基于混合最小二乘支持向量机网络模型的非线性系统辨识

针对基于输入输出数据的非线性系统辨识问题,提出一种新的混合最小二乘支持向量机(LS-SVMs)网络模型及相应的学习算法.该算法将系统的辨识问题动态自适应的划分为若干子问题,将支持向量机(SVM)用于各子模块辨识;通过分析模型的统计学特性,给出基于整体框架优化的系统参数辨识方法.针对系统中参数相关联的特性,采用期望条件最大化(ECM)算法对其进行条件辨识,同时结合正则化理论和最小二乘法,保证各专家模块的结构风险最小化辨识原则.试验结果表明,该方法兼具良好的辨识精度和泛化性能.     

PSO并行优化LSSVR非线性黑箱模型辨识

针对非线性黑箱系统辨识中存在不确定性、高阶次,采用常规辨识方法建立其精确数学模型十分困难等问题,提出一种基于自适应粒子群算法的最小二乘支持向量机回归(PSO-LSSVR)非线性系统辨识方法.该方法采用2组自适应粒子群算法并行计算模型,分别利用自适应粒子群算法对LSSVR中的参数进行自动选取和矩阵迭代求解,既克服了传统LSSVR参数难以确定的缺点,提高了辨识精度,同时避免了复杂矩阵求逆运算,加快了计算速度.将该方法应用于船舶操纵性模型非线性系统辨识,仿真结果表明,由该方法得到的LSSVR能够有效地对系统进行建模,仿真精度高,结构简单,具有一定的理论推广意义.     

PDE Toolbox和最小二乘法在导热问题中的应用

设计金属加热的控制策略,首先要获得金属导热体的开环系统模型.针对一个带有矩形孔的金属薄板上的热传导问题,采用PDE Toolbox进行求解和仿真,并用最小二乘方法进行热传导系统的建模与仿真,以获得模型中的参数.将此参数与求解微分方程方法所得到的数据进行对比,结果表明,采用最小二乘法可以更清楚地了解金属板的外部特性,并获得输入输出信号的差分方程,而求解微分方程的方法则显示了金属板的内部特性,两种方法是等效的.     

齐次等式约束线性回归模型条件根方估计的效率

对齐次等式约束线性回归模型回归系数的约束最小二乘估计提出改进,引入一种估计的相对效率,证明在一定条件下,狭义条件根方估计、广义条件根方估计的效率均高于约束最小二乘估计的效率．     

Estimating the fundamental matrix based on least absolute deviation

The epipolar geometry is the intrinsic projective geometry between two views, and the algebraic representation of it is the fundamental matrix. Estimating the fundamental matrix requires solving an over-determined equation. Many classical approaches assume that the error values of the over-determined equation obey a Gaussian distribution. However, the performances of these approaches may decrease significantly when the noise is large and heterogeneous. This paper proposes a novel technique for estimating the fundamental matrix based on least absolute deviation (LAD), which is also known as the L₁ method. Then a linear iterative algorithm is presented. The experimental results on some indoor and outdoor scenes show that the proposed algorithm yields the accurate and robust estimates of the fundamental matrix when the noise is non-Gaussian.     

The automatic model selection and variable kernel width for RBF neural networks

The Orthogonal Least Squares (OLS) algorithm has been extensively used in basis selection for RBF networks, but it is unable to perform model selection automatically because the tolerance ρ must be specified manually. This introduces noise and it is difficult to implement in the parametric complexity of real-time system. Therefore, a generic criterion that detects the optimum number of its basis functions is proposed. In this paper, not only the Bayesian Information Criterion (BIC) method, used for fitness calculation, is incorporated into the basis function selection process of the OLS algorithm for assigning its appropriate number, but also a new method is developed to optimize the widths of the Gaussian functions in order to improve the generalization performance. The augmented algorithm is employed to the Radial Basis Function Neural Networks (RBFNN) for known and unknown noise nonlinear dynamic systems and its performance is compared with the standard OLS; experimental results show that both the efficacy of BIC for fitness calculation and the importance of proper choice of basis function widths are significant.     

Comparison of different classifier algorithms for diagnosing macular and optic nerve diseases

Abstract: The aim of this research was to compare classifier algorithms including the C4.5 decision tree classifier, the least squares support vector machine (LS-SVM) and the artificial immune recognition system (AIRS) for diagnosing macular and optic nerve diseases from pattern electroretinography signals. The pattern electroretinography signals were obtained by electrophysiological testing devices from 106 subjects who were optic nerve and macular disease subjects. In order to show the test performance of the classifier algorithms, the classification accuracy, receiver operating characteristic curves, sensitivity and specificity values, confusion matrix and 10-fold cross-validation have been used. The classification results obtained are 85.9%, 100% and 81.82% for the C4.5 decision tree classifier, the LS-SVM classifier and the AIRS classifier respectively using 10-fold cross-validation. It is shown that the LS-SVM classifier is a robust and effective classifier system for the determination of macular and optic nerve diseases.     

Recursive reduced least squares support vector regression

Combining reduced technique with iterative strategy, we propose a recursive reduced least squares support vector regression. The proposed algorithm chooses the data which make more contribution to target function as support vectors, and it considers all the constraints generated by the whole training set. Thus it acquires less support vectors, the number of which can be arbitrarily predefined, to construct the model with the similar generalization performance. In comparison with other methods, our algorithm also gains excellent parsimoniousness. Numerical experiments on benchmark data sets confirm the validity and feasibility of the presented algorithm. In addition, this algorithm can be extended to classification.     

Improving the generalization performance of RBF neural networks using a linear regression technique

In this paper we present a method for improving the generalization performance of a radial basis function (RBF) neural network. The method uses a statistical linear regression technique which is based on the orthogonal least squares (OLS) algorithm. We first discuss a modified way to determine the center and width of the hidden layer neurons. Then, substituting a QR algorithm for the traditional Gram–Schmidt algorithm, we find the connected weight of the hidden layer neurons. Cross-validation is utilized to determine the stop training criterion. The generalization performance of the network is further improved using a bootstrap technique. Finally, the solution method is used to solve a simulation and a real problem. The results demonstrate the improved generalization performance of our algorithm over the existing methods.     

基于约束最小二乘的光学遥感图像融合

在光学遥感图像融合方法中,最小二乘法常被用于求解多光谱图像拟合低分辨率全色图像的线性回归系数,但是回归系数常常出现负数,导致其物理意义不明确。针对这种实际情况,提出了基于约束最小二乘的低分辨率全色图像构造方法。通过IKONOS-2全色与多光谱图像的融合实验,结果表明：该方法所求得的回归系数具有明确物理意义,符合实际情况,并且与光谱响应函数法、最小二乘法相比,其融合质量基本保持一致,并且由于该方法不需要先验知识,故其实用性较强。