How to extract meaningful shapes from noisy time-series subsequences?

A method for extracting and classifying shapes from noisy time series is proposed. The method consists of two steps. The first step is to perform a noise test on each subsequence extracted from the series using a sliding window. All the subsequences recognised as noise are removed from further analysis, and the shapes are extracted from the remaining non-noise subsequences. The second step is to cluster these extracted shapes. Although extracted from subsequences, these shapes form a non-overlapping set of time series subsequences and are hence amenable to meaningful clustering. The method is primarily designed for extracting and classifying shapes from very noisy real-world time series. Tests using artificial data with different levels of white noise and the red noise, and the real-world atmospheric turbulence data naturally characterised by strong red noise show that the method is able to correctly extract and cluster shapes from artificial data and that it has great potential for locating shapes in very noisy real-world time series.