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In this work, we study distance metric learning (DML) for high dimensionaldata. A typical approach for DML with high dimensional data is to perform thedimensionality reduction first before learning the distance metric. The mainshortcoming of this approach is that it may result in a suboptimal solution dueto the subspace removed by the dimensionality reduction method. In this work,we present a dual random projection frame for DML with high dimensional datathat explicitly addresses the limitation of dimensionality reduction for DML.The key idea is to first project all the data points into a low dimensionalspace by random projection, and compute the dual variables using the projectedvectors. It then reconstructs the distance metric in the original space usingthe estimated dual variables. The proposed method, on one hand, enjoys thelight computation of random projection, and on the other hand, alleviates thelimitation of most dimensionality reduction methods. We verify both empiricallyand theoretically the effectiveness of the proposed algorithm for highdimensional DML.

Towards Making High Dimensional Distance Metric Learning Practical