Safe Triplet Screening for Distance Metric Learning
This work addresses computational efficiency for researchers and practitioners in metric learning by reducing the huge number of triplets, though it is incremental as it builds on existing safe screening methods.
The paper tackles the problem of efficiently optimizing distance metric learning by identifying and removing redundant triplets from the optimization problem without affecting optimality, demonstrating effectiveness through numerical experiments on benchmark datasets.
We study safe screening for metric learning. Distance metric learning can optimize a metric over a set of triplets, each one of which is defined by a pair of same class instances and an instance in a different class. However, the number of possible triplets is quite huge even for a small dataset. Our safe triplet screening identifies triplets which can be safely removed from the optimization problem without losing the optimality. Compared with existing safe screening studies, triplet screening is particularly significant because of (1) the huge number of possible triplets, and (2) the semi-definite constraint in the optimization. We derive several variants of screening rules, and analyze their relationships. Numerical experiments on benchmark datasets demonstrate the effectiveness of safe triplet screening.