# A Novel Trend Symbolic Aggregate Approximation for Time Series

## TL;DR

This paper introduces TFSAX, an enhanced symbolic approximation method for time series that incorporates trend information, leading to improved classification accuracy over traditional SAX methods.

## Contribution

The paper proposes TFSAX, which integrates trend features into SAX, providing a more informative representation for time series analysis.

## Key findings

- TFSAX outperforms original SAX in classification tasks.
- The new distance measure offers a tighter lower bound to Euclidean distance.
- Experimental results validate the effectiveness of TFSAX across datasets.

## Abstract

Symbolic Aggregate approximation (SAX) is a classical symbolic approach in many time series data mining applications. However, SAX only reflects the segment mean value feature and misses important information in a segment, namely the trend of the value change in the segment. Such a miss may cause a wrong classification in some cases, since the SAX representation cannot distinguish different time series with similar average values but different trends. In this paper, we present Trend Feature Symbolic Aggregate approximation (TFSAX) to solve this problem. First, we utilize Piecewise Aggregate Approximation (PAA) approach to reduce dimensionality and discretize the mean value of each segment by SAX. Second, extract trend feature in each segment by using trend distance factor and trend shape factor. Then, design multi-resolution symbolic mapping rules to discretize trend information into symbols. We also propose a modified distance measure by integrating the SAX distance with a weighted trend distance. We show that our distance measure has a tighter lower bound to the Euclidean distance than that of the original SAX. The experimental results on diverse time series data sets demonstrate that our proposed representation significantly outperforms the original SAX representation and an improved SAX representation for classification.

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Source: https://tomesphere.com/paper/1905.00421