Fuzzy SVM with a new fuzzy membership function

It is known that with a proper fuzzy membership function, a fuzzy support vector machine can effectively reduce the effects of outliers when solving the classification problem. In this paper, a new fuzzy membership function is proposed to the nonlinear fuzzy support vector machine. The fuzzy membership is calculated in the feature space and is represented by kernels. This method gives good performance on reducing the effects of outliers and significantly improves the classification accuracy and generalization.     

一种新颖隶属度函数的模糊支持向量机

传统的支持向量机(SVM)训练含有外部点或噪音数据时,容易产生过拟合(over-fitting)。通过模糊隶属度函数来降低外部点或被污染数据的选择。本文提出了一种新的核隶属度函数,这种新的隶属度函数不仅依赖于每个样本点到类型中心的距离,还依赖于该样本点最邻近的K个其他样本点的距离。实验结果表明了具有该隶属度函数的模糊支持向量机的有效性。     

基于类向心度的模糊支持向量机

传统支持向量机(SVM)训练含有噪声或野值点的数据时,容易产生过拟合,而模糊支持向量机可以有效地处理这种问题。针对使用样本与类中心之间的距离关系来构建模糊支持向量机隶属度函数的不足,提出了一种基于类向心度的模糊支持向量机(CCD FSVM)。该方法不仅考虑到样本与类中心之间的关系,还考虑到类中各个样本之间的联系,并用类向心度来表示。将类向心度应用于模糊隶属度函数的设计,能够很好地将有效样本与噪声、野值点样本区分开来,而且可以通过向心度的大小,对混合度比较高的样本进行区分,从而达到提高分类精度的效果。实验结果表明,基于类向心度的模糊支持向量机其分类正确率比支持向量机高,在使用三种不同隶属度函数的FSVM中,该方法的抗噪性能最好,分类性能最强。     

模糊支持向量机中隶属度的确定与分析

针对目前模糊支持向量机方法中，一般使用特征空间中样本与类中心之间的距离关系构建隶属度函数的不足，提出了一种新的有效地反映样本不确定性的隶属度计算方法——基于样本紧密度的隶属度方法。在确定样本的隶属度时，不仅考虑了样本与类中心之间的关系，还考虑了类中各个样本之间的关系，并采用模糊连接度来度量类中各个样本之间的关系。将其应用于模糊支持向量机方法中，较好地将支持向量与含噪声或野值样本区分开。实验结果表明，采用模糊支持向量机方法，其分类错误率比采用支持向量机方法的错误率低，在使用的3种隶属度函数中，采用基于紧密度隶属度的模糊支持向量机方法抗噪性能最好，分类性能最强。     

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．     

基于样本之间紧密度的模糊支持向量机方法

针对传统支持向量机方法中存在对噪声或野值敏感的问题,提出了一种基于紧密度的模糊支持向量机方法.在确定样本的隶属度时,不仅考虑了样本与类中心之间的关系,还考虑了类中各个样本之间的关系.通过样本之间的紧密度来描述类中各个样本之间的关系,利用包围同一类中样本的最小球半径大小来度量样本之间的紧密度.样本的隶属度依据样本在球中的位置,按照不同的规律确定与基于样本与类中心之间关系构建的模糊支持向量机方法相比,该方法有利于将野值或含噪声样本与有效样本进行区分.实验结果表明,与传统支持向量机方法及基于样本与类中心之间关系的模糊支持向量机方法相比,基于紧密度的模糊支持向量机方法具有更好的抗噪性能及分类能力.     

双隶属度模糊支持向量机算法

对现有的模糊支持向量机进行分析，提出一种改进的模糊支持向量机算法——双隶属度模糊支持向量机法（DM FSVM）。在传统的模糊支持向量机模型中，每一个训练样本的隶属函数中只有一个隶属度，而DM FSVM中每一个训练样本拥有两个隶属度。它既能保持传统模糊支持向量机的优点，又能充分利用有限样本，增加其分类推广能力。实验表明该算法较好地提高了分类精度。     

基于核方法的一种新的模糊支持向量机

由于支持向量机对样本中的噪声及孤立点非常敏感,因而在解决非线性、高维数、不确定问题时,使用模糊支持向量机比使用支持向量机的效果要好。在模糊支持向量机中,模糊隶属度函数的建立是关键也是难点。一般,模糊隶属度是在原始空间中根据样本点的相互距离及到类中心的距离创建的。考虑样本间的密切度,在特征空间中利用混合核函数建立一种新的模糊隶属度。通过试验比较多项式核函数、高斯径向基核函数与混合核函数,可看出新方法表现出了它的优越性。     

基于海量样本的模糊分类系统的设计

使用支持向量机理论直接求海量数据的模糊分类系统是比较困难的。为了解决这个问题，该文提出了基于邻域原理计算支持向量，利用支持向量求出分类超平面，再设计模糊分类系统的方法。实验结果表明，该方法可以有效地解决对海量数据的模糊分类系统的设计 问题。     

DP聚类的可信性加权模糊支持向量机

由于SVM（Support Vector Machine）在有离群点和不平衡数据的问题中分类性能相对较低，有研究者提出了一种面向不均衡分类的隶属度加权模糊支持向量机，只是文中的模糊隶属度并不能较好衡量样本点对确定最佳分划超平面所做的贡献大小。针对以上问题提出了密度峰（Density Peaks，DP）聚类的可信性加权模糊支持向量机。首先由DP聚类找到离群点后剔除。再根据点到由DEC（Different Error Costs）确定的超平面的距离，得到初始隶属度，并用改进的FSVM-CIL（Fuzzy Support Vector Machines for Class Imbalance Learning）更新隶属度。之后剔除部分样本点，起到简约样本的作用，并减少数据不平衡带来的影响。通过实验验证了所提出算法的有效性。     

Quantum Fuzzy Support Vector Machine for Binary Classification

In the objective world, how to deal with the complexity and uncertainty of big data efficiently and accurately has become the premise and key to machine learning. Fuzzy support vector machine (FSVM) not only deals with the classification problems for training samples with fuzzy information, but also assigns a fuzzy membership degree to each training sample, allowing different training samples to contribute differently in predicting an optimal hyperplane to separate two classes with maximum margin, reducing the effect of outliers and noise, Quantum computing has super parallel computing capabilities and holds the promise of faster algorithmic processing of data. However, FSVM and quantum computing are incapable of dealing with the complexity and uncertainty of big data in an efficient and accurate manner. This paper research and propose an efficient and accurate quantum fuzzy support vector machine (QFSVM) algorithm based on the fact that quantum computing can efficiently process large amounts of data and FSVM is easy to deal with the complexity and uncertainty problems. The central idea of the proposed algorithm is to use the quantum algorithm for solving linear systems of equations (HHL algorithm) and the least-squares method to solve the quadratic programming problem in the FSVM. The proposed algorithm can determine whether a sample belongs to the positive or negative class while also achieving a good generalization performance. Furthermore, this paper applies QFSVM to handwritten character recognition and demonstrates that QFSVM can be run on quantum computers, and achieve accurate classification of handwritten characters. When compared to FSVM, QFSVM’s computational complexity decreases exponentially with the number of training samples.     

面向不均衡分类的隶属度加权模糊支持向量机

针对不均衡分类问题,提出了一种基于隶属度加权的模糊支持向量机模型。使用传统支持向量机对样本进行训练,并通过样本点与所得分类超平面之间的距离构造模糊隶属度,这不仅能够消除噪点和野值点的影响,而且可以在一定程度上约减样本;利用正负类的平均隶属度和样本数量求得平衡调节因子,消除数据不平衡时造成的分类超平面的偏移现象;通过实验结果验证了该算法的可行性和有效性。实验结果表明,该算法能有效提高分类精度,特别是对不平衡数据效果更加明显,在训练速度和分类性能上比传统支持向量机和模糊支持向量机有进一步的提升。     

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。     

结合正态分布概率的FSVM

针对当前模糊支持向量机（FSVM）一般使用特征空间样本与类中心之间的距离构建隶属度函数的不足,提出了一种计算FSVM的隶属度的新方法。首次使用基于正态分布概率的π型隶属度函数来计算隶属度,根据正态分布的特性,在考虑数据分布规律的同时求得数据点的隶属值,使得求得的数据能够更加准确地反应数据的特点,进而获得更好的分类函数。实验表明,这种方法较SVM和FSVM相比,降低了噪声数据的影响,并且有效地提高了分类的准确率。     

基于支持矢量机特征空间距离的多目标分类方法

支持矢量机是近年来在统计学习理论的基础上发展起来的一种新的模式识别方法,主要解决的是两类目标分类问题.多类目标分类一般是分解为多个两类目标分类.多类目标分类之后通常会对某些目标错误分类或者某些目标不能判定其类别,这就是支持矢量机多类目标分类中的错分、拒分现象.针对这个问题,该文提出了一种基于支持矢量机特征空间距离的模糊隶属度函数,根据模糊隶属度的大小对错分和拒分目标重新分类.对美国资源探测卫星数据的多目标分类仿真结果表明,采用这种方法重新分类后,能够有效地减少错分和拒分目标的数量,提高了正确识别率.     

A new fuzzy support vector machine to evaluate credit risk

Due to recent financial crises and regulatory concerns, financial intermediaries' credit risk assessment is an area of renewed interest in both the academic world and the business community. In this paper, we propose a new fuzzy support vector machine to discriminate good creditors from bad ones. Because in credit scoring areas we usually cannot label one customer as absolutely good who is sure to repay in time, or absolutely bad who will default certainly, our new fuzzy support vector machine treats every sample as both positive and negative classes, but with different memberships. By this way we expect the new fuzzy support vector machine to have more generalization ability, while preserving the merit of insensitive to outliers, as the fuzzy support vector machine (SVM) proposed in previous papers. We reformulate this kind of two-group classification problem into a quadratic programming problem. Empirical tests on three public datasets show that it can have better discriminatory power than the standard support vector machine and the fuzzy support vector machine if appropriate kernel and membership generation method are chosen.     

Class imbalance learning via a fuzzy total margin based support vector machine

The classification of imbalanced data is a major challenge for machine learning. In this paper, we presented a fuzzy total margin based support vector machine (FTM-SVM) method to handle the class imbalance learning (CIL) problem in the presence of outliers and noise. The proposed method incorporates total margin algorithm, different cost functions and the proper approach of fuzzification of the penalty into FTM-SVM and formulates them in nonlinear case. We considered an excellent type of fuzzy membership functions to assign fuzzy membership values and got six FTM-SVM settings. We evaluated the proposed FTM-SVM method on two artificial data sets and 16 real-world imbalanced data sets. Experimental results show that the proposed FTM-SVM method has higher G_Mean and F_Measure values than some existing CIL methods. Based on the overall results, we can conclude that the proposed FTM-SVM method is effective for CIL problem, especially in the presence of outliers and noise in data sets.     

The support vector machine based on intuitionistic fuzzy number and kernel function

Fuzzy support vector machine applied a degree of membership to each training point and reformulated the traditional support vector machines, which reduced the effects of noises and outliers for classification. However, the degree of membership only considered the distance from samples to the class center in the sample space, while neglected the situation of samples in the feature space and easily mistook the edge support vectors as noises. To deal with the aforementioned problems, the support vector machine based on intuitionistic fuzzy number and kernel function is proposed. In the high-dimensional feature space, each training point is assigned with a corresponding intuitionistic fuzzy number by the use of kernel function. Then, a new score function of the intuitionistic fuzzy numbers is introduced to measure the contribution of each training point. In the end, the new support vector machine is constructed according to the score value of each training point. The simulation results demonstrate the effectiveness and superiority of the proposed method.     

模糊支持向量机在路面识别中的应用

利用模糊支持向量机进行路面不平度识别。针对支持向量机对样本中的噪声点和野值点特别敏感的缺点,采用将样本到类中心的距离作为样本的模糊隶属度,并结合改进的粒子群算法对模糊支持向量机的参数进行优化。通过对实验数据的训练和测试,该方法的最高平均识别率提高到了77.5%,高于一般支持向量机的72.5%的识别率。数据处理表明模糊隶属度的引入强化了有效样本对分类的影响,减弱了噪声点和野值点对分类的影响,提高了路面不平度识别率。