基于人工鱼群算法的孪生支持向量机

孪生支持向量机（twin support vector machine, TWSVM）是在支持向量机的基础上产生的机器学习算法,具有训练速度快、分类性能优越等优点。但是孪生支持向量机无法很好地处理参数选择问题,不合适的参数会降低分类能力。人工鱼群算法（artificial fish swarm algorithm, AFSA）是一种群智能优化算法,具有较强的全局寻优能力和并行处理能力。本文将孪生支持向量机与人工鱼群算法结合,来解决孪生支持向量机的参数选择问题。首先将孪生支持向量机的参数作为人工鱼的位置信息,同时将分类准确率作为目标函数,然后通过人工鱼的觅食、聚群、追尾和随机行为来更新位置和最优解,最后迭代结束时得到最优参数和最优分类准确率。该算法在训练过程中自动确定孪生支持向量机的参数,避免了参数选择的盲目性,提高了孪生支持向量机的分类性能。     

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．     

孪生支持向量机综述

孪生支持向量机(Twin Support Vector Machine,TWSVM)是在支持向量机(Support Vector Machine,SVM)的基础上发展而来的一种新的机器学习方法。作为一种二分类的分类器,其基本思想为寻找两个超平面,使得每一个分类面靠近本类样本点而远离另一类样本点。作为一种新兴的机器学习方法,孪生支持向量机自提出以来便引起了国内外学者的广泛关注,已经成为机器学习领域的研究热点。对孪生支持向量机的最新研究进展进行综述,首先介绍了孪生支持向量机的基本概念与基本模型;然后对近几年来新型的孪生支持向量机模型与研究进展进行了总结,并对其代表算法进行了优缺点分析和实验比较;最后对将来的研究工作进行了展望。     

Forecasting volatility based on wavelet support vector machine

One of the challenging problems in forecasting the conditional volatility of stock market returns is that general kernel functions in support vector machine (SVM) cannot capture the cluster feature of volatility accurately. While wavelet function yields features that describe of the volatility time series both at various locations and at varying time granularities, so this paper construct a multidimensional wavelet kernel function and prove it meeting the mercer condition to address this problem. The applicability and validity of wavelet support vector machine (WSVM) for volatility forecasting are confirmed through computer simulations and experiments on real-world stock data.     

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.     

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.

     

基于能量的结构化最小二乘孪生支持向量机

针对最小二乘孪生支持向量机对噪声和离群值非常敏感的问题,本文提出了一种基于能量的结构化最小二乘孪生支持向量机。首先对每个类进行聚类分析,然后计算类中各个簇的协方差矩阵并将其引入到目标函数中。其次,为了降低噪声和离群值对算法的影响,本文为每个超平面引入能量因子,在最小二乘的基础上将等式约束转换为基于能量的形式。最后采用“多对一”的策略将提出的算法用于处理多分类问题。研究结果表明:本文提出的基于能量的结构化最小二乘孪生支持向量机具有良好的分类性能。     

基于压缩感知的多尺度最小二乘支持向量机

提出一种基于压缩感知(Compressive sensing, CS)和多分辨分析(Multi-resolution analysis, MRA)的多尺度最小二乘支持向量机(Least squares support vector machine, LS-SVM). 首先将多尺度小波函数作为支持向量核, 推导出多尺度最小二乘支持向量机模型, 然后基于压缩感知理论, 利用最小二乘匹配追踪(Least squares orthogonal matching pursuit, LS-OMP)算法对多尺度最小二乘支持向量机的支持向量进行稀疏化, 最后用稀疏的支持向量实现函数回归. 实验结果表明, 本文方法利用不同尺度小波核逼近信号的不同细节, 而且以比较少的支持向量能达到很好的泛化性能, 大大降低了运算成本, 相比普通最小二乘支持向量机, 具有更优越的表现力.     

Wavelet support vector machine

An admissible support vector (SV) kernel (the wavelet kernel), by which we can construct a wavelet support vector machine (SVM), is presented. The wavelet kernel is a kind of multidimensional wavelet function that can approximate arbitrary nonlinear functions. The existence of wavelet kernels is proven by results of theoretic analysis. Computer simulations show the feasibility and validity of wavelet support vector machines (WSVMs) in regression and pattern recognition.     

最小二乘Littlewood-Paley小波支持向量机

基于小波分解理论和支持向量机核函数的条件，提出了一种多维允许支持向量核函数——Littlewood-Paley小波核函数．该核函数不仅具有平移正交性，而且可以以其正交性逼近二次可积空间上的任意曲线，从而提升了支持向量机的泛化性能．在Littlewood-Paley小波函数作为支持向量核函数的基础上，提出了最小二乘Littlewood-Paley小波支持向量机(LS-LPWSVM)．实验结果表明，LS-LPWSVM在同等条件下比最小二乘支持向量机的学习精度要高，因而更适用于复杂函数的学习问题．     

小波支持向量机在SAR图像降噪中的应用

基于支持向量回归理论和小波支持向量核函数,提出了一种新的SAR滤波方法。首先对支持向量回归方法做了分析,通过对复杂信号进行逼近实验,验证了其应用于图像滤波的可行性和合理性。之后将SAR图像看成是一个二维连续信号,将对复杂信号具有更好逼近能力的小波支持向量核函数用于SAR图像滤波,小波核函数由Morlet小波构建。实验结果表明本文提出的方法能很好的降低SAR图像噪声,而且能比传统方法更好的保持边缘。     

基于混合模糊隶属度的模糊双支持向量机研究

双支持向量机是近年提出的一种新的支持向量机.在处理模式分类问题时,双支持向量机速度远远超过传统支持向量机,而且显示出较好的推广能力.但双支持向量机没有考虑不同输入样本点可能会对分类超平面的形成产生不同影响,在某些实际问题中具有局限性.为了克服这个缺点,提出了一种基于混合模糊隶属度的模糊双支持向量机.该算法设计了一种结合距离和紧密度的模糊隶属度函数,给不同的训练样本赋予不同的模糊隶属度,构建两个最优非平行超平面,最终实现二值分类.实验证明,该模糊双支持向量机的分类性能优于传统的双支持向量机.     

基于MCKD-EEMD近似熵和TWSVM的齿轮箱故障诊断

在复杂环境下齿轮箱信号往往会淹没在噪声信号中,特征向量难以提取;为了有效地进行故障诊断,提出了基于最大相关反褶积(MCKD)总体平均经验模态分解(EEMD)近似熵和双子支持向量机(TWSVM)的齿轮箱故障诊断方法;首先采用MCKD方法对强噪声信号进行滤波处理,在采用EEMD方法对齿轮箱信号进行分解,分解后得到本征模函数(IMF)分量进行近似熵求解,得到齿轮特征向量,最后将其输入到TWSVM分类器中进行故障识别;仿真实验表明,采用MCKD-EEMD方法能够有效地提取原始信号,与其他分类器相比,TWSVM的计算时间短,分类效果好等优点。     

A novel approach to wavelet selection and tree kernel construction for diagnosis of rolling element bearing fault

A novel methodology for early diagnosis of rolling element bearing fault is employed based on continuous wavelet transform (CWT) and support vector machine (SVM). CWT is especially suited for analyzing non-stationary signals in time–frequency domain where time information is retained as well as frequency content. To better approximate non-stationary vibration signals from rolling element bearing, a wavelet choice criterion is established to select an appropriate mother wavelet for feature extraction. The Shannon wavelet is picked out of several considered wavelets. The classification tree kernels (CTK) are constructed to address nonlinear classification of the characteristic samples derived from the wavelet coefficients. By using Fuzzy pruning strategy, a large variety of classification trees are generated. The trees with diverse structures can effectively explore intrinsic information among samples. Then, the tree kernel matrices can be acquired through ensemble statistical learning, which eventually reveal the similarity of samples objectively and stably. Under such architecture of kernel methods, a classification tree kernel based support vector machine (CTKSVM) is proposed to identify bearing fault. The performance of the methodology involving CWT and CTKSVM (CWT–CTKSVM) is evaluated by cross validation and independent test. The results show that the CWT–CTKSVM totally is superior to other SVM methods with common kernels. Therefore, it is a prospective technique for detection and identification of rolling element bearing fault.     

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．     

一种新的孪生大间隔分布机算法

为了提高孪生支持向量机的泛化能力,提出一种新的孪生大间隔分布机算法,以增加间隔分布对于训练模型的影响.理论研究表明,间隔分布对于模型的泛化性能有着非常重要的影响.该算法在标准孪生支持向量机优化目标函数上增加了间隔分布的影响,间隔分布通过一阶和二阶数据统计特征来体现.在标准数据集上的实验结果表明,所提出的算法比SVM、TWSVM、TBSVM算法的分类精确度更高.     

基于小波核LS—SVM的网络流量预测

网络流量预测对大规模网络管理、规划、设计具有重要意义。支持向量机方法是近年来发展起来的新型机器学习算法,用于解决高度非线性分类及回归问题。介绍了基于小波核最小二乘支持向量机的网络流量预测方法,利用小波核函数的多分辨特性提高了支持向量机的非线性建模能力。通过对实测网络流量数据的学习,对未来网络流量进行预测。实验结果表明,取得了较好的预测效果。     

小波核支持向量机的网络入侵检测

将小波理论和统计学习运用到网络入侵检测中,使用小波核支持向量机(WSVM)对网络连接信息进行攻击检测和异常发现。仿真试验结果表明,与RBF核相比,小波核支持向量机在泛化能力和检测能力方面都有所提高。     

Robust minimum class variance twin support vector machine classifier

The recently proposed twin support vector machine (TWSVM) obtains much faster training speed and comparable performance than classical support vector machine. However, it only considers the empirical risk minimization principle, which leads to poor generalization for real-world applications. In this paper, we formulate a robust minimum class variance twin support vector machine (RMCV-TWSVM). RMCV-TWSVM effectively overcomes the shortcoming in TWSVM by introducing a pair of uncertain class variance matrices in its objective functions. As a special case, we present a special type of the uncertain class variance matrices by combining the empirical positive and negative class variance matrices. Computational results on several synthetic as well as benchmark datasets indicate the significant advantages of proposed classifier in both computational time and test accuracy.     

灰狼优化的混合参数多分类孪生支持向量机

孪生支持向量机(TWSVM)是在支持向量机(SVM)的基础上产生的一种高效二分类算法,由于现实中存在的问题大多数是多分类的,将二分类孪生支持向量机扩展到多分类孪生支持向量机(MTWSVM)是非常重要的。目前常用的MTWSVM一般是基于“一对一”策略,但该策略中各子分类器都采用相同的惩罚参数以及核参数,忽略了不同子分类器之间的差异,不能使其发挥最好的作用。通过提出一种基于混合参数的多分类孪生支持向量机(MP-MTWSVM),为不同的子分类器选取合适的参数,保持分类器的多样性,进而根据“一对一”策略构建MTWSVM。TWSVM本就面临着参数难确定的问题,而MP-MTWSVM算法又引入了大量的参数,通过灰狼算法(GWO)对MP-MTWSVM的参数进行寻优,进一步提出了基于灰狼优化的混合参数多分类孪生支持向量机(GWO-MP-MTWSVM)。通过实验表明,GWO可以快速找到各子分类器的最优参数,并进一步提升了算法的准确率。