Data-Adaptive Metric Learning with Scale Alignment

The central problem for most existing metric learning methods is to find a suitable projection matrix on the differences of all pairs of data points. However, a single unified projection matrix can hardly characterize all data similarities accurately as the practical data are usually very complicated, and simply adopting one global projection matrix might ignore important local patterns hidden in the dataset. To address this issue, this paper proposes a novel method dubbed “Data-Adaptive Metric Learning” (DAML), which constructs a data-adaptive projection matrix for each data pair by selectively combining a set of learned candidate matrices. As a result, every data pair can obtain a specific projection matrix, enabling the proposed DAML to flexibly fit the training data and produce discriminative projection results. The model of DAML is formulated as an optimization problem which jointly learns candidate projection matrices and their sparse combination for every data pair. Nevertheless, the over-fitting problem may occur due to the large amount of parameters to be learned. To tackle this issue, we adopt the Total Variation (TV) regularizer to align the scales of data embedding produced by all candidate projection matrices, and thus the generated metrics of these learned candidates are generally comparable. Furthermore, we extend the basic linear DAML model to the kernerlized version (denoted “KDAML”) to handle the non-linear cases, and the Iterative Shrinkage-Thresholding Algorithm (ISTA) is employed to solve the optimization model. Intensive experimental results on various applications including retrieval, classification, and verification clearly demonstrate the superiority of our algorithm to other state-of-the-art metric learning methodologies.