Wavelets on Streams
Unlike conventional database query-processing engines that require several passes over a static data image, streaming data-analysis algorithms must often rely on building concise, approximate (but highly accurate) synopses of the input stream(s) in real-time (i.e., in one pass over the streaming data). Such synopses typically require space that is significantly sublinear in the size of the data and can be used to provide approximate query answers.
The collection of the top (i.e., largest) coefficients in the wavelet transform (or, decomposition) of an input data vector is one example of such a key feature of the stream. Wavelets provide a mathematical tool for the hierarchical decomposition of functions, with a long history of successful applications in signal and image processing . Applying the wavelet transform to a (one- or multi-dimensional) data vector and retaining a select small collection of the largest wavelet coefficient gives a very effective form of lossy...
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