A non-parametric symbolic approximate representation for long time series

Abstract

For long time series, it is crucial to design low-dimensional representations that preserve the fundamental characteristics of a series. However, most of the approximate representations require the setting of many input parameters. The main defect of working with parameter-laden algorithms is that incorrect settings may cause an algorithm to fail in achieving the best performance, which is the ability of reducing the dimensionality and retaining the shape information. This is especially likely when the selection of the suitable parameter is not trivial or easy for the user. In this paper, we introduce a new approximate representation of time series, the non-parametric symbolic approximate representation (NSAR), which is based on multi-scale, the approximate coefficients of discrete wavelet transform (DWT) and key points. The novelty of the proposed representation is firstly that it uses a hierarchical mechanism to retain shape information of the original time series. Next, the proposed representation is symbolic in employing key points and encoding in approximate coefficients, so it can greatly reduce the dimension of the original time series and potentially allows the application of text-based retrieval techniques. The proposed representation is fast, automatic, and with no parameter tuning by user. To show the efficacy of the new representation, we performed experiments with real and synthetic data. Experimental results show that NSAR can preserve more fundamental characteristics of a series than symbolic approximate representation (SAX) in the same compression ratio, automatically determine the optimal decomposition level for DWT, and has better performance than SAX in the best matching queries.