  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.
