In this paper,the authors propose a nonlinear dimension reduction technique based on Fréchet inverse regression to achieve sufficient dimension reduction for responses in metric spaces and predictors in Riemannia...In this paper,the authors propose a nonlinear dimension reduction technique based on Fréchet inverse regression to achieve sufficient dimension reduction for responses in metric spaces and predictors in Riemannian manifolds.The authors rigorously establish statistical properties of the estimators,providing formal proofs of their consistency and asymptotic behaviors.The effectiveness of our method is demonstrated through extensive simulations and applications to real-world datasets which highlight its practical utility for complex data with non-Euclidean structures.展开更多
文摘In this paper,the authors propose a nonlinear dimension reduction technique based on Fréchet inverse regression to achieve sufficient dimension reduction for responses in metric spaces and predictors in Riemannian manifolds.The authors rigorously establish statistical properties of the estimators,providing formal proofs of their consistency and asymptotic behaviors.The effectiveness of our method is demonstrated through extensive simulations and applications to real-world datasets which highlight its practical utility for complex data with non-Euclidean structures.
文摘合成孔径雷达(synthetic aperture radar,SAR)图像分类作为SAR图像应用的重要底层任务受到了广泛关注与研究。SAR图像分类是处理和分析遥感图像的重要手段,在环境监测、目标侦察和地质勘探等任务中发挥着关键作用,但是目前基于深度学习的SAR图像分类任务存在小样本问题。本文针对小样本SAR图像分类方法进行全面的论述和分析。1)介绍了SAR图像分类任务的重要性和早期的SAR图像分类方法,并阐述了小样本SAR图像分类任务的必要性。2)介绍了小样本SAR图像分类任务的定义、常用的数据集、评价指标和应用。3)整理了各类方法的贡献点和使用的数据集,将已有的小样本SAR图像分类方法分为基于迁移学习的方法、基于元学习的方法、基于度量学习的方法和综合性方法 4类。根据分类总结了4类方法存在的缺陷,为后续工作提供了一定的参考。在统一的框架内测试了16种可见光数据集方法迁移到SAR图像数据集上的分类性能,并从分类精度和运行时间两个方面综合评估了小样本学习模型迁移效果。该项工作利用SAR图像分类通用数据集MSTAR(moving and stationary target acquisition and recognition)完成,极大地补充了小样本SAR图像分类任务的测评基准。4)对小样本SAR图像分类方法的发展趋势进行了展望,提出了未来可能的一些严峻挑战。
