POLAR WAVELET TRANSFORM FOR TIME SERIES DATA

Abstract

In this paper, we propose the novel wavelet transform, called the Polar wavelet, which can improve the search performance in large time series databases. In general, Harr wavelet has been popularly used to extract features from time series data. However, Harr wavelet shows the poor performance for locally distributed time series data which are clustered around certain values, since it uses the averages to reduce the dimensionality of data. Moreover, Harr wavelet has the limitation that it works best if the length of time series is 2n, and otherwise it approximates the left side of real signal by substituting the right side with 0 elements to make the length of time series to 2n, which consequently, distortion of a signal occurs. The Polar wavelet does not only suggest the solution of the low distinction between time sequences of similar averages in Harr wavelet transform, but also improves the search performance as the length of time series is increased. Actually, several kinds of data such as rainfall are locally distributed and have the similar averages, so Harr wavelet which transforms data using their averages has shortcomings, naturally. To solve this problem, the Polar wavelet uses the polar coordinates which are not affected from averages and can improve the search performance especially in locally distributed time series databases. In addition, we show that the Polar wavelet guarantees no false dismissals. The effectiveness of the Polar wavelet is evaluated empirically on real weather data and the syntactic data, reporting the significant improvements in reducing the search space.