of the problem which explore quality guarantees in different forms. We develop online algorithms with linear time complexity and constant cost in space. Our algorithms are optimal in the sense they generate the minimum number of segments that approximate a time series with the required quality guarantee. To meet the resource constraints in sensor networks, we also develop a fast algorithm which creates connecting segments with very simple computation. The low cost nature of our methods leads to a unique edge on the applications of massive and fast streaming environment, low bandwidth networks, and heavily constrained nodes in computational power. We implement and evaluate our methods in the application of an acoustic wireless sensor network.
The past decade has seen a wealth of research on time series representations, because the manipulation, storage, and indexing of large volumes of raw time series data is impractical. The vast majority of research has concentrated on representations that are calculated in batch mode and represent each value with approximately equal fidelity. However, the increasing deployment of mobile devices and real time sensors has brought home the need for representations that can be incrementally updated, and can approximate the data with fidelity proportional to its age. The latter property allows us to answer queries about the recent past with greater precision, since in many domains recent information is more useful than older information. We call such representations amnesic. While there has been previous work on amnesic representations, the class of amnesic functions possible was dictated by the representation itself. We introduce a novel representation of time series that can represent arbitrary, user-specified amnesic functions. For example, a meteorologist may decide that data that is twice as old can tolerate twice as much error, and thus, specify a linear amnesic function. In contrast, an econometrist might opt for an exponential amnesic function. We propose online algorithms for our representation, and discuss their properties. Finally, we perform an extensive empirical evaluation on 40 datasets, and show that our approach can efficiently maintain a high quality amnesic approximation.