Abstract: Time series clustering is widely applied in various areas. Existing research work focuses mainly on distance measures between two time series, such as DTW-based (dynamic time warping) methods, edit distance-based methods, and shapelets-based methods. In this work, we experimentally demonstrate, for the first time, that no single distance measure performs significantly better than others on clustering data sets of time series where spectral clustering is used. As such, a question arises as to how to choose an appropriate measure for a given data set of time series. To answer this question, we propose an integration scheme that incorporates multiple distance measures using semi-supervised clustering. Our approach is able to integrate all the measures by extracting valuable underlying information for the clustering. To our best knowledge, this work demonstrates for the first time that semi-supervised clustering method based on constraints is able to enhance time series clustering by combining multiple distance measures. Having tested on clustering various time series data sets, we show that our method outperforms individual measures, as well as typical integration approaches.