Image recognition is an essential baseline for deep metric learning. Hierarchical knowledge about image classes depicts inter-class similarities or dissimilarities. Effective fusion of hierarchical knowledge about image classes to enhance image recognition remains a challenging topic to advance. In this paper, we propose a novel deep metric learning based method to effectively fuse hierarchical prior knowledge about image classes and enhance image recognition performances in an end-to-end supervised regression manner. Existing deep metric learning incorporated image classification mainly exploits qualitative relativity between image classes, i.e., whether sampled images are from the same class. A new triplet loss function term that exploits quantitative relativity and aligns distances in model latent space with those in knowledge space is also proposed and incorporated in the proposed dual-modality fusion method. Experimental results indicate that the proposed method enhanced image recognition performances and outperformed baseline and existing methods on CIFAR-10, CIFAR-100, Mini-ImageNet, and ImageNet-1K datasets.