基于最小二乘支持向量机的汽轮机故障诊断

提出一种小波包分析与最小二乘支持向量机相结合的汽轮机故障诊断模型．对故障信号功率谱进行小波分解,简化了故障特征向量的提取．用二次损失函数取代支持向量机中的不敏感损失函数,将不等式约束条件变为等式约束．从而将二次规划问题转变为线性方程组的求解．选用RBF函数作为核函数。并提出对核函数的参数进行动态选取。提高了诊断的准确率．仿真结果表明该模型具有较强的非线性处理和抗干扰能力．     

基于遗传优化最小二乘支持向量机的导引头故障诊断

为提高导引头故障诊断准确率,提出了一种采用改进遗传算法优化的最小二乘支持向量机（LSSVM）构造导引头多故障分类模型的方法。该方法基于一对一策略及改进的投票法建立两层LSSVM多故障分类器,并利用一种自适应变步长搜索策略改进的遗传算法对LSSVM的核参数和正则化参数进行自动优选。通过对某型导引头实测数据的仿真并和标准SVM及BP神经网络诊断方法相比较,结果表明该方法具有更高诊断准确率和计算效率。     

An unbiased LSSVM model for classification and regression

Aiming at the common support vector machine’s biased disadvantage and computational complexity, an unbiased least squares support vector machine (LSSVM) model is proposed in this paper. The model eliminates the bias item of LSSVM by improving the form of structure risk, then the unbiased least squares support vector classifier and the unbiased least squares support vector regression are deduced. Based on this model, we design a new learning algorithm using Cholesky factorization according to the characteristic of kernel function matrix, in this way the calculation of Lagrangian multipliers is greatly simplified. Several experiments on diffenert datasets are carried out, including the common datasets classification, synthetic aperture radar image automatic target recognition and chaotic time series prediction. The experimental results of correct recognition rate and the fitting precision testify that the unbiased LSSVM model has good universal ability and fitting accuracy, better generalization capability and stability, and have a great improvement in learning speed.     

Multiclass LS-SVMs: Moderated Outputs and Coding-Decoding Schemes

A common way of solving the multiclass categorization problem is to reformulate the problem into a set of binary classification problems. Discriminative binary classifiers like, e.g., Support Vector Machines (SVMs), directly optimize the decision boundary with respect to a certain cost function. In a pragmatic and computationally simple approach, Least Squares SVMs (LS-SVMs) are inferred by minimizing a related regression least squares cost function. The moderated outputs of the binary classifiers are obtained in a second step within the evidence framework. In this paper, Bayes' rule is repeatedly applied to infer the posterior multiclass probabilities, using the moderated outputs of the binary plug-in classifiers and the prior multiclass probabilities. This Bayesian decoding motivates the use of loss function based decoding instead of Hamming decoding. For SVMs and LS-SVMs with linear kernel, experimental evidence suggests the use of one-versus-one coding. With a Radial Basis Function kernel one-versus-one and error correcting output codes yield the best performances, but simpler codings may still yield satisfactory results. This revised version was published online in August 2006 with corrections to the Cover Date.     

基于SADE的混合核LSSVM在压缩机故障预测中的应用

螺杆式制冷压缩机具有种类的多样性以及故障的复杂性，存在难以获得有效的预测模型的问题。提出了一种基于自适应差分进化算法（SADE）优化的混合核最小二乘支持向量机（LSSVM）的预测模型，该模型的SADE相比其他智能寻优算法理论，其结构简单、参数设置少且搜索能力强。在寻优过程中，SADE分别从差分策略、缩放因子、交叉概率做到了自适应，保证了寻优初期的全局搜索能力和种群多样性，提高了局部搜索能力和收敛速度；利用SADE对核参数、LSSVM参数、混合核调节参数进行寻优，提高了混合核LSSVM预测模型的精度。将该模型运用到压缩机的故障预测实验中，结果表明，该模型能有效的预测出压缩机的故障，验证了该模型的可行性。     

KPCA-LSSVM建模方法及在钢材淬透性中的应用研究

通过等式约束条件修改普通的支持向量机可以得到最小二乘支持向量机,不需要再次求解复杂的二次规划问题,提出了利用核主元分析进行特征提取,在高维特征空间中计算主元,降低样本的维数,然后用最小二乘支持向量机进行建模．仿真结果表明了该方法的有效性和优越性．     

一种新型的多元分类支持向量机

最小二乘支持向量机采用最小二乘线性系统代替传统的支持向量机采用二次规划方法解决模式识别问题。该文详细推理和分析了二元分类最小二乘支持向量机算法，构建了多元分类最小二乘支持向量机，并通过典型样本进行测试，结果表明采用多元分类最小二乘支持向量机进行模式识别是有效、可行的。     

Online chaotic time series prediction using unbiased composite kernel machine via Cholesky factorization

The kernel method has proved to be an effective machine learning tool in many fields. Support vector machines with various kernel functions may have different performances, as the kernels belong to two different types, the local kernels and the global kernels. So the composite kernel, which can bring more stable results and good precision in classification and regression, is an inevitable choice. To reduce the computational complexity of the kernel machine’s online modeling, an unbiased least squares support vector regression model with composite kernel is proposed. The bias item of LSSVR is eliminated by improving the form of structure risk in this model, and then the calculating method of the regression coefficients is greatly simplified. Simultaneously, through introducing the composite kernel to the LSSVM, the model can easily adapt to the irregular variation of the chaotic time series. Considering the real-time performance, an online learning algorithm based on Cholesky factorization is designed according to the characteristic of extended kernel function matrix. Experimental results indicate that the unbiased composite kernel LSSVR is effective and suitable for online time series with both the steep variations and the smooth variations, as it can well track the dynamic character of the series with good prediction precisions, better generalization and stability. The algorithm can also save much computation time comparing to those methods using matrix inversion, although there is a little more loss in time than that with the usage of single kernels.     

基于FOA优化混合核LSSVM的铁路货运量预测

单一核最小二乘支持向量机(LSSVM)在铁路货运量预测中难以准确描述货运量的复杂变化特征,限制了预测精度的提高。针对该问题,提出一种基于果蝇算法(FOA)优化混合核LSSVM的预测方法。以多项式核与径向基核组合的混合核函数作为LSSVM核函数,构建铁路货运量的混合核LSSVM预测模型,同时利用FOA全局寻优能力强、计算速度快等优点优化选择混合核LSSVM参数。以我国铁路货运量为例进行方法验证。结果表明,所提方法的RMSE、MAE、MAPE和THEIL值分别为8433.0、6670.8、0.0180和0.0117,均小于其他模型,FOA算法搜索混合核LSSVM参数的时间为40.2948秒,分别比GA和PSO算法减少了2.6208秒和20.7016秒,适合于铁路货运量的短期预测。     

A Kernel-Based Two-Class Classifier for Imbalanced Data Sets

Many kernel classifier construction algorithms adopt classification accuracy as performance metrics in model evaluation. Moreover, equal weighting is often applied to each data sample in parameter estimation. These modeling practices often become problematic if the data sets are imbalanced. We present a kernel classifier construction algorithm using orthogonal forward selection (OFS) in order to optimize the model generalization for imbalanced two-class data sets. This kernel classifier identification algorithm is based on a new regularized orthogonal weighted least squares (ROWLS) estimator and the model selection criterion of maximal leave-one-out area under curve (LOO-AUC) of the receiver operating characteristics (ROCs). It is shown that, owing to the orthogonalization procedure, the LOO-AUC can be calculated via an analytic formula based on the new regularized orthogonal weighted least squares parameter estimator, without actually splitting the estimation data set. The proposed algorithm can achieve minimal computational expense via a set of forward recursive updating formula in searching model terms with maximal incremental LOO-AUC value. Numerical examples are used to demonstrate the efficacy of the algorithm     

基于- 范数约束的LSSVR 多核学习算法

针对核函数选择对最小二乘支持向量机回归模型泛化性的影响, 提出一种新的基于????- 范数约束的最小二乘支持向量机多核学习算法. 该算法提供了两种求解方法, 均通过两重循环进行求解, 外循环用于更新核函数的权值, 内循环用于求解最小二乘支持向量机的拉格朗日乘数, 充分利用该多核学习算法, 有效提高了最小二乘支持向量机的泛化能力, 而且对惩罚参数的选择具有较强的鲁棒性. 基于单变量和多变量函数的仿真实验表明了所提出算法的有效性.

     

一种改进的最小二乘支持向量机及其应用

为了克服传统支持向量机训练速度慢、计算资源需求大等缺点,本文应用最小二乘支持向量机算法来解决分类问题。同时,本文指出了决策导向循环图算法的缺陷,采用自适应导向循环图思想来实现多类问题的分类。为了提高样本的学习速度,本文还将序贯最小优化算法与最小二乘支持向量机相结合,最终形成了ADAGLSSVM算法。考虑到最小二
乘支持向量机算法失去了支持向量的稀疏性,本文对支持向量作了修剪。实验结果表明,修剪后,分类器的识别精度和识别速度都得到了提高。     

稀疏最小二乘支持向量机及其应用研究

提出一种构造稀疏化最小二乘支持向量机的方法．该方法首先通过斯密特正交化法对核矩阵进 行简约,得到核矩阵的基向量组;再利用核偏最小二乘方法对最小二乘支持向量机进行回归计算,从而使最 小二乘向量机具有一定稀疏性．基于稀疏最小二乘向量机建立了非线性动态预测模型,对铜转炉造渣期吹炼 时间进行滚动预测．仿真结果表明,基于核偏最小二乘辨识的稀疏最小二乘支持向量机具有计算效率高、预 测精度好的特点．     

Functional iterative approaches for solving support vector classification problems based on generalized Huber loss

Classical support vector machine (SVM) and its twin variant twin support vector machine (TWSVM) utilize the Hinge loss that shows linear behaviour, whereas the least squares version of SVM (LSSVM) and twin least squares support vector machine (LSTSVM) uses L₂-norm of error which shows quadratic growth. The robust Huber loss function is considered as the generalization of Hinge loss and L₂-norm loss that behaves like the quadratic L₂-norm loss for closer error points and the linear Hinge loss after a specified distance. Three functional iterative approaches based on generalized Huber loss function are proposed in this paper to solve support vector classification problems of which one is based on SVM, i.e. generalized Huber support vector machine and the other two are in the spirit of TWSVM, namely generalized Huber twin support vector machine and regularization on generalized Huber twin support vector machine. The proposed approaches iteratively find the solutions and eliminate the requirements to solve any quadratic programming problem (QPP) as for SVM and TWSVM. The main advantages of the proposed approach are: firstly, utilize the robust Huber loss function for better generalization and for lesser sensitivity towards noise and outliers as compared to quadratic loss; secondly, it uses functional iterative scheme to find the solution that eliminates the need to solving QPP and also makes the proposed approaches faster. The efficacy of the proposed approach is established by performing numerical experiments on several real-world datasets and comparing the result with related methods, viz. SVM, TWSVM, LSSVM and LSTSVM. The classification results are convincing.

     

基于改进PSO优化LSSVM的MEMS陀螺随机漂移预测

提出一种基于改进粒子群算法（PSO）优化最小二乘支持向量机（LSSVM）的MEMS陀螺随机漂移的预测模型建立方法。该方法首先应用最小二乘支持向量机对MEMS陀螺随机漂移建立预测模型,然后应用改进粒子群算法对该模型进行优化,最后应用参数优化后的LSSVM预测模型对随机漂移进行预测。该方法不仅解决了支持向量机训练速度慢和所需计算资源多的问题,而且文中提出的改进的惯性权值递减策略使PSO算法在全局或局部搜索能力上的侧重具有更好的适应度。实验结果表明,该预测模型可以有效地进行陀螺随机漂移的预测,且预测效果优于基本PSO优化的最小二乘支持向量机。     

Evolving Least Squares Support Vector Machines for Stock Market Trend Mining

In this paper, an evolving least squares support vector machine (LSSVM) learning paradigm with a mixed kernel is proposed to explore stock market trends. In the proposed learning paradigm, a genetic algorithm (GA), one of the most popular evolutionary algorithms (EAs), is first used to select input features for LSSVM learning, i.e., evolution of input features. Then, another GA is used for parameters optimization of LSSVM, i.e., evolution of algorithmic parameters. Finally, the evolving LSSVM learning paradigm with best feature subset, optimal parameters, and a mixed kernel is used to predict stock market movement direction in terms of historical data series. For illustration and evaluation purposes, three important stock indices, S&P 500 Index, Dow Jones Industrial Average (DJIA) Index, and New York Stock Exchange (NYSE) Index, are used as testing targets. Experimental results obtained reveal that the proposed evolving LSSVM can produce some forecasting models that are easier to be interpreted by using a small number of predictive features and are more efficient than other parameter optimization methods. Furthermore, the produced forecasting model can significantly outperform other forecasting models listed in this paper in terms of the hit ratio. These findings imply that the proposed evolving LSSVM learning paradigm can be used as a promising approach to stock market tendency exploration.     

最小二乘隐空间支持向量机

在隐空间中采用最小二乘损失函数,提出了最小二乘隐空间支持向量机（LSHSSVMs）．同隐空间支持向量机（HSSVMs）一样,最小二乘隐空间支持向量机不需要核函数满足正定条件,从而扩展了支持向量机核函数的选择范围．由于采用了最小二乘损失函数,最小二乘隐空问支持向量机产生的优化问题为无约束凸二次规划,这比隐空间支持向量机产生的约束凸二次规划更易求解．仿真实验结果表明所提算法在计算时间和推广能力上较隐空间支持向量机存在一定的优势．     

基于最小二乘支持向量回归的水质预测

水质系统是一个开放的、复杂的、非线性动力学系统,具有时变复杂性,针对水质预测方法的研究虽然已经取得了一些成果,但也存在预测精度与计算复杂度等难题。为此,本文提出一种基于最小二乘支持向量回归的水质预测算法。支持向量机是机器学习中一种常用的分类模型,通过核函数将非线性数据从低维映射到高维空间,在高维空间实现线性分类和回归,最小二乘支持向量回归（LS-SVR）利用所有的样本参与回归拟合,使得回归的损失函数不再只与小部分支持向量样本有关,而是由所有样本参与学习修正误差,提高预测精度;同时该算法将标准SVR求解问题由不等式的约束条件及凸二次规划问题转化成线性方程组来求解,提高了运算速度,解决了非线性复杂特性的水质预测问题。     

基于二阶振荡微粒群最小二乘支持向量机的物流需求预测

为了提高物流需求的预测精度,在分析物流需求影响因素基础上,建立了物流需求的二阶振荡微粒群最小二乘支持向量机预测模型。利用最小二乘支持向量机(LSSVM)描述物流需求与其影响因素间的复杂非线性关系,并通过二阶振荡微粒群(TOOPSO)算法优化选择LSSVM参数。实例分析表明,模型具有较高的预测精度,TOOPSO算法搜索LSSVM最优参数时间明显少于传统交叉验证法,是一种有效的物流需求预测方法。     

多尺度最小二乘小波支持向量机的回归建模

普通最小二乘支持向量机算法用于多尺度回归建模时精度较低。针对该问题,选取墨西哥草帽小波函数作为最小二乘支持向量机的核函数,设计一种基于小波核的多尺度最小二乘小波支持向量机。在此基础上,通过解二次优化问题求出多尺度回归建模问题的全局最优解,最终得出的多尺度回归模型能够有效地逼近多尺度信号。仿真结果表明,该算法具有较高的精度。