Mining time series data is of great significance in various areas. To efficiently find representative patterns in these data, this article focuses on the definition of a valid dissimilarity measure and the acceleration of partitioning clustering, a common group of techniques used to discover typical shapes of time series. Dissimilarity measure is a crucial component in clustering. It is required, by some particular applications, to be invariant to specific transformations. The rationale for using the angle between two time series to (...) define a dissimilarity is analyzed. Moreover, our proposed measure satisfies the triangle inequality with specific restrictions. This property can be employed to accelerate clustering. An integrated algorithm is proposed. The experiments show that angle-based dissimilarity captures the essence of time series patterns that are invariant to amplitude scaling. In addition, the accelerated algorithm outperforms the standard one as redundancies are pruned. Our approach has been applied to discover typical patterns of information diffusion in an online social network. Analyses revealed the formation mechanisms of different patterns. (shrink)