Recognition of objects with subtle differences has been used in many practical applications, such as car model recognition and maritime vessel identification. For discrimination of the objects in fine-grained detail, we focus on deep embedding learning by using a multi-task learning framework, in which the hierarchical labels (coarse and fine labels) of the samples are utilized both for classification and a quadruplet-based loss function. In order to improve the recognition strength of the learned features, we present a novel feature selection method specifically designed for four training samples of a quadruplet. By experiments, it is observed that the selection of very hard negative samples with relatively easy positive ones from the same coarse and fine classes significantly increases some performance metrics in a fine-grained dataset when compared to selecting the quadruplet samples randomly. The feature embedding learned by the proposed method achieves favorable performance against its state-of-the-art counterparts.
Moreover, the loss function for the quadruplets is similar to the triplet based methods @cite_15 . On the other hand, in @cite_7 , the use of the global loss has been proposed, while the quadruplet samples are selected randomly (Note that these quadruplets hold the constraints). The global loss penalizes the network in case of the mean and variance of the distances between the samples in a quadruplet are not appropriate, as given in In , @math , @math , and @math , @math as defined in @cite_21 . , where @math and @math are the margins, similar to .
@cite_15 @cite_21 @cite_7
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Person re-identification (ReID) is an important task in wide area video surveillance which focuses on identifying people across different cameras. Recently, deep learning networks with a triplet loss become a common framework for person ReID. However, the triplet loss pays main attentions on obtaining correct orders on the training set. It still suffers from a weaker generalization capability from the training set to the testing set, thus resulting in inferior performance. In this paper, we design a quadruplet loss, which can lead to the model output with a larger inter-class variation and a smaller intra-class variation compared to the triplet loss. As a result, our model has a better generalization ability and can achieve a higher performance on the testing set. In particular, a quadruplet deep network using a margin-based online hard negative mining is proposed based on the quadruplet loss for the person ReID. In extensive experiments, the proposed network outperforms most of the state-of-the-art algorithms on representative datasets which clearly demonstrates the effectiveness of our proposed method. We propose Quadruplet Convolutional Neural Networks (Quad-CNN) for multi-object tracking, which learn to associate object detections across frames using quadruplet losses. The proposed networks consider target appearances together with their temporal adjacencies for data association. Unlike conventional ranking losses, the quadruplet loss enforces an additional constraint that makes temporally adjacent detections more closely located than the ones with large temporal gaps. We also employ a multi-task loss to jointly learn object association and bounding box regression for better localization. The whole network is trained end-to-end. For tracking, the target association is performed by minimax label propagation using the metric learned from the proposed network. We evaluate performance of our multi-object tracking algorithm on public MOT Challenge datasets, and achieve outstanding results. We study the problem of learning multivariate log-concave densities with respect to a global loss function. We obtain the first upper bound on the sample complexity of the maximum likelihood estimator (MLE) for a log-concave density on @math , for all @math . Prior to this work, no finite sample upper bound was known for this estimator in more than @math dimensions. In more detail, we prove that for any @math and @math , given @math samples drawn from an unknown log-concave density @math on @math , the MLE outputs a hypothesis @math that with high probability is @math -close to @math , in squared Hellinger loss. A sample complexity lower bound of @math was previously known for any learning algorithm that achieves this guarantee. We thus establish that the sample complexity of the log-concave MLE is near-optimal, up to an @math factor.