An improvement of symbolic aggregate approximation distance measure for time series

• We define an intuitive trend distance measure on time series segments.
• We integrate the SAX distance with our weighted trend distance.
• The proposed distance has a tighter lower bound to Euclidean distance than SAX.
• Our method outperforms the original SAX on classification significantly.

Symbolic Aggregate approXimation (SAX) as a major symbolic representation has been widely used in many time series data mining applications. However, because a symbol is mapped from the average value of a segment, the SAX ignores 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 firstly design a measure to compute the distance of trends using the starting and the ending points of segments. Then we 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.