Adaptive piecewise and symbolic aggregate approximation as an improved representation method for heat waves detection

Mining time series has attracted an increasing interest due to its wide applications in finance, industry, biology, environment, and so on. In order to reduce execution time and storage space, many high level representations or abstractions of the raw time series data have been proposed including Discrete Fourier Transform (DFT), Discrete Wavelet Transform (DWT), Piecewise Aggregate Approximation (PAA) and Symbolic Aggregate approXimation (SAX). In this paper, we introduce a novel adaptive piecewise and symbolic aggregate approximation (APAA/ASAX) which creates segments of variable length in order to automatically adapt any segment length to its local condition of variability and difference to the average value of the current values in which the segment is defined. The average of each variable segment length from APAA is represented as a symbol from an ordered alphabet generating a modified version for SAX called adaptive SAX (ASAX). This straightforwardly allows to handle a more versatile definition for the event duration. The method APAA/ASAX was used for locating heat waves patterns in a real-world time series datasets of daily temperature information, from the year 1970 until 2009. The experimental results show that APAA/ASAX representation was able to locate heatwave events in a huge databases. Advantages of APAA regarding traditional PAA are mainly based on being constrain-free of fixed schemes of segment length. It also highlights the ability of self-tuning this length depending on local time series characteristics. This means that for flat time series APAA proposes a lower number of segments to reduce dimensionality than in the case to deal with time series of high variability. The approach will be of use to those looking extreme events in any time series.