Performing data mining tasks on raw time series is inefficient as these data are high-dimensional by nature. Instead, time series are first pre-processed using several techniques before the different data mining tasks can be performed. In general, there are two main approaches to pre-process time series. The first is what we call landmark methods. These methods are based on finding characteristic features in the target time series. The other approach is based on data transformations. These methods transform the time series from the original space into a reduced space so that they can be managed more efficiently. The method we present in this paper applies a third approach, as it projects a time series onto a lower-dimensional space by selecting important points in the time series. The novelty of our method is that these points are not chosen according to a geometric criterion which is subjective in most cases. The other important difference is that these important points are selected on a dataset-level and not on a single time series-level. The direct advantage of this strategy is that the distance defined on the low-dimensional space lower bounds the original distance applied to raw data. This enables us to apply the popular GEMINI algorithm. The promising results of our experiments on a wide variety of time series datasets validate our new method.