In real applications it is not rare for time series of the same class to exhibit dis- similarities in their overall behaviors, or that time series from different classes have slightly similar shapes. To discriminate between such challenging time se- ries, we present a new approach for training discriminative matching that con- nects 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 real datasets. The experiments performed demonstrate the ability of learned match- ing 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.