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In few-shot learning, the Brownian distance covariance improves classification accuracy by enhancing feature embeddings, but it does not focus on the issue of sample-related features in classification. This paper proposed the deep masked Brownian distance covariance method that generated query-guided masks based on high-dimensional semantic relationships between each pair of query and support samples, and employed the masked Brownian distance covariance matrix as the image features. Under the 5way-1shot and 5way-5shot scenarios, it carried out validation and evaluation on CUB-200-211, MiniImageNet, and Tiered-ImageNet datasets. The experiments show that this method achieves superior classification accuracy. [ABSTRACT FROM AUTHOR]

The purpose of the few-shot segmentation task is to segment images containing new categories using only a few labeled samples. Existing methods typically extract features for support and query branches through a Siamese encoder and learn category-related information from the labeled support image to guide the segmentation of the query image. However, the extracted features are usually low- or middle-resolution, and these methods only exploit marginal distributions and neglect joint distributions. To address these issues, a High-Resolution representation and Brownian distance covariance learning (HRB) method is proposed for the task. Firstly, a high-resolution Siamese encoder is adopted to extract high-to-low-resolution features for two branches. Then, a pyramid feature joint module is proposed to learn high-resolution feature representations, and meanwhile, a new cross-excitation module is designed to enhance their common semantic information. Furthermore, a new similarity metric module is developed, i.e., the Brownian distance covariance metric, which estimates the semantic mapping relationship between the joint distribution features of the two branches. Extensive experiments on three benchmark datasets (PASCAL-5i, FSS-1000, and COCO-20i) prove that the proposed HRB attains state-of-the-art performance. The code is available at https://github.com/Saralyliu/HRB. [ABSTRACT FROM AUTHOR]

Few-shot image classification remains a persistent challenge due to the intrinsic difficulty faced by visual recognition models in achieving generalization with limited training data. Existing methods primarily focus on exploiting marginal distributions and overlook the disparity between the product of marginals and the joint characteristic functions. This can lead to less robust feature representations. In this paper, we introduce DBDC-SSL, a method that aims to improve few-shot visual recognition models by learning a feature extractor that produces image representations that are more robust. To improve the robustness of the model, we integrate DeepBDC (DBDC) during the training process to learn better feature embeddings by effectively computing the disparity between product of the marginals and joint characteristic functions of the features. To reduce overfitting and improve the generalization of the model, we utilize an auxiliary rotation loss for self-supervised learning (SSL) in the training of the feature extractor. The auxiliary rotation loss is derived from a pretext task, where input images undergo rotation by predefined angles, and the model classifies the rotation angle based on the features it generates. Experimental results demonstrate that DBDC-SSL is able to outperform current state-of-the-art methods on 4 common few-shot image classification benchmark, which are miniImageNet, tieredImageNet, CUB and CIFAR-FS. For 5-way 1-shot and 5-way 5-shot tasks respectively, the proposed DBDC-SSL achieved the accuracy of 68.64±0.43 and 86.02±0.28 on miniImageNet, 73.88±0.48 and 89.03±0.29 on tieredImageNet, 84.67±0.39 and 94.76±0.16 on CUB, and 75.60±0.44 and 88.49±0.31 on CIFAR-FS.

The balance held by Brownian motion between temporal regularity and randomness is embodied in a remarkable way by Levy's forgery of continuous functions. Here we describe how this property can be extended to forge arbitrary dependences between two statistical systems, and then establish a new Brownian independence test based on fluctuating random paths. We also argue that this result allows revisiting the theory of Brownian covariance from a physical perspective and opens the possibility of engineering nonlinear correlation measures from more general functional integrals.

Due to the variability of working conditions and the scarcity of fault samples, the existing diagnosis models still have a big gap under the condition of covering more practical application scenarios. Therefore, it is of great significance to study an intelligent diagnosis scheme that takes few samples in the training source domain and zero samples in the test target domain (FST-ZST) into account. A Brownian correlation metric prototypical network (BCMPN) algorithm based on a multi-scale mask preprocessing mechanism is proposed for the above problem. First, this paper constructs a multi-scale mask preprocessing mechanism (MMP) to improve the optimization starting point. Second, the multi-scale feature embedding is realized through the dilation convolution module and the effective light channel attention (ELCA) module. Third, based on the Brownian distance similarity measurement, we learn the feature representation by measuring the difference between the joint feature function and the edge product in the field of diagnosis. Finally, based on the gear data set of the Connecticut university (UConn) and the data collected in the laboratory, it is proved that the BCMPN has better performance in the problem of FST-ZST. [ABSTRACT FROM AUTHOR]

We introduce a novel approach to sufficient dimension-reduction problems using distance covariance. Our method requires very mild conditions on the predictors. It estimates the central subspace effectively even when many predictors are categorical or discrete. Our method keeps the model-free advantage without estimating link function. Under regularity conditions, root-nconsistency and asymptotic normality are established for our estimator. We compare the performance of our method with some existing dimension-reduction methods by simulations and find that our method is very competitive and robust across a number of models. We also analyze the Auto MPG data to demonstrate the efficacy of our method. Supplemental materials for this article are available online. [ABSTRACT FROM AUTHOR]

Abstract: We introduce a new method for estimating the direction in single-index models via distance covariance. Our method keeps model-free advantage as a dimension reduction approach. In addition, no smoothing technique is needed, which enables our method to work efficiently when many predictors are discrete or categorical. Under regularity conditions, we show that our estimator is root- consistent and asymptotically normal. We compare the performance of our method with some dimension reduction methods and the single-index estimation method by simulations and show that our method is very competitive and robust across a number of models. Finally, we analyze the UCI Adult Data Set to demonstrate the efficacy of our method. [Copyright &y& Elsevier]