An Integrated Framework for High Dimensional Distance Metric Learning and Its Application to Fine-Grained Visual Categorization

In this paper, we focus on distance metric learning (DML) for high dimensional data and its application to fine-grained visual categorization. The challenges of high dimensional DML arise in three aspects. First, the high dimensionality leads to a large-scale optimization problem to be solved that is computationally expensive. Second, the high dimensionality requires a large storage space (i.e. $\mathcal{O}(d^2)$ where $d$ is the dimensionality) for saving the learned metric. Third, the high dimensionality requires a large number of constraints for training that adds more complexity to the already difficult optimization problem. We develop an integrated framework for high dimensional DML that explicitly addresses the three challenges by exploiting the techniques of {\it dual random projection}, {\it randomized low rank matrix approximation}, and {\it adaptive sampling}. We demonstrate the effectiveness of the proposed algorithm for high dimensional DML by fine-grained visual categorization (FGVC), a challenging prediction problem that needs to capture the subtle difference among image classes. Our empirical study shows that the proposed algorithm is both effective and efficient for FGVC compared to the state-of-the-art approaches.