Deep Metric Learning with Alternating Projections onto Feasible Sets

TL;DR

This paper introduces an alternating projections method for deep metric learning that reformulates the problem as finding a feasible point within a constraint set, improving performance on image retrieval tasks without extra computational cost.

Contribution

The paper proposes a novel alternating projections approach to enforce proximity constraints in metric learning, enhancing existing loss functions with systematic batch construction and hard class mining.

Findings

Outperforms state-of-the-art on Stanford Online Products, CAR196, and CUB200-2011 datasets.

Improves metric learning performance without additional computational cost.

Effectively utilizes class representatives for hard negative mining.

Abstract

During the training of networks for distance metric learning, minimizers of the typical loss functions can be considered as "feasible points" satisfying a set of constraints imposed by the training data. To this end, we reformulate distance metric learning problem as finding a feasible point of a constraint set where the embedding vectors of the training data satisfy desired intra-class and inter-class proximity. The feasible set induced by the constraint set is expressed as the intersection of the relaxed feasible sets which enforce the proximity constraints only for particular samples (a sample from each class) of the training data. Then, the feasible point problem is to be approximately solved by performing alternating projections onto those feasible sets. Such an approach introduces a regularization term and results in minimizing a typical loss function with a systematic batch set construction where these batches are constrained to contain the same sample from each class for a certain number of iterations. Moreover, these particular samples can be considered as the class representatives, allowing efficient utilization of hard class mining during batch construction. The proposed technique is applied with the well-accepted losses and evaluated on Stanford Online Products, CAR196 and CUB200-2011 datasets for image retrieval and clustering. Outperforming state-of-the-art, the proposed approach consistently improves the performance of the integrated loss functions with no additional computational cost and boosts the performance further by hard negative class mining.