A Bit Level Representation for Time Series Data 1 Mining with Shape Based Similarity

Clipping is the process of transforming a real valued series into a sequence of bits representing whether 10 each data is above or below the average. In this paper we argue that clipping is a useful and flexible transformation 11 for the exploratory analysis of large time dependent data sets. We demonstrate how time series stored as bits 12 can be very efficiently compressed and manipulated and that, under some assumptions, the discriminatory power 13 with clipped series is asymptotically equivalent to that achieved with the raw data. Unlike other transformations, 14 clipped series can be compared directly to the raw data series. We show that this means we can form a tight 15 lower bounding metric for Euclidean and Dynamic Time Warping distance and hence efficiently query by content. 16 Clipped data can be used in conjunction with a host of algorithms and statistical tests that naturally follow from 17 the binary nature of the data. A series of experiments illustrate how clipped series can be used in increasingly 18 complex ways to achieve better results than with other popular techniques. The usefulness of the representation 19 is demonstrated by the fact that the results with clipped data are consistently better than those achieved with 20 a Wavelet or Discrete Fourier Transformation at the same compression ratio for both clustering and query by 21 content. The flexibility of the representation is shown by the fact that we can take advantage of a variable run 22 length encoding of clipped series to define an approximation of the Kolmogorov complexity and hence perform 23 Kolmogorov based clustering. 24