Distance metric learning (DML) has been studied extensively in the past decades for its superior performance with distance-based algorithms. Most of the existing methods propose to learn a distance metric with pairwise or triplet constraints. However, the number of constraints is quadratic or even cubic in the number of the original examples, which makes it challenging for DML to handle the large-scale data set. Besides, the real-world data may contain various uncertainty, especially for the image data. The uncertainty can mislead the learning procedure and cause the performance degradation. By investigating the image data, we find that the original data can be observed from a small set of clean latent examples with different distortions. In this work, we propose the margin preserving metric learning framework to learn the distance metric and latent examples simultaneously. By leveraging the ideal properties of latent examples, the training efficiency can be improved significantly while the learned metric also becomes robust to the uncertainty in the original data. Furthermore, we can show that the metric is learned from latent examples only, but it can preserve the large margin property even for the original data. The empirical study on the benchmark image data sets demonstrates the efficacy and efficiency of the proposed method.
Besides the research about conventional DML, deep metric learning has attracted much attention recently @cite_0 @cite_5 @cite_1 @cite_2 . These studies also indicate that sampling active triplets is essential for accelerating the convergence. FaceNet @cite_1 keeps a large size of mini-batch and searches hard constraints within a mini-batch. LeftedStruct @cite_2 generates the mini-batch with the randomly selected positive examples and the corresponding hard negative examples. Proxy-NCA @cite_0 adopts proxy examples to reduce the size of triplet constraints. Once an anchor example is given, the similar and dissimilar examples will be searched within the set of proxies. In this work we propose to learn the metric only with latent examples which can dramatically reduce the computational cost of obtaining the active set. Besides, the triangle inequality dose not hold for the squared distance, which makes our analysis significantly different from the existing work.
@cite_0 @cite_5 @cite_1 @cite_2
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We address the problem of distance metric learning (DML), defined as learning a distance consistent with a notion of semantic similarity. Traditionally, for this problem supervision is expressed in the form of sets of points that follow an ordinal relationship – an anchor point x is similar to a set of positive points Y , and dissimilar to a set of negative points Z, and a loss defined over these distances is minimized. While the specifics of the optimization differ, in this work we collectively call this type of supervision Triplets and all methods that follow this pattern Triplet-Based methods. These methods are challenging to optimize. A main issue is the need for finding informative triplets, which is usually achieved by a variety of tricks such as increasing the batch size, hard or semi-hard triplet mining, etc. Even with these tricks, the convergence rate of such methods is slow. In this paper we propose to optimize the triplet loss on a different space of triplets, consisting of an anchor data point and similar and dissimilar proxy points which are learned as well. These proxies approximate the original data points, so that a triplet loss over the proxies is a tight upper bound of the original loss. This proxy-based loss is empirically better behaved. As a result, the proxy-loss improves on state-of-art results for three standard zero-shot learning datasets, by up to 15 points, while converging three times as fast as other triplet-based losses. Metric learning aims at finding a distance that approximates a task-specific notion of semantic similarity. Typically, a Mahalanobis distance is learned from pairs of data labeled as being semantically similar or not. In this paper, we learn such metrics in a weakly supervised setting where "bags" of instances are labeled with "bags" of labels. We formulate the problem as a multiple instance learning (MIL) problem over pairs of bags. If two bags share at least one label, we label the pair positive, and negative otherwise. We propose to learn a metric using those labeled pairs of bags, leading to MildML, for multiple instance logistic discriminant metric learning. MildML iterates between updates of the metric and selection of putative positive pairs of examples from positive pairs of bags. To evaluate our approach, we introduce a large and challenging data set, Labeled Yahoo! News, which we have manually annotated and contains 31147 detected faces of 5873 different people in 20071 images. We group the faces detected in an image into a bag, and group the names detected in the caption into a corresponding set of labels. When the labels come from manual annotation, we find that MildML using the bag-level annotation performs as well as fully supervised metric learning using instance-level annotation. We also consider performance in the case of automatically extracted labels for the bags, where some of the bag labels do not correspond to any example in the bag. In this case MildML works substantially better than relying on noisy instance-level annotations derived from the bag-level annotation by resolving face-name associations in images with their captions. Deep metric learning has gained much popularity in recent years, following the success of deep learning. However, existing frameworks of deep metric learning based on contrastive loss and triplet loss often suffer from slow convergence, partially because they employ only one negative example while not interacting with the other negative classes in each update. In this paper, we propose to address this problem with a new metric learning objective called multi-class N-pair loss. The proposed objective function firstly generalizes triplet loss by allowing joint comparison among more than one negative examples - more specifically, N-1 negative examples - and secondly reduces the computational burden of evaluating deep embedding vectors via an efficient batch construction strategy using only N pairs of examples, instead of (N+1) x N. We demonstrate the superiority of our proposed loss to the triplet loss as well as other competing loss functions for a variety of tasks on several visual recognition benchmark, including fine-grained object recognition and verification, image clustering and retrieval, and face verification and identification. This paper presents a new discriminative deep metric learning (DDML) method for face verification in the wild. Different from existing metric learning-based face verification methods which aim to learn a Mahalanobis distance metric to maximize the inter-class variations and minimize the intra-class variations, simultaneously, the proposed DDML trains a deep neural network which learns a set of hierarchical nonlinear transformations to project face pairs into the same feature subspace, under which the distance of each positive face pair is less than a smaller threshold and that of each negative pair is higher than a larger threshold, respectively, so that discriminative information can be exploited in the deep network. Our method achieves very competitive face verification performance on the widely used LFW and YouTube Faces (YTF) datasets.