最小二乘支持向量机的一种稀疏化算法

介绍了一种稀疏化最小二乘支持向量机的剪枝算法。由于支持值图谱中小的支持值所对应的训练样本在算法执行阶段所起的作用较小,所以删除它们不会引起性能的显著下降。仿真实验表明,该算法不但简单、易于实现,而且能够保持良好的分类性能。     

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．     

Digital Least Squares Support Vector Machines

This paper presents a very simple digital architecture that implements a Least-Squares Support Vector Machine. The simplicity of the whole system and its good behavior when used to solve classification problems hold good prospects for the application of such a kind of learning machines to build embedded systems.     

最小二乘双支持向量机的在线学习算法

针对具有两个非并行分类超平面的最小二乘双支持向量机,提出了一种在线学习算法。通过利用矩阵求逆分解引理,所提在线学习算法能充分利用历史的训练结果,避免了大型矩阵的求逆计算过程,从而降低了计算的复杂性。仿真结果验证了所提学习算法的有效性。     

Generalized Predictive Control with Online Least Squares Support Vector Machines

This paper proposes a practical generalized predictive control （GPC） algorithm based on online least squares support vector machines （LS-SVM） which can deal with nonlinear systems effectively. At each sampling period the algorithm recursively modifies the model by adding a new data pair and deleting the least important one out of the consideration on realtime property. The data pair deleted is determined by the absolute value of lagrange multiplier from last sampling period. The paper gives the recursive algorithm of model parameters when adding a new data pair and deleting an existent one, respectively, and thus the inversion of a large matrix is avoided and the memory can be controlled by the algorithm entirely. The nonlinear LS-SVM model is applied in GPC algorithm at each sampling period. The experiments of generalized predictive control on pH neutralizing process show the effectiveness and practicality of the proposed algorithm.     

最小二乘支持向量机在医疗数据分析中的应用

以医疗数据为应用对象,应用网格搜索和交叉验证的方法选择参数,建立最小二乘支持向量机分类器,进行实际验证,并与使用K近邻分类器(K-NN)和C4.5决策树两种方法的结果进行比较.结果表明,LS-SVM分类器取得较高的准确率,表明最小二乘支持向量机在医疗诊断研究中具有很大的应用潜力.     

Benchmarking Least Squares Support Vector Machine Classifiers

In Support Vector Machines (SVMs), the solution of the classification problem is characterized by a (convex) quadratic programming (QP) problem. In a modified version of SVMs, called Least Squares SVM classifiers (LS-SVMs), a least squares cost function is proposed so as to obtain a linear set of equations in the dual space. While the SVM classifier has a large margin interpretation, the LS-SVM formulation is related in this paper to a ridge regression approach for classification with binary targets and to Fisher's linear discriminant analysis in the feature space. Multiclass categorization problems are represented by a set of binary classifiers using different output coding schemes. While regularization is used to control the effective number of parameters of the LS-SVM classifier, the sparseness property of SVMs is lost due to the choice of the 2-norm. Sparseness can be imposed in a second stage by gradually pruning the support value spectrum and optimizing the hyperparameters during the sparse approximation procedure. In this paper, twenty public domain benchmark datasets are used to evaluate the test set performance of LS-SVM classifiers with linear, polynomial and radial basis function (RBF) kernels. Both the SVM and LS-SVM classifier with RBF kernel in combination with standard cross-validation procedures for hyperparameter selection achieve comparable test set performances. These SVM and LS-SVM performances are consistently very good when compared to a variety of methods described in the literature including decision tree based algorithms, statistical algorithms and instance based learning methods. We show on ten UCI datasets that the LS-SVM sparse approximation procedure can be successfully applied.     

Least Squares Support Vector Machine Classifiers

In this letter we discuss a least squares version for support vector machine (SVM) classifiers. Due to equality type constraints in the formulation, the solution follows from solving a set of linear equations, instead of quadratic programming for classical SVM's. The approach is illustrated on a two-spiral benchmark classification problem.     

基于在线最小二乘支持向量机的广义预测控制

This paper proposes a practical generalized predictive control (GPC) algorithm based on online least squares support vector machines (LS-SVM) which can deal with nonlinear systems effectively. At each sampling period the algorithm recursively modifies the model by adding a new data pair and deleting the least important one out of the consideration on realtime property. The data pair deleted is determined by the absolute value of lagrange multiplier from last sampling period. The paper gives the recursive algorithm of model parameters when adding a new data pair and deleting an existent one, respectively, and thus the inversion of a large matrix is avoided and the memory can be controlled by the algorithm entirely. The nonlinear LS-SVM model is applied in GPC algorithm at each sampling period. The experiments of generalized predictive control on pH neutralizing process show the effectiveness and practicality of the proposed algorithm.     

基于最小二乘支持向量机的短期电力负荷预测

提出了结合遗传算法(Genetic Algorithm,GA)和最小二乘支持向量机(Least Squares Support Vector Machines,LS-SVM)的短期电力负荷预测。由于影响负荷预测因素的复杂性和最小二乘支持向量机参数选择的不确定性,提出了采用遗传算法同时对电力负荷训练样本进行特征提取和最小二乘支持向量机的参数选择,然后利用提取出的数据序列和选择的参数,建立最小二乘支持向量机预测模型。通过实际算例分析,证明了该算法可以改善预测模型的精度和泛化能力。     

最小二乘支持向量机算法研究

1 引言支持向量机(SVM,Support Vector Machines)是基于结构风险最小化的统计学习方法,它具有完备的统计学习理论基础和出色的学习性能,在模式识别和函数估计中得到了有效的应用(Vapnik,1995,1998)。支持向量机方法一方面通过把数据映射到高维空间,解决原始空间中数据线性不可分问题;另一方面,通过构造最优分类超平面进行数据分类。神经网络通过基于梯度迭代的方法进行数据学习,容易陷入局部最小值,支持向量机是通过解决一个二次规划问题,来获得     

基于LS-SVM的小样本费用智能预测

最小二乘支持向量机引入最小二乘线性系统到支持向量机中,代替传统的支持向量机采用二次规划方法解决函数估计问题。该文推导了用于函数估计的最小二乘支持向量机算法,构建了基于最小二乘支持向量机的智能预测模型,并对机载电子设备费用预测进行了研究。结果表明最小二乘支持向量机具有比多元对数回归更高的小样本费用预测精度。     

基于稀疏化LS-SVM的宽频段波达方向估计

天线阵列的宽频段测向特性十分复杂,使采用智能学习的方法对波达方向进行估计时,面临着一个海量数据的复杂学习问题.采用LS-SVM建立来波方位估计模型,对LS-SVM的支持向量进行稀疏化,利用支持度高的支持向量作为训练样本,并通过二次学习获取了天线阵列的复杂测向能力,实现了宽频段波达方向的估计.实验结果表明,用稀疏化的支持向量进行二次学习,能显著提高来波方位估计的精度,在宽频段来波方位估计中有巨大的应用价值.     

基于最小二乘支持向量机和混沌优化的非线性预测控制

针对非线性多入多出（MIMO）系统,提出一种基于最小二乘支持向量机（LSSVM）和混沌优化的预测 控制策略．预测模型是预测控制的三要素之一．本文给出了基于混沌优化的Chaos-LSSVM 算法,在可行域内反复搜 索,从而得到最优的LSSVM 算法参数,以及最优的LSSVM 模型．在线优化是另一个要素．提出了基于变尺度混沌 优化的MSC-MPC（变尺度混沌－模型预测控制）算法,可根据控制误差的大小,决定是否缩小搜索范围,从而迅速 收敛到最优解．该算法计算简单,容易实现,避免了同类方法复杂的求导、求逆运算．仿真结果显示：Chaos-LSSVM 算法和MSC-MPC 算法分别具有良好的建模、控制性能．     

细菌群体趋药性算法优化LS_SVM参数方法

针对支持向量机的参数选择问题,本文提出了一种采用细菌群体趋药性智能优化算法优化最小二乘支持向量机参数的方法。细菌群体趋药性智能优化算法引入了群体信息交互策略,单个细菌不仅利用自身信息随机移动,而且细菌群体之间交换种群的信息,有效地改善了个体移动时的随机性和盲目性,加强了细菌趋于最优的移动策略。该方法提高了支持向量机的参数选择效率,避免了人为设定参数的不足,大大缩短了优化时间。经过细菌群体趋药性智能优化算法优化得到的最小二乘支持向量机的参数对,用于测试样本的多分类实验和函数拟合实验,其分类结果和函数拟合效果验证了本文方法的有效性。     

基于最小二乘支持向量机的无线网络信道检测

为了获得理想的无线网络信息检测结果,提出了基于最小二乘支持向量机的无线网络信道机制.首先对当前无线网络信道检测的研究现状进行分析,并建立无线网络信道检测的假设模型,然后采用最小二乘支持向量机构建无线网络信道检测模型,并通过粒子群算法对最小二乘支持向量机参数进行优化,最后在Matlab 2014平台上进行了无线网络信道检测的仿真实验,以验证无线网络信道检测的有效性.结果表明,最小二乘支持向量机获得了高精度的无线网络信道检测结果,无线网络的数据传输成功率得以改善,大幅度降低了数据传输的误码率,在相同实验条件下,无线网络信道检测结果明显高于当前经典检测机制,验证本文机制的优越性.     

动态加权最小二乘支持向量机

提出一种基于动态加权最小二乘支持向量机（LS—SVM）的时间序列预测方法．动态加权LS—SVM能够跟踪时变非线性系统的动态特性,适合于系统辨识和时间序列预测;同时采用鲁棒方法确定权系数,以减小噪声的影响．将动态加权LS-SVM算法应用于工业PTA氧化过程中的4-CBA浓度预测,结果显示,动态加权LS—SVM预测精度高,能够有效减小噪声的影响．     

New Least Squares Support Vector Machines Based on Matrix Patterns

Support vector machine (SVM), as an effective method in classification problems, tries to find the optimal hyperplane that maximizes the margin between two classes and can be obtained by solving a constrained optimization criterion using quadratic programming (QP). This QP leads to higher computational cost. Least squares support vector machine (LS-SVM), as a variant of SVM, tries to avoid the above shortcoming and obtain an analytical solution directly from solving a set of linear equations instead of QP. Both SVM and LS-SVM operate directly on patterns represented by vector, i.e., before applying SVM or LS-SVM to a pattern, any non-vector pattern such as an image has to be first vectorized into a vector pattern by some techniques like concatenation. However, some implicit structural or local contextual information may be lost in this transformation. Moreover, as the dimension d of the weight vector in SVM or LS-SVM with the linear kernel is equal to the dimension d ₁ × d ₂ of the original input pattern, as a result, the higher the dimension of a vector pattern is, the more space is needed for storing it. In this paper, inspired by the method of feature extraction directly based on matrix patterns and the advantages of LS-SVM, we propose a new classifier design method based on matrix patterns, called MatLSSVM, such that the new method can not only directly operate on original matrix patterns, but also efficiently reduce memory for the weight vector (d) from d ₁ × d ₂ to d ₁ + d ₂. However like LS-SVM, MatLSSVM inherits LS-SVM’s existence of unclassifiable regions when extended to multi-class problems. Thus with the fuzzy version of LS-SVM, a corresponding fuzzy version of MatLSSVM (MatFLSSVM) is further proposed to remove unclassifiable regions effectively for multi-class problems. Experimental results on some benchmark datasets show that the proposed method is competitive in classification performance compared to LS-SVM, fuzzy LS-SVM (FLS-SVM), more-recent MatPCA and MatFLDA. In addition, more importantly, the idea used here has a possibility of providing a novel way of constructing learning model.     

基于LSSVM的混沌时间序列的多步预测

结合相空间重构理论和统计学习理论,实现混沌时间序列的多步预测．采用擞熵率法求得最优嵌入维数和时延参数,重构系统相空间,用最小二乘支持向量机建立渑沌时间序列的多步预测模型,并与径向基函数网络预测模型比较．结果表明,所建立的模型能够捕捉到原混沌系统的动力学特征．前者的归一化均方根预测误差远小于径向基函数网络预测模型的预测误差,泛化能力较强．其预测效果较好．     

资源约束网络中基于LSSVM的预测反馈调度

针对资源约束网络负载的动态变化,设计了一个基于最小二乘支持向量机(LSSVM)的反馈调度器.它可以周期性地监测网络资源,在线预测下一周期的可适用网络利用率,并根据预测值采用插值法得到控制回路的下一个采样周期,从而实现系统资源的动态分配.对采用固定带宽分配、基于LSSVM以及基于Elman神经网络的反馈调度进行了比较,结果表明,所提出的策略能使系统在可变负载情况下稳定运行,并在控制质量和网络服务质量之间取得平衡.