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State-of-the-art language recognition systems are based on discriminative embeddings called x-vectors. Channel and gender distortions produce mismatch in such x-vector space where embeddings corresponding to the same language are not grouped in an unique cluster. To control this mismatch, we propose to train the x-vector DNN with metric learning objective functions. Combining a classification loss with the metric learning n-pair loss allows to improve the language recognition performance. Such a system achieves a robustness comparable to a system trained with a domain adaptation loss function but without using the domain information. We also analyze the mismatch due to channel and gender, in comparison to language proximity, in the x-vector space. This is achieved using the Maximum Mean Discrepancy divergence measure between groups of x-vectors. Our analysis shows that using the metric learning loss function reduces gender and channel mismatch in the x-vector space, even for languages only observed on one channel in the train set.