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We propose a method that substantially improves the efficiency of deep distance metric learning based on the optimization of the triplet loss function. One epoch of such training process based on a naive optimization of the triplet loss function has a run-time complexity O(N^3), where N is the number of training samples. Such optimization scales poorly, and the most common approach proposed to address this high complexity issue is based on sub-sampling the set of triplets needed for the training process. Another approach explored in the field relies on an ad-hoc linearization (in terms of N) of the triplet loss that introduces class centroids, which must be optimized using the whole training set for each mini-batch - this means that a naive implementation of this approach has run-time complexity O(N^2). This complexity issue is usually mitigated with poor, but computationally cheap, approximate centroid optimization methods. In this paper, we first propose a solid theory on the linearization of the triplet loss with the use of class centroids, where the main conclusion is that our new linear loss represents a tight upper-bound to the triplet loss. Furthermore, based on the theory above, we propose a training algorithm that no longer requires the centroid optimization step, which means that our approach is the first in the field with a guaranteed linear run-time complexity. We show that the training of deep distance metric learning methods using the proposed upper-bound is substantially faster than triplet-based methods, while producing competitive retrieval accuracy results on benchmark datasets (CUB-200-2011 and CAR196).
We present a novel hierarchical triplet loss (HTL) capable of automatically collecting informative training samples (triplets) via a defined hierarchical tree that encodes global context information. This allows us to cope with the main limitation of
We address the problem of distance metric learning in visual similarity search, defined as learning an image embedding model which projects images into Euclidean space where semantically and visually similar images are closer and dissimilar images ar
Distance metric learning (DML) is to learn the embeddings where examples from the same class are closer than examples from different classes. It can be cast as an optimization problem with triplet constraints. Due to the vast number of triplet constr
Deep metric learning, which learns discriminative features to process image clustering and retrieval tasks, has attracted extensive attention in recent years. A number of deep metric learning methods, which ensure that similar examples are mapped clo
Deep Metric Learning (DML) is helpful in computer vision tasks. In this paper, we firstly introduce DML into image co-segmentation. We propose a novel Triplet loss for Image Segmentation, called IS-Triplet loss for short, and combine it with traditio