A new symbolic representation method for time series

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Time series symbolic representation methods have been a research hot issue. Among them, the most representative symbolic methods such as Symbol Aggregation Approximation(SAX) and Symbol Fourier Approximation(SFA) have been widely used in various scenarios. However, they all have some flaws in some way. For SAX, the converted data in the approximation phase displays a shrinkage distribution(standard deviation σ shrinkage) that does not meet the assumptions in the definition. For SFA, it only obtains global frequency domain information, which leads to poor recognition ability for reciprocating frequency conversion sequence. Simultaneously, the symbol distance defined has poor interpretability due to spanning two spaces.In this paper, we propose a novel symbolic method called Symbol Fractional Fourier Approximation(SFFA), which shows multivariate approximation capabilities by Fractional Fourier Transform (FrFT) and adds a new supervised strategy for symbol mapping based on the chi-square distribution. It not only effectively avoids the influence of shrinkage distribution, but also has a strong ability to distinguish special sequences. Moreover, the SFFA symbol distance is proved to satisfy the low boundary lemma. Furthermore, it can achieve the same effect as SFA when the appropriate parameters and strategies are selected. Finally, when combined with the Vector Space Model (VSM) to classify time series, a large number of experiments show that SFFA-VSM outperforms SFA on all open-source data sets.