For time series discrimination, this paper proposes a new approach to align time series with respect to the commonly shared features within classes and the most differential ones between classes. The main idea behind the proposed approach is to use a variance/covariance criterion to strengthen or weaken aligned observations according to their contribution to the variability within and between classes. To this end, the classical variance/covariance expression is extended to a set of time series, as well as to a partition of time series based on classes. A new algorithm is then proposed to learn alignments between time series so as to minimize the within variance and maximize the between variance. The relevance of the learned alignments is studied through a nearest neighbor time series classification on real and synthetic datasets. The carried out experiments reveal that the proposed approach is able to capture fine-grained distinctions between time series across classes, and outperforms standard approaches on several different datasets, all the more so that the correspondence between time series within the same class is complex.