基于可能性理论的模糊支持向量分类机

研究模糊支持向量分类机的构建问题.其特点是:训练点输出的类型和最终的模糊分类函数的函数值均为三角模糊数.首先,以模糊事件的可能性测度为基础,将模糊分类问题转化为求解模糊机会约束规划问题.然后,利用模糊机会约束规划化为清晰等价规划的方法,将其转化为与其等价的二次规划.据此给出模糊支持向量分类机(算法).同时用一个简单算例说明该算法的合理性.     

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。     

基于混合隶属度的模糊简约双支持向量机研究

双支持向量机是一种新的非平行二分类算法,其处理速度比传统支持向量机快很多,但是双支持向量机在训练之前要进行大量的复杂逆矩阵计算;在非线性情况下,它不能像传统支持向量机那样把核技巧直接运用到对偶优化问题中;并且双支持向量机没有考虑不同输入样本点会对最优分类超平面产生不同的影响。针对这些情况,提出了一种模糊简约双支持向量机。该模糊简约双支持向量机通过对二次规划函数和拉格朗日函数的改进,省略大量的逆矩阵计算,同时核技巧能直接运用到非线性分类情况下;对于混合模糊隶属度函数,不仅每个样本点到类中心的距离影响着该混合模糊隶属度,而且该样本点的邻域密度同样影响着该混合模糊隶属度。实验结果表明,与支持向量机、标准双支持向量机、双边界支持向量机、模糊双支持向量机相比,具有该混合模糊隶属度函数的简约双支持向量机不仅分类时间短,计算简单,而且分类精度高。     

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。     

总间隔v-模糊支持向量机研究

为获得更好的分类性能,对传统模糊支持向量机(FSVM)进行扩展,提出一种总间隔v-模糊支持向量机(TM-v-FSVM)。通过使用差异成本及引入总间隔和模糊隶属度,同时解决不平衡训练样本问题和传统软间隔分类机的过拟合问题,从而提升学习机的泛化能力。采用UCI实际数据集进行模式分类实验,结果表明TM-v-FSVM具有稳定的分类性能。     

基于加权模糊隶属度的二叉树多分类算法

针对二叉树支持向量机多分类算法准确率与分类效率较低的问题,提出了一种基于加权模糊隶属度的二叉树支持向量机多分类算法（binary tree support vector machines multi-classification algorithm based on weighted fuzzy membership,PF-BTSVM）。该算法依据最大最小样本距离与质心距离构造出一个近似完全二叉树,提高了整体结构的分类效率;利用模糊隶属度函数以及正负辅助惩罚因子对训练集进行筛选,剔除掉对分类无用的样本与噪声值,实现了训练集的提纯并且削弱了不平衡分类时超平面的偏移。在数据集上的实验结果表明,与其他二叉树多分类算法相比,该算法在提高了分类准确率以及稳定性的的同时还加快了训练与分类的速度,而且这种优势当分类的不平衡度越大时越明显。     

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.     

基于类内超平面的改进模糊支持向量机

基于类中心设计隶属度函数的模糊支持向量机能够有效地解决支持向量机对噪声、野值点敏感的问题。但是它对支持向量赋予较小的隶属度值,从而降低了其分类效果。因此,提出一种改进的隶属度函数设计方法,该方法降低了对样本几何分布的依赖,而且考虑到了支持向量机的本质特征。用类内超平面代替类中心,根据每类数据与其类内超平面的距离定义隶属度函数,以加大对容易被错分样本的惩罚,同时对离分类超平面较远且不可能成为支持向量的样本赋予较小的隶属度值。实验表明,改进的模糊支持向量机能够有效地提高分类精度。     

一类新型快速模糊支持向量机

针对一般模糊支持向量机训练时间过长,训练效率低下的问题,通过定义了一种新的隶属度函数的方法,来改进算法,从而得到了一种快速模糊支持向量机。本算法中的新定义的隶属度函数能够对离分类超平面较远、不可能成为支持向量的数据赋予较小的隶属度,使训练样本集中的数据大大减少。同时,在将二类模糊支持向量机推广到k类时,采用了DAGSVMs方法,进一步提高了多类分类问题的分类效率。实验表明,提出的快速模糊支持向量机在保证测试精度的同时,减少了训练时间。     

一类新型快速模糊支持向量机

针对一般模糊支持向量机训练时间过长,训练效率低下的问题,通过定义了一种新的隶属度函数的方法,来改进算法,从而得到了一种快速模糊支持向量机。本算法中的新定义的隶属度函数能够对离分类超平面较远、不可能成为支持向量的数据赋予较小的隶属度,使训练样本集中的数据大大减少。同时,在将二类模糊支持向量机推广到k类时,采用了DAGSVMs方法,进一步提高了多类分类问题的分类效率。实验表明,提出的快速模糊支持向量机在保证测试精度的同时,减少了训练时间。     

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.     

基于F-SVMs的多模型建模方法

针对全局模型难以精确描述复杂工业过程的问题,提出一种基于模糊支持向量机(F-SVMs)的多模型(F-SVMs MM)建模方法。用模糊支持向量分类算法(F-SVC)对输入数据进行预处理,得到多模型模糊隶属度;用模糊支持回归算法(F-SVR)建立多模型(MM)估计器。应用该方法对pH中和滴定过程进行建模,仿真结果表明,F-SVMs MM跟踪性能好、泛化能力强,比USOCPN方法和标准支持向量机(SVMs)方法具有更好的性能和推广能力。     

An accuracy-oriented self-splitting fuzzy classifier with support vector learning in high-order expanded consequent space

This paper proposes a self-splitting fuzzy classifier with support vector learning in expanded high-order consequent space (SFC-SVHC) for classification accuracy improvement. The SFC-SVHC expands the rule-mapped consequent space of a first-order Takagi-Sugeno (TS)-type fuzzy system by including high-order terms to enhance the rule discrimination capability. A novel structure and parameter learning approach is proposed to construct the SFC-SVHC. For structure learning, a variance-based self-splitting clustering (VSSC) algorithm is used to determine distributions of the fuzzy sets in the input space. There are no rules in the SFC-SVHC initially. The VSSC algorithm generates a new cluster by splitting an existing cluster into two according to a predefined cluster-variance criterion. The SFC-SVHC uses trigonometric functions to expand the rule-mapped first-order consequent space to a higher-dimensional space. For parameter optimization in the expanded rule-mapped consequent space, a support vector machine is employed to endow the SFC-SVHC with high generalization ability. Experimental results on several classification benchmark problems show that the SFC-SVHC achieves good classification results with a small number of rules. Comparisons with different classifiers demonstrate the superiority of the SFC-SVHC in classification accuracy.     

基于模糊支持向量机的数据域描述

受模糊支持向量机的启发，本文系统论述了带有模糊隶属度的数据域描述方法，称为模糊支持向量域描述。适用于数据集中的数据不完全肯定来自于假设总体的情形，不同的数据对数据集的域描述可以有不同的贡献。     

Classification model for product form design using fuzzy support vector machines

Consumer preferences regarding product design are often affected by a large variety of form features. Traditionally, the quality of product form design depended heavily on designers’ intuitions and did not always prove to be successful in the marketplace. In this study, to help product designers develop appealing products in a more effective manner, an approach based on fuzzy support vector machines (fuzzy SVM) is proposed. This constructs a classification model of product form design based on consumer preferences. The one-versus-one (OVO) method is adopted to handle a multiclass problem by breaking it into various two-class problems. Product samples were collected and their form features were systematically examined. To formulate a classification problem, each product sample was assigned a class label and a fuzzy membership that corresponded to this label. The OVO fuzzy SVM model was constructed using collected product samples. The optimal training parameter set for the model was determined by a two-step cross-validation. A case study of mobile phone design is given to demonstrate the effectiveness of the proposed methodology. The performance of fuzzy SVM is also compared with SVM. The results of the experiment show that fuzzy SVM performed better than SVM.     

SVM-FuzCoC: A novel SVM-based feature selection method using a fuzzy complementary criterion

An efficient filter feature selection (FS) method is proposed in this paper, the SVM-FuzCoC approach, achieving a satisfactory trade-off between classification accuracy and dimensionality reduction. Additionally, the method has reasonably low computational requirements, even in high-dimensional feature spaces. To assess the quality of features, we introduce a local fuzzy evaluation measure with respect to patterns that embraces fuzzy membership degrees of every pattern in their classes. Accordingly, the above measure reveals the adequacy of data coverage provided by each feature. The required membership grades are determined via a novel fuzzy output kernel-based support vector machine, applied on single features. Based on a fuzzy complementary criterion (FuzCoC), the FS procedure iteratively selects features with maximum additional contribution in regard to the information content provided by previously selected features. This search strategy leads to small subsets of powerful and complementary features, alleviating the feature redundancy problem. We also devise different SVM-FuzCoC variants by employing seven other methods to derive fuzzy degrees from SVM outputs, based on probabilistic or fuzzy criteria. Our method is compared with a set of existing FS methods, in terms of performance capability, dimensionality reduction, and computational speed, via a comprehensive experimental setup, including synthetic and real-world datasets.     

支持向量机和一类模糊推理系统的等效性及其应用

支持向量机（ＳＶＭ）和模糊推理系统（ＦＩＳ）分别源于统计学习理论（ＳＬＴ）和认知学两个不同的领域．在一定约束条件下,提出并证明了ＳＶＭ 和一类基于规则的ＦＩＳ的函数等效性定理．在此基础上,提出基于ＳＶＭ 学习过程的ＦＩＳ（ＭＢＦＩＳ）的设计方法．ＭＢＦＩＳ继承了ＳＶＭ 良好的泛化能力和对“维数灾难”的避免能力,也继承了基于规则的ＦＩＳ的显式推理能力．Ｂｅｎｃｈｍａｒｋ数据实验表明,ＭＢＦＩＳ具有良好的分类性能．     

Support vector fuzzy adaptive network in regression analysis

Neural-fuzzy systems have been proved to be very useful and have been applied to modeling many humanistic problems. But these systems also have problems such as those of generalization, dimensionality, and convergence. Support vector machines, which are based on statistical learning theory and kernel transformation, are powerful modeling tools. However, they do not have the ability to represent and to aggregate vague and ill-defined information. In this paper, these two systems are combined. The resulting support vector fuzzy adaptive network (SVFAN) overcomes some of the difficulties of the neural-fuzzy system. To illustrate the proposed approach, a simple nonlinear function is estimated by first generating the training and testing data needed. The results show that the proposed network is a useful modeling tool.     

A parsimony fuzzy rule-based classifier using axiomatic fuzzy set theory and support vector machines

This paper proposes a classification method that is based on easily interpretable fuzzy rules and fully capitalizes on the two key technologies, namely pruning the outliers in the training data by SVMs (support vector machines), i.e., eliminating the influence of outliers on the learning process; finding a fuzzy set with sound linguistic interpretation to describe each class based on AFS (axiomatic fuzzy set) theory. Compared with other fuzzy rule-based methods, the proposed models are usually more compact and easily understandable for the users since each class is described by much fewer rules. The proposed method also comes with two other advantages, namely, each rule obtained from the proposed algorithm is simply a conjunction of some linguistic terms, there are no parameters that are required to be tuned. The proposed classification method is compared with the previously published fuzzy rule-based classifiers by testing them on 16 UCI data sets. The results show that the fuzzy rule-based classifier presented in this paper, offers a compact, understandable and accurate classification scheme. A balance is achieved between the interpretability and the accuracy.     

On-line fuzzy modeling via clustering and support vector machines

In this paper, we propose a novel approach to identify unknown nonlinear systems with fuzzy rules and support vector machines. Our approach consists of four steps which are on-line clustering, structure identification, parameter identification and local model combination. The collected data are firstly clustered into several groups through an on-line clustering technique, then structure identification is performed on each group using support vector machines such that the fuzzy rules are automatically generated with the support vectors. Time-varying learning rates are applied to update the membership functions of the fuzzy rules. The modeling errors are proven to be robustly stable with bounded uncertainties by a Lyapunov method and an input-to-state stability technique. Comparisons with other related works are made through a real application of crude oil blending process. The results demonstrate that our approach has good accuracy, and this method is suitable for on-line fuzzy modeling.