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.
Earlier works on metric learning are based on @cite_19 . In that study, two identical neural networks extract the features of two arbitrary images. Next, these features are compared by a metric which is based on a radial function The distance between any two members in the feature space is defined as the cosine of the angle between them @cite_19 . . While their loss function forces the samples in the same class to be closer to each other in the sense of the selected distance function, the samples in the different classes are forced to be mapped far from each other. The cost function of such a network is given below @cite_2 where @math represents the operation of @math , and @math are distances in between samples.
@cite_19 @cite_2
2127589108 2138621090
We investigate the minimization of Newton's functional for the problem of the body of minimal resistance with maximal height @math cite butt in the class of convex developable functions defined in a disc. This class is a natural candidate to find a (non-radial) minimizer in accordance with the results of cite lrp2. We prove that the minimizer in this class has a minimal set in the form of a regular polygon with @math sides centered in the disc, and numerical experiments indicate that the natural number @math is a non-decreasing function of @math . The corresponding functions all achieve a lower value of the functional than the optimal radially symmetric function with the same height @math . Image-generating machine learning models are typically trained with loss functions based on distance in the image space. This often leads to over-smoothed results. We propose a class of loss functions, which we call deep perceptual similarity metrics (DeePSiM), that mitigate this problem. Instead of computing distances in the image space, we compute distances between image features extracted by deep neural networks. This metric better reflects perceptually similarity of images and thus leads to better results. We show three applications: autoencoder training, a modification of a variational autoencoder, and inversion of deep convolutional networks. In all cases, the generated images look sharp and resemble natural images. Let @math be a set of elements and d a distance function defined among them. Let NNk(u) be the k elements in @math having the smallest distance to u. The k-nearest neighbor graph (knng) is a weighted directed graph @math such that E= (u,v), v∈NNk(u) . Several knng construction algorithms are known, but they are not suitable to general metric spaces. We present a general methodology to construct knngs that exploits several features of metric spaces. Experiments suggest that it yields costs of the form c1n1.27 distance computations for low and medium dimensional spaces, and c2n1.90 for high dimensional ones. We propose a class of loss functions, which we call deep perceptual similarity metrics (DeePSiM), allowing to generate sharp high resolution images from compressed abstract representations. Instead of computing distances in the image space, we compute distances between image features extracted by deep neural networks. This metric reflects perceptual similarity of images much better and, thus, leads to better results. We demonstrate two examples of use cases of the proposed loss: (1) networks that invert the AlexNet convolutional network; (2) a modified version of a variational autoencoder that generates realistic high-resolution random images.