Compression of time series by extracting major extrema

We formalise the notion of important extrema of a time series, that is, its major minima and maxima; analyse the basic mathematical properties of important extrema; and apply these results to the problem of time-series compression. First, we define the numeric importance levels of extrema in a series, and present algorithms for identifying major extrema and computing their importances. Then, we give a procedure for fast lossy compression of a time series at a given rate, by extracting its most important minima and maxima, and discarding the other points.