In the area of time series data mining, a challenging task is to design an effectively and efficiently low-dimensional representation of high-dimensional time series data. Such an effective and efficient representation is important for dimensionality reduction of time series while preserving the core information embedded in the original one. Among popular representations of time series, Symbolic Aggregate approXimation (SAX) has been widely used and is the core of many successful time series data mining systems. SAX firstly normalizes the given time series, then divides a time series into segments and finally assigns each segment a symbol based on its average value. In fact, many segments have different shapes but the same average value are mapped to a sole symbol. In order to overcome this drawback, in this work, we propose an improvement of SAX by using complexity invariance, namely Complexity-invariant SAX (CSAX). In particular, our proposed method transforms a time series into a sequence of symbols based on both average values and the complexity invariance of its segments. By experiments, we demonstrate that CSAX outperforms the SAX and its improvements, i.e., ESAX, SAX_TD, SAX_SD, in time series classification.

中文翻译：

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利用复杂度不变性改进时间序列的SAX表示

在时间序列数据挖掘领域，一项艰巨的任务是设计一种有效且高效的高维时间序列数据的低维表示形式。这种有效而有效的表示方法对于减少时间序列的维数，同时保留嵌入原始数据中的核心信息非常重要。在时间序列的流行表示中，符号聚合近似（SAX）已被广泛使用，并且是许多成功的时间序列数据挖掘系统的核心。SAX首先将给定的时间序列归一化，然后将时间序列划分为多个段，最后根据其平均值为每个段分配一个符号。实际上，许多段具有不同的形状，但相同的平均值映射到单个符号。为了克服这个缺点，在这项工作中，我们提出通过使用复杂度不变性，即复杂度不变SAX（CSAX）对SAX进行改进。特别地，我们提出的方法基于平均值和其片段的复杂性不变性将时间序列转换为符号序列。通过实验，我们证明CSAX在时间序列分类方面胜过SAX及其改进，即ESAX，SAX_TD，SAX_SD。