多分类光滑支持向量机及Gabor滤波应用研究

在传统SVM的分类求解算法中,严格凸的无约束最优化问题中单变量函数x 是不可微的。将原来不可微的模型变为可微的模型,可以使用通常的最优化的算法进行求解。Gabor滤波器采用不同方向、不同尺度,对烘焙面包切片区域灰度图像直接进行小波变换,用能量均值"和均方差#来表示灰度图像的纹理特征。针对样本数少的特点,提出使用多分类光滑支持向量机的方法实现对烘焙面包品质的快速分类。实验结果表明了该方法的实用性和可行性。     

Matrix conditioning and nonlinear optimization

In a series of recent papers, Oren, Oren and Luenberger, Oren and Spedicato, and Spedicato have developed the self-scaling variable metric algorithms. These algorithms alter Broyden's single parameter family of approximations to the inverse Hessian to a double parameter family. Conditions are given on the new parameter to minimize a bound on the condition number of the approximated inverse Hessian while insuring improved step-wise convergence.Davidon has devised an update which also minimizes the bound on the condition number while remaining in the Broyden single parameter family.This paper derives initial scalings for the approximate inverse Hessian which makes members of the Broyden class self-scaling. The Davidon, BFGS, and Oren—Spedicato updates are tested for computational efficiency and stability on numerous test functions, with the results indicating strong superiority computationally for the Davidon and BFGS update over the self-scaling update, except on a special class of functions, the homogeneous functions.