Hierarchical Distance Metric Learning for Large Margin Nearest Neighbor Classification

Distance metric learning is a powerful tool to improve performance in classification, clustering and regression tasks. Many techniques have been proposed for distance metric learning based on convex programming, kernel learning, dimension reduction and large margin. The recently proposed large margin nearest neighbor classification (LMNN) improves the performance of k-nearest neighbors classification (k-nn) by a learned global distance metric. However, it does not consider the locality of data distributions. We demonstrate a novel local distance metric learning method called hierarchical distance metric learning (HDM) which first builds a hierarchical structure by grouping data points according to the overlapping ratios defined by us and then learns distance metrics sequentially. In this paper, we combine HDM with LMNN and further propose a new method named hierarchical distance metric learning for large margin nearest neighbor classification (HLMNN). Experiments are performed on many artificial and real-world data sets. Comparisons with the traditional k-nn and the state-of-the-art LMNN show the effectiveness of the proposed HLMNN.