Learning Compact and Effective Distance Metrics with Diversity Regularization

Learning a proper distance metric is of vital importance for many distance based applications. Distance metric learning aims to learn a set of latent factors based on which the distances between data points can be effectively measured. The number of latent factors incurs a tradeoff: a small amount of factors are not powerful and expressive enough to measure distances while a large number of factors cause high computational overhead. In this paper, we aim to achieve two seemingly conflicting goals: keeping the number of latent factors to be small for the sake of computational efficiency, meanwhile making them as effective as a large set of factors. The approach we take is to impose a diversity regularizer over the latent factors to encourage them to be uncorrelated, such that each factor can capture some unique information that is hard to be captured by other factors. In this way, a small amount of latent factors can be sufficient to capture a large proportion of information, which retains computational efficiency while preserving the effectiveness in measuring distances. Experiments on retrieval, clustering and classification demonstrate that a small amount of factors learned with diversity regularization can achieve comparable or even better performance compared with a large factor set learned without regularization.