If a spatial-domain function has a finite support,its Fourier transform is an entire function.The Taylor series expansion of an entire function converges at every finite point in the complex plane.The analytic continu...If a spatial-domain function has a finite support,its Fourier transform is an entire function.The Taylor series expansion of an entire function converges at every finite point in the complex plane.The analytic continuation theory suggests that a finite-sized object can be uniquely determined by its frequency components in a very small neighborhood.Trying to obtain such an exact Taylor expansion is difficult.This paper proposes an iterative algorithm to extend the measured frequency components to unmeasured regions.Computer simulations show that the proposed algorithm converges very slowly,indicating that the problem is too ill-posed to be practically solvable using available methods.展开更多
半监督学习方法通过少量标记数据和大量未标记数据来提升学习性能.Tri-training是一种经典的基于分歧的半监督学习方法,但在学习过程中可能产生标记噪声问题.为了减少Tri-training中的标记噪声对未标记数据的预测偏差,学习到更好的半监...半监督学习方法通过少量标记数据和大量未标记数据来提升学习性能.Tri-training是一种经典的基于分歧的半监督学习方法,但在学习过程中可能产生标记噪声问题.为了减少Tri-training中的标记噪声对未标记数据的预测偏差,学习到更好的半监督分类模型,用交叉熵代替错误率以更好地反映模型预估结果和真实分布之间的差距,并结合凸优化方法来达到降低标记噪声的目的,保证模型效果.在此基础上,分别提出了一种基于交叉熵的Tri-training算法、一个安全的Tri-training算法,以及一种基于交叉熵的安全Tri-training算法.在UCI(University of California Irvine)机器学习库等基准数据集上验证了所提方法的有效性,并利用显著性检验从统计学的角度进一步验证了方法的性能.实验结果表明,提出的半监督学习方法在分类性能方面优于传统的Tri-training算法,其中基于交叉熵的安全Tri-training算法拥有更高的分类性能和泛化能力.展开更多
基金This research is partially supported by NIH,No.R15EB024283.
文摘If a spatial-domain function has a finite support,its Fourier transform is an entire function.The Taylor series expansion of an entire function converges at every finite point in the complex plane.The analytic continuation theory suggests that a finite-sized object can be uniquely determined by its frequency components in a very small neighborhood.Trying to obtain such an exact Taylor expansion is difficult.This paper proposes an iterative algorithm to extend the measured frequency components to unmeasured regions.Computer simulations show that the proposed algorithm converges very slowly,indicating that the problem is too ill-posed to be practically solvable using available methods.
文摘半监督学习方法通过少量标记数据和大量未标记数据来提升学习性能.Tri-training是一种经典的基于分歧的半监督学习方法,但在学习过程中可能产生标记噪声问题.为了减少Tri-training中的标记噪声对未标记数据的预测偏差,学习到更好的半监督分类模型,用交叉熵代替错误率以更好地反映模型预估结果和真实分布之间的差距,并结合凸优化方法来达到降低标记噪声的目的,保证模型效果.在此基础上,分别提出了一种基于交叉熵的Tri-training算法、一个安全的Tri-training算法,以及一种基于交叉熵的安全Tri-training算法.在UCI(University of California Irvine)机器学习库等基准数据集上验证了所提方法的有效性,并利用显著性检验从统计学的角度进一步验证了方法的性能.实验结果表明,提出的半监督学习方法在分类性能方面优于传统的Tri-training算法,其中基于交叉熵的安全Tri-training算法拥有更高的分类性能和泛化能力.
