Temporal data analytics based on eigenmotif and shape space representations of time series

For temporal data analytics it is essential to assess the similarity of time series numerically. For similarity measures, in turn, appropriate time series representation techniques are needed. We present and discuss two techniques for time series representation. Eigenspace representations are based on a principal component analysis of time series. Shape space representations are based on polynomial least-squares approximations. Both aim at capturing the essential characteristics of time series while abstracting from less significant information, e.g., noise. The similarity of time series can then be measured using a standard Euclidean distance in the eigenspace or the shape space, respectively. Experiments on a number of benchmark data sets for time series classification show that the measure based on a shape space representation outperforms some other linear (non-elastic) similarity measures-including a standard Euclidean measure applied to the raw time series, which is a standard approach in temporal data analytics-regarding classification accuracy and run-time.