Abstract: The feature representation method of time series data is the key technology of time series data mining task,and the symbolic aggregate approximation (SAX) method is most commonly used in feature representation methods.A symbolic aggregate approximation method based on beginning and end distance (SAX_SM) was proposed because SAX algorithm can not distinguish the similarity between time series when the symbol is consistent in each sequence segment of time series.Time series data have a strong morphological trend,so the proposed method uses the beginning point and the end point to represent the morphological feature of each sequence segment,and then uses the morphological feature and representation symbol of each sequence segment to approximate the time series data,in order to map it from high-dimensional space to low-dimensional space.Next,in order to calculate the morphological distance between the two sequences,this paper constructed beginning and end distance based on the beginning point and the end point.Finally,to measure the similarity between time series more objectively,a new distance metric approach was defined by combining the beginning and end distance and the symbol distance.The theoretical analysis shows that the new distance measure satisfies the lower bound theorem.Experiments on 20 sets of UCR time series data sets show that the proposed SAX_SM method achieves the highest classification accuracy (including the largest side by side) in 13 data sets,while SAX only gets the largest classification accuracy in 6 data sets (including the largest side by side).Therefore,SAX_SM has better classification result than SAX.

Key words: Beginning and end distance, Sequence segment, Symbol distance, Time series data