In real applications it is not rare for time series of the same class to exhibit dissimilarities in their overall behaviors, or that time series from different classes have slightly similar shapes \cite{DouzalPR}. To discriminate between such challenging time series, we present a new approach for training discriminative matching that connects time series with respect to the commonly shared features within classes, and the greatest differential across classes. For this, we rely on a variance/covariance criterion to strengthen or weaken matched observations according to the induced variability within and between classes. In this paper, learned discriminative matching is used to define a locally weighted time series metric, which restricts time series comparison to discriminative features. The relevance of the proposed approach is studied through a nearest neighbor time series classification on simulated and real datasets. The experiments performed demonstrate the ability of learned matching to capture fine-grained distinctions between time series, and outperform the standard approaches, all the more so that time series behaviors within the same class are complex