A geometrical solution to time series searching invariant to shifting and scaling

摘要

The technique of searching for similar patterns among time series data is very useful in many applications. The problem becomes difficult when shifting and scaling are considered. We find that we can treat the problem geometrically and the major contribution of this paper is that a uniform geometrical model that can analyze the existing related methods is proposed. Based on the analysis, we conclude that the angle between two vectors after the Shift-Eliminated Transformation is a more intrinsical similarity measure invariant to shifting and scaling. We then enhance the original conical index to adapt to the geometrical properties of the problem and compare its performance with that of sequential search and R*-tree. Experimental results show that the enhanced conical index achieves larger improvement on R*-tree and sequential search in high dimension. It can also keep a steady performance as the selectivity increases.