Fuzzy functions with support vector machines

A new fuzzy system modeling (FSM) approach that identifies the fuzzy functions using support vector machines (SVM) is proposed. This new approach is structurally different from the fuzzy rule base approaches and fuzzy regression methods. It is a new alternate version of the earlier FSM with fuzzy functions approaches. SVM is applied to determine the support vectors for each fuzzy cluster obtained by fuzzy c-means (FCM) clustering algorithm. Original input variables, the membership values obtained from the FCM together with their transformations form a new augmented set of input variables. The performance of the proposed system modeling approach is compared to previous fuzzy functions approaches, standard SVM, LSE methods using an artificial sparse dataset and a real-life non-sparse dataset. The results indicate that the proposed fuzzy functions with support vector machines approach is a feasible and stable method for regression problems and results in higher performances than the classical statistical methods.     

Interval regression analysis using quadratic loss support vector machine

Support vector machines (SVMs) have been very successful in pattern recognition and function estimation problems for crisp data. This paper proposes a new method to evaluate interval linear and nonlinear regression models combining the possibility and necessity estimation formulation with the principle of quadratic loss SVM. This version of SVM utilizes quadratic loss function, unlike the traditional SVM. For data sets with crisp inputs and interval outputs, the possibility and necessity models have been recently utilized, which are based on quadratic programming approach giving more diverse spread coefficients than a linear programming one. The quadratic loss SVM also uses quadratic programming approach whose another advantage in interval regression analysis is to be able to integrate both the property of central tendency in least squares and the possibilistic property in fuzzy regression. However, this is not a computationally expensive way. The quadratic loss SVM allows us to perform interval nonlinear regression analysis by constructing an interval linear regression function in a high dimensional feature space. The proposed algorithm is a very attractive approach to modeling nonlinear interval data, and is model-free method in the sense that we do not have to assume the underlying model function for interval nonlinear regression model with crisp inputs and interval output. Experimental results are then presented which indicate the performance of this algorithm.     

Relaxed constraints support vector machine

This paper presents a new model of support vector machines (SVMs) that handle data with tolerance and uncertainty. The constraints of the SVM are converted to fuzzy inequality. Giving more relaxation to the constraints allows us to consider an importance degree for each training samples in the constraints of the SVM. The new method is called relaxed constraints support vector machines (RSVMs). Also, the fuzzy SVM model is improved with more relaxed constraints. The new model is called fuzzy RSVM. With this method, we are able to consider importance degree for training samples both in the cost function and constraints of the SVM, simultaneously. In addition, we extend our method to solve one‐class classification problems. The effectiveness of the proposed method is demonstrated on artificial and real‐life data sets.     

Support vector machines‐based generalized predictive control

In this study, we propose a novel control methodology that introduces the use of support vector machines (SVMs) in the generalized predictive control (GPC) scheme. The SVM regression algorithms have extensively been used for modelling nonlinear systems due to their assurance of global solution, which is achieved by transforming the regression problem into a convex optimization problem in dual space, and also their higher generalization potential. These key features of the SVM structures lead us to the idea of employing a SVM model of an unknown plant within the GPC context. In particular, the SVM model can be employed to obtain gradient information and also it can predict future trajectory of the plant output, which are needed in the cost function minimization block. Simulations have confirmed that proposed SVM‐based GPC scheme can provide a noticeably high control performance, in other words, an unknown nonlinear plant controlled by SVM‐based GPC can accurately track the reference inputs with different shapes. Moreover, the proposed SVM‐based GPC scheme maintains its control performance under noisy conditions. Copyright © 2006 John Wiley & Sons, Ltd.     

基于模糊支持向量机的多分类算法研究

针对支持向量机理论中的多分类问题以及SVM对噪声数据的敏感性问题,提出了一种基于二叉树的模糊支持向量机多分类算法。该算法是在基于二叉树的支持向量机多分类算法的基础上引入模糊隶属度函数,根据每个样本数据对分类结果的不同影响,通过基于KNN的模糊隶属度的度量方法计算出相应的值,由此得到不同的惩罚值,这样在构造分类超平面时,就可以忽略对分类结果不重要的数据。通过实验证明,该算法有较好的抗干扰能力和分类效果。     

基于数据域描述的模糊支持向量回归

针对支持向量机中由于噪声和孤立点带来的过拟合问题，提出了一种基于支持向量数据域描述的模糊隶属度函数模型，根据样本到特征空间最小包含超球球心的距离来确定其模糊隶属度．将提出的隶属度模型用于模糊支持向量回归中，二维数据集仿真以及工业PTA氧化过程中4-CBA浓度预测的实例表明，提出的模型可以有效减小回归误差，提高支持向量机抗噪声的能力．     

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.     

Face Recognition Using Total Margin-Based Adaptive Fuzzy Support Vector Machines

This paper presents a new classifier called total margin-based adaptive fuzzy support vector machines (TAF-SVM) that deals with several problems that may occur in support vector machines (SVMs) when applied to the face recognition. The proposed TAF-SVM not only solves the overfitting problem resulted from the outlier with the approach of fuzzification of the penalty, but also corrects the skew of the optimal separating hyperplane due to the very imbalanced data sets by using different cost algorithm. In addition, by introducing the total margin algorithm to replace the conventional soft margin algorithm, a lower generalization error bound can be obtained. Those three functions are embodied into the traditional SVM so that the TAF-SVM is proposed and reformulated in both linear and nonlinear cases. By using two databases, the Chung Yuan Christian University (CYCU) multiview and the facial recognition technology (FERET) face databases, and using the kernel Fisher's discriminant analysis (KFDA) algorithm to extract discriminating face features, experimental results show that the proposed TAF-SVM is superior to SVM in terms of the face-recognition accuracy. The results also indicate that the proposed TAF-SVM can achieve smaller error variances than SVM over a number of tests such that better recognition stability can be obtained     

Interval Fuzzy Model Identification Using$l_infty$-Norm

In this paper, we present a new method of interval fuzzy model identification. The method combines a fuzzy identification methodology with some ideas from linear programming theory. We consider a finite set of measured data, and we use an optimality criterion that minimizes the maximum estimation error between the data and the proposed fuzzy model output. The idea is then extended to modeling the optimal lower and upper bound functions that define the band which contains all the measurement values. This results in lower and upper fuzzy models or a fuzzy model with a set of lower and upper parameters. The model is called the interval fuzzy model (INFUMO). We also showed that the proposed structure uniformly approximates the band of any nonlinear function. The interval fuzzy model identification is a methodology to approximate functions by taking into account a finite set of input and output measurements. This approach can also be used to compress information in the case of large amount of data and in the case of robust system identification. The method can be efficiently used in the case of the approximation of the nonlinear functions family. If the family is defined by a band containing the whole measurement set, the interval of parameters is obtained as the result. This is of great importance in the case of nonlinear circuits' modeling, especially when the parameters of the circuits vary within certain tolerance bands     

Automatic detection of erythemato-squamous diseases using PSO–SVM based on association rules

In this paper, we develop a diagnosis model based on particle swarm optimization (PSO), support vector machines (SVMs) and association rules (ARs) to diagnose erythemato-squamous diseases. The proposed model consists of two stages: first, AR is used to select the optimal feature subset from the original feature set; then a PSO based approach for parameter determination of SVM is developed to find the best parameters of kernel function (based on the fact that kernel parameter setting in the SVM training procedure significantly influences the classification accuracy, and PSO is a promising tool for global searching). Experimental results show that the proposed AR_PSO–SVM model achieves 98.91% classification accuracy using 24 features of the erythemato-squamous diseases dataset taken from UCI (University of California at Irvine) machine learning database. Therefore, we can conclude that our proposed method is very promising compared to the previously reported results.     

贝叶斯分类器的关联向量机多模型软测量建模

为了改善软测量模型的估计精度,提出了一种基于贝叶斯分类算法和关联向量机的多模型软测量建模方法。采用贝叶斯分类器对样本数据集进行分类,并对不同类别的输入数据分别建立关联向量回归机子模型,用“切换开关”方式组合作为最终的软测量模型输出。将该方法应用于双酚A生产过程的质量指标软测量建模,仿真结果表明：与单模型支持向量机相比,该方法估计精度较高,具有一定的应用价值。     

一种基于核密度估计的模拟电路故障诊断方法

为解决模拟电路中含有噪声等异常信息给支持向量机的最优分类面建立带来的困难,提出了一种基于核密度估计方法的模拟电路故障诊断新方法。首先提取电路的时域信号统计参数作为故障特征,然后运用核密度估计方法构造模糊隶属度函数,将该隶属度函数应用到模糊支持向量机上进行故障诊断。通过训练模糊支持向量机获得故障诊断模型,实现对电路单故障和多故障的诊断分类,能有效消除特征中噪声和野点的影响。将该方法应用于CSTV滤波电路进行仿真实验,结果表明该方法能突出不同故障的特性并正确有效地诊断出多故障类型,综合诊断正确率达到95%,为模拟电路故障诊断提供了新的技术途径。     

一种新的分裂层次聚类SVM多值分类器

提出一种分裂层次聚类SVM分类树分类方法.该方法通过融合模糊聚类技术和支持向量机算法,利用分裂的层次聚类策略,有选择地重新构造学习样本集和SVM子分类器,得到了一种树形多值分类器.研究结果表明,对于k类别模式识别问题,该方法只需构造k-1个SVM子分类器,克服了SVM子分类器过多以及存在不可区分区域的缺点,具有良好的分类性能.实验结果验证了该方法的优越性.     

基于改进灰狼算法优化多核支持向量回归机及其应用

为更好发现数据中的复杂规律,避免核函数选择的盲目性和局部最优等非线性优化问题,本文提出一种基于改进灰狼算法优化多核支持向量回归机算法.首先,基于全局核函数和局部核函数构建多核支持向量机采油速度预测模型;其次,利用基于云模型和二次插值算法改进灰狼优化算法对核函数权值和参数的选取进行优化;最后,应用灰色关联分析理论确定采油速度影响因素集,并作为多核支持向量回归机预测模型的输入.与6种采油速度预测方法进行对比,所提方法具有较好的全局寻优能力和较高的预测率的优点.     

核对齐多核模糊支持向量机

支持向量机（SVMs）是当前被广泛使用的机器学习技术,其通过最优分割超平面来提高分类器的泛化能力,在实际应用中表现优异。然而SVM也存在易受噪声影响,以及核函数选择等难题。针对以上问题,本文将基于核对齐的多核学习方法引入到模糊支持向量机（fuzzy support vector machine, FSVM）中,提出了模糊多核支持向量机模型（multiple kernel fuzzy support vector machine,MFSVM）。MFSVM通过模糊粗糙集方法计算每一样例隶属度;其次,利用核对齐的多核方法计算每一单核权重,并将组合核引入到模糊支持向量机中。该方法不仅提高了支持向量机的抗噪声能力,也有效避免了核选择难题。在UCI数据库上进行实验,结果表明本文所提方法具有较高的分类精度,验证了该方法的可行性与有效性。     

Fuzzy rule-based support vector regression system

In this paper,we design a fuzzy rule-based support vector regression system.The proposed system utilizes the advantages of fuzzy model and support vector regression to extract support vectors to generate fuzzy if-then rules from the training data set.Based on the first-order linear Tagaki-Sugeno (TS) model,the structure of rules is identified by the support vector regression and then the consequent parameters of rules are tuned by the global least squares method.Our model is applied to the real world regression task.The simulation results gives promising performances in terms of a set of fuzzy rules,which can be easily interpreted by humans.     

Fuzzy nile-based support vector regression system

In this paper, we design a fuzzy rule-based support vector regression system. The proposed system utilizes the advantages of fuzzy model and support vector regression to extract support vectors to generate fuzzy if-then rules from the training data set. Based on the first-order hnear Tagaki-Sugeno （TS） model, the structure of rules is identified by the support vector regression and then the consequent parameters of rules are tuned by the global least squares method. Our model is applied to the real world regression task. The simulation results gives promising performances in terms of a set of fuzzy hales, which can be easily interpreted by humans.     

基于支持向量机的TSK模糊模型辨识与控制

研究非线性系统TSK模糊模型的辨识与控制,利用TSK模型,可以将线性控制理论应用于非线性系统控制。基于支持向量机和递推最小二乘法,辨识出TSK模糊模型,并且通过遗传算法优化隶属度函数参数,最小化辨识误差。针对TSK模型进行控制,控制器包括两个部分：权重最大子系统反馈控制及其监督控制,监督控制保证了系统的稳定性。辨识和控制仿真结果证明了算法的有效性。     

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。     

模糊最小二乘支持向量机回归研究及应用

针对传统支持向量机对训练样本内的噪声和孤立点比较敏感,导致建模精度不高的问题,将模糊集理论引入到最小二乘支持向量机回归中,建立一种基于数据域描述的模糊最小二乘支持向量机回归的数学模型,该方法将样本映射到高维空间,在高维空间中寻找最小包含超球,然后根据样本到超球心的距离确定模糊隶属度的大小,通过仿真实验验证,该算法提高了支持向量机回归的训练精度,将此模型应用于谷氨酸发酵过程菌体浓度预测,结果表明此方法的有效性。