基于类内超平面的模糊支持向量机

分析基于样本与类中心距离设计模糊支持向量机隶属度函数的缺点,使用类内超平面代替类中心,提出基于样本到超平面距离的隶属度函数设计方法.该方法降低隶属度函数对样本集几何形状的依赖,提高模糊支持向量机的泛化能力.最后数值实验表明,与传统的支持向量机和现有的3种不同隶属度函数的模糊支持向量机相比,新隶属度函数可达到最好的分类效果而且速度快.     

基于尺度核函数的最小二乘支持向量机

支持向量机的核函数一直是影响其学习效果的重要因素.本文基于小波分解理论和支持向量机核函数的条件,提出一种多维允许支持向量尺度核函数.该核函数不仅具有平移正交性,且可以以其正交性逼近二次可积空间上的任意曲线,从而提升支持向量机的泛化性能.在尺度函数作为支持向量核函数的基础之上,提出基于尺度核函数的最小二乘支持向量机(LS-SSVM).实验结果表明,LS-SSVM在同等条件下比传统支持向量机的学习精度更高,因而更适用于复杂函数的学习问题.     

一种基于Morlet小波核的约简支持向量机

针对支持向量机（SVM）的训练数据量仅局限于较小样本集的问题,结合Morlet小波核函数,提出了一种基于Morlet小波核的约倚支持向量机（MWRSVM—DC）．算法的核心是通过密度聚类寻找聚类中每个簇的边缘点作为约倚集合,并利用该约倚集合寻找支持向量．实验表明,利用小波核,该算法不仅提高了分类的准确率,而且提高了整体分类效率．     

一种新的模糊支持向量机

基于类中心设计隶属度函数的模糊支持向量机能有效地解决支持向量机对噪声或孤立点敏感度高的问题,但是,由于它对支持向量赋予较小的隶属度,从而降低了其分类作用。基于此,提出一种新的隶属度函数设计方法;同时,针对模糊支持向量机普遍存在因核函数计算量大,而导致训练时间长的问题,通过使用一种高效的截集模糊C-均值聚类方法对训练样本进行聚类,然后以聚类中心作为样本进行训练,以减少训练样本来提高训练速度。根据上述新的隶属度函数设计方法和截集模糊C-均值聚类方法,构建了一种基于截集模糊C-均值聚类并改进了隶属度函数的模糊支持向量机,数值试验表明这种新的模糊支持向量机有效地提高了训练速度和分类精度。     

基于插值的核函数构造

近年来，统计学习(SLT)和支持向量机(SVM)理论的研究日益受到当前国际机器学习领域的重视．有关核函数的研究则一直是研究的重点．这是因为不同的核函数会导致SVM的泛化能力有很大的不同．如何根据所给数据选择合适的核函数成为人们所关注的核心问题．该文首先指出满足Mercer条件的核函数的具体表达式并非问题关键，在此基础上，该文进一步提出利用散乱数据插值的办法确定特征空间中感兴趣点的内积值以代替传统核函数的一般表达式所起的作用．实验表明该方法不仅能够有效改善支持向量机的设计训练过程中的不确定性，而且泛化能力要优于绝大部分的基于传统核函数的支持向量机．     

基于粒子群算法和支持向量机的故障诊断研究

支持向量机是采用结构风险最小化原则代替传统统计学中的基于大样本的经验风险最小化原则的新型机器学习方法,具有出色的学习分类能力和推广能力,广泛地应用于模式识别和函数拟合中;支持向量机中核函数的参数选择非常重要,它决定着故障诊断的精确度;为了提高电气设备故障诊断的精度和效率,将粒子群优化算法和最小二乘支持向量机相结合,提出了一种基于粒子群支持向量机的故障诊断方法,能够实现对核函数的σ参数进行快速动态选取,提高故障诊断的准确率和效率;实验表明,该方法能够有效地找出合适的核参数,并能取得较好的分类效果。     

改进的增量式SVM在网络入侵检测中的应用

针对传统的增量式支持向量机(Incremental Support Vector Machine,ISVM)在处理数据集时易受数据噪声和学习过程中振荡问题影响的缺点,将改进的核函数U-RBF和构造备用集的同心圆方法相结合,提出了基于备用集的增量式支持向量机(Reserved Set-Incremental Support Vector Machine,RS-ISVM)方法.该方法首先将特征属性的均值和均方差值嵌入到核函数RBF中,并通过同心圆方法将后续学习过程中最有可能成为支持向量的样本划入备用集.入侵检测实验证明RS-ISVM能够降低学习过程的振荡现象,提高了学习的速度,有非常好的性能和可靠性.     

超核函数支持向量机

支持向量机是当前机器学习、模式识别和数据挖掘等领域的重要学习方法,核函数的构造是研究和应用支持向量机的关键问题.针对这一问题,提出了核函数构造的组合理论,定义了超核函数概念,并通过多项式组合现有核函数构造出一类超核函数.具体地,首先分析了一般核函数存在的过学习和欠学习现象,然后证明了组合理论构造的核函数的Mercer性质,并通过在仿真数据集和标准数据集上的对比实验,验证了超核函数的性能.理论分析和实验结果阐明了所提出的超核函数组合构造理论的合理性和有效性,开拓了模型选择组合方法的研究途径.     

模糊多核支持向量机研究进展

模糊多核支持向量机将模糊支持向量机与多核学习方法结合,通过构造隶属度函数和利用多个核函数的组合形式有效缓解了传统支持向量机模型对噪声数据敏感和多源异构数据学习困难等问题,广泛应用于模式识别和人工智能领域.综述了模糊多核支持向量机的理论基础及其研究现状,详细介绍模糊多核支持向量机中的关键问题,即模糊隶属度函数设计与多核学习方法,最后对模糊多核支持向量机算法未来的研究进行展望.     

自适应模糊支持向量机算法研究

一个有效的核方法通常取决于选择一个合适的核函数。目前研究核方法的热点是从数据中自动地进行核学习。提出基于最优分类标准的核学习方法,这个标准类似于线性鉴别分析和核Fisher判别式。并把此算法应用于模糊支持向量机多类分类器设计上,在ORL人脸数据集和Iris数据集上的实验验证了该算法的可行性。     

A wavelet extreme learning machine

Extreme learning machine (ELM) has been widely used in various fields to overcome the problem of low training speed of the conventional neural network. Kernel extreme learning machine (KELM) introduces the kernel method to ELM model, which is applicable in Stat ML. However, if the number of samples in Stat ML is too small, perhaps the unbalanced samples cannot reflect the statistical characteristics of the input data, so that the learning ability of Stat ML will be influenced. At the same time, the mix kernel functions used in KELM are conventional functions. Therefore, the selection of kernel function can still be optimized. Based on the problems above, we introduce the weighted method to KELM to deal with the unbalanced samples. Wavelet kernel functions have been widely used in support vector machine and obtain a good classification performance. Therefore, to realize a combination of wavelet analysis and KELM, we introduce wavelet kernel functions to KELM model, which has a mix kernel function of wavelet kernel and sigmoid kernel, and introduce the weighted method to KELM model to balance the sample distribution, and then we propose the weighted wavelet–mix kernel extreme learning machine. The experimental results show that this method can effectively improve the classification ability with better generalization. At the same time, the wavelet kernel functions perform very well compared with the conventional kernel functions in KELM model.     

回归最小二乘支持向量机的增量和在线式学习算法

首先给出回归最小二乘支持向量机的数学模型,并分析了它的性质,然后在此基础上根据分块矩阵计算公式和核函数矩阵本身的特点设计了支持向量机的增量式学习算法和在线学习算法．该算法能充分利用历史的训练结果,减少存储空间和计算时间．仿真实验表明了这两种学习方法的有效性．     

基于模糊sigmoid核的支持向量机回归建模

支持向量机中对核函数的要求为对称的半正定矩阵.来自于神经网络的sigm o id核函数在其参数满足一定条件时才成为半正定矩阵,但是这种核函数在SVM中却有很多成功的应用.本文将sigm o id核函数与模糊逻辑相结合并使其模糊化,从而简化了SVM的计算并便于用硬件实现.通过对混沌时间序列预测以及图像去噪滤波器两个实例的实验研究发现,使用模糊sigm o id核函数可以使SVM回归建模在损失较小精度的代价下,较大地降低平均CPU执行时间,便于硬件实现     

Kernel based support vector machine via semidefinite programming: Application to medical diagnosis

Support vector machine (SVM) is a well sound learning method and a robust classification procedure. Choosing a suitable kernel function in SVM is crucial for obtaining good performance; the difficulty is how to choose a suitable data transformation for the given problem. To this end, multiple kernel matrices, each of them corresponding to a given similarity measure, can be linearly combined. In this paper, the optimal kernel matrix, obtained as linear combination of known kernel matrices, is generated using a semidefinite programming approach. A suitable model formulation assures that the obtained kernel matrix is positive semidefinite and is optimal with respect to the dataset under consideration. The proposed approach has been applied to some very important medical diagnostic decision making problems and the results obtained by carrying out preliminary numerical experiments demonstrated the effectiveness of the proposed solution approach.     

Gabor-based kernel PCA with fractional power polynomial models for face recognition

This paper presents a novel Gabor-based kernel Principal Component Analysis (PCA) method by integrating the Gabor wavelet representation of face images and the kernel PCA method for face recognition. Gabor wavelets first derive desirable facial features characterized by spatial frequency, spatial locality, and orientation selectivity to cope with the variations due to illumination and facial expression changes. The kernel PCA method is then extended to include fractional power polynomial models for enhanced face recognition performance. A fractional power polynomial, however, does not necessarily define a kernel function, as it might not define a positive semidefinite Gram matrix. Note that the sigmoid kernels, one of the three classes of widely used kernel functions (polynomial kernels, Gaussian kernels, and sigmoid kernels), do not actually define a positive semidefinite Gram matrix either. Nevertheless, the sigmoid kernels have been successfully used in practice, such as in building support vector machines. In order to derive real kernel PCA features, we apply only those kernel PCA eigenvectors that are associated with positive eigenvalues. The feasibility of the Gabor-based kernel PCA method with fractional power polynomial models has been successfully tested on both frontal and pose-angled face recognition, using two data sets from the FERET database and the CMU PIE database, respectively. The FERET data set contains 600 frontal face images of 200 subjects, while the PIE data set consists of 680 images across five poses (left and right profiles, left and right half profiles, and frontal view) with two different facial expressions (neutral and smiling) of 68 subjects. The effectiveness of the Gabor-based kernel PCA method with fractional power polynomial models is shown in terms of both absolute performance indices and comparative performance against the PCA method, the kernel PCA method with polynomial kernels, the kernel PCA method with fractional power polynomial models, the Gabor wavelet-based PCA method, and the Gabor wavelet-based kernel PCA method with polynomial kernels.     

Sparse data-dependent kernel principal component analysis based on least squares support vector machine for feature extraction and recognition

Kernel learning is widely used in many areas, and many methods are developed. As a famous kernel learning method, kernel principal component analysis (KPCA) endures two problems in the practical applications. One is that all training samples need to be stored for the computing the kernel matrix during kernel learning. Second is that the kernel and its parameter have the heavy influence on the performance of kernel learning. In order to solve the above problem, we present a novel kernel learning namely sparse data-dependent kernel principal component analysis through reducing the training samples with sparse learning-based least squares support vector machine and adaptive self-optimizing kernel structure according to the input training samples. Experimental results on UCI datasets, ORL and YALE face databases, and Wisconsin Breast Cancer database show that it is feasible to improve KPCA on saving consuming space and optimizing kernel structure.     

Wavelet twin support vector machine

Twin support vector machine (TWSVM) is a research hot spot in the field of machine learning in recent years. Although its performance is better than traditional support vector machine (SVM), the kernel selection problem still affects the performance of TWSVM directly. Wavelet analysis has the characteristics of multivariate interpolation and sparse change, and it is suitable for the analysis of local signals and the detection of transient signals. The wavelet kernel function based on wavelet analysis can approximate any nonlinear functions. Based on the wavelet kernel features and the kernel function selection problem, wavelet twin support vector machine (WTWSVM) is proposed by this paper. It introduces the wavelet kernel function into TWSVM to make the combination of wavelet analysis techniques and TWSVM come true. The experimental results indicate that WTWSVM is feasible, and it improves the classification accuracy and generalization ability of TWSVM significantly.     

核学习机研究

该文概述了近年来机器学习研究领域的一个热点问题———核学习机。首先分析了核方法的主要思想,然后着重介绍了几种新近发展的核学习机,包括支持向量机、核的Fisher判别分析等有监督学习算法及核的主分量分析等无监督学习算法,最后讨论了其应用及前景展望。     

两阶段不定核支持向量机

近年来,在机器学习的各个领域出现了越来越多不定的度量核矩阵,使得不定核支持向量机(IKSVM)得到了广泛关注。但是,现有IKSVM算法通常不能较好地解决高维数据所带来的信息冗余和样本稀疏等问题。针对此研究现状,对现有主流的IKSVM算法进行了研究,并基于再生核Kre?n空间(RKKS)中对IKSVM问题的稳定化定义,从理论上证明了IKSVM问题的本质为不定核主成分分析(IKPCA)降维后空间中的支持向量机(SVM)问题,进一步地提出求解IKSVM问题的新型学习框架TP-IKSVM。TP-IKSVM通过将IKSVM问题的求解拆分为IKPCA和SVM两个阶段,充分地发挥了IKPCA在处理高维数据的信息冗余和样本稀疏等方面的优势,同时结合SVM以有效分类。在真实数据集上的实验结果表明,TP-IKSVM的分类精度优于现有主流的IKSVM算法。     

基于混合核函数的SVM在文本自动分类的应用

核函数是SVM的关键技术,核函数的选择将影响着学习机器的学习能力和泛化能力。不同的核函数确定了不同的非线性变换和特征空间,选取不同核函数训练SVM就会得到不同的分类效果。本文提出了一种混合的核函数[1]Kmix=λKpoly+(1-λ)Krbf,从而兼并二项式核函数及径向基核函数的优势。实验证明选用混合核函数的支持向量机,与普通核函数构造的支持向量机的评估效果进行比较,混合核函数支持向量机具有较高的分类精度。