Distance metric learning has been considered an effective strategy to represent data in computer vision problems such as image retrieval and face verification. Metric learning attempts to minimize a loss function in order to transform data into a more optimal representation for further applications. In this paper, we compare 4 different types of loss functions, e.g. 2 pair-based losses (Contrastive loss and Triplet Margin Ranking loss), and 2 proxy-based losses (Proxy-NCA loss and Proxy-Anchor loss) in a multi-class classification task. Our experiments show that the Proxy-Anchor loss could achieve 70.8% accuracy on average compared to the Proxy-NCA loss, Triplet Margin Ranking loss and Contrastive loss which could only achieve 65.5%, 62.2%, and 36.6% respectively. Furthermore, we also present the qualitative results using high dimensional plot visualization in order to evaluate data distribution and sample image retrieval results. Overall, the Proxy-Anchor loss performs better than the other losses in terms of accuracy, recall, data separation, and image retrieval.