The multiobjective group decision-making problem under risk is common in reality. This paper focuses on the study about risky multiobjective group decision-making problem where the index value is not certain. We give ...The multiobjective group decision-making problem under risk is common in reality. This paper focuses on the study about risky multiobjective group decision-making problem where the index value is not certain. We give indexes classifying method and index normalizing formula of this type problem. By building objective function that minimizes general weighted distance from every alternative to the relatively best and worst alternative, the optimal membership degree of every decision-maker to every alternative can be obtained, and by building another objective function that minimizes general weighted distance from the optimal membership degree of every decision-maker to every alternative to the group optimal alternative and the group inferior alternative, the optimal membership degree of every decision-maker to every alternative can be obtained, which are both based on probability theory and fuzzy theory. Aftermost a model is established which collects group preferences. This method provides a new idea and approach for solving multiobjective decision-making problem among uncertain system, which is applicable for practical problem. Finally a case study shows a satisfactory result.展开更多
提出了一种模糊最优间隔分布矩阵分类器(Fuzzy Optimal-margin Distribution Matrix Classifier,FODMC)。该模型通过整合模糊隶属度理论与间隔分布优化机制,实现了矩阵结构信息的有效提取与异常值的鲁棒处理。具体而言,FODMC采用基于间...提出了一种模糊最优间隔分布矩阵分类器(Fuzzy Optimal-margin Distribution Matrix Classifier,FODMC)。该模型通过整合模糊隶属度理论与间隔分布优化机制,实现了矩阵结构信息的有效提取与异常值的鲁棒处理。具体而言,FODMC采用基于间隔分布的损失函数来优化分类边界,结合核范数正则化策略保持矩阵的低秩特性,并利用交替方向乘子法(Alternating Direction Method of Multipliers,ADMM)实现模型的高效训练。在多个基准数据集上的实验结果表明:与现有方法相比,FODMC在分类准确率、鲁棒性和泛化能力等方面均展现出显著优势,为矩阵数据分类问题提供了一种有效的解决方案。展开更多
Smooth support vector machine （SSVM） changs the normal support vector machine （SVM） into the unconstrained op- timization by using the smooth sigmoid function. The method can be solved under the Broyden-Fletcher-G...Smooth support vector machine （SSVM） changs the normal support vector machine （SVM） into the unconstrained op- timization by using the smooth sigmoid function. The method can be solved under the Broyden-Fletcher-Goldfarb-Shanno （BFGS） algorithm and the Newdon-Armijio （NA） algorithm easily, however the accuracy of sigmoid function is not as good as that of polyno- mial smooth function. Furthermore, the method cannot reduce the influence of outliers or noise in dataset. A fuzzy smooth support vector machine （FSSVM） with fuzzy membership and polynomial smooth functions is introduced into the SVM. The fuzzy member- ship considers the contribution rate of each sample to the optimal separating hyperplane and makes the optimization problem more accurate at the inflection point. Those changes play a positive role on trials. The results of the experiments show that those FSSVMs can obtain a better accuracy and consume the shorter time than SSVM and lagrange support vector machine （LSVM）.展开更多
Support vector machine(SVM)is easily affected by noises and outliers,and its training time dramatically increases with the growing in number of training samples.Satellite cloud image may easily be deteriorated by nois...Support vector machine(SVM)is easily affected by noises and outliers,and its training time dramatically increases with the growing in number of training samples.Satellite cloud image may easily be deteriorated by noises and intensity non-uniformity with a huge amount of data needs to be processed regularly,so it is hard to detect convective clouds in satellite image using traditional SVM.To deal with this problem,a novel method for detection of convective clouds was proposed based on fast fuzzy support vector machine(FFSVM).FFSVM was constructed by eliminating feeble samples and designing new membership function as two aspects.Firstly,according to the distribution characteristics of fuzzy inseparable sample set and the fact that the classification hyper-plane is only determined by support vectors,this paper uses SVDD,Gaussian model and border vector extraction model comprehensively to design a sample selection method in three steps,which can eliminate most of redundant samples and keep possible support vectors.Then,by defining adaptive parameters related to attenuation rate and critical membership on the basis of the distribution characteristics of training set,an adaptive membership function is designed.Finally,the FFSVM is trained by the remaining samples using adaptive membership function to detect convective clouds.The experiments on FY-2D satellite images show that the proposed method,compared with traditional FSVM,not only remarkably reduces training time,but also further improves the accuracy of convective clouds detection.展开更多
A new fuzzy support vector machine algorithm with dual membership values based on spectral clustering method is pro- posed to overcome the shortcoming of the normal support vector machine algorithm, which divides the ...A new fuzzy support vector machine algorithm with dual membership values based on spectral clustering method is pro- posed to overcome the shortcoming of the normal support vector machine algorithm, which divides the training datasets into two absolutely exclusive classes in the binary classification, ignoring the possibility of ＂overlapping＂ region between the two training classes. The proposed method handles sample ＂overlap＂ effi- ciently with spectral clustering, overcoming the disadvantages of over-fitting well, and improving the data mining efficiency greatly. Simulation provides clear evidences to the new method.展开更多
针对最小二乘双参数间隔支持向量机(LSTPMSVM)对噪声敏感且在分类过程中易受异常值影响的问题,提出了一种鲁棒的模糊最小二乘双参数间隔支持向量机算法(RFLSTPMSVM).该算法利用松弛变量的2范数使得优化问题具有强凸性,再根据隶属度为每...针对最小二乘双参数间隔支持向量机(LSTPMSVM)对噪声敏感且在分类过程中易受异常值影响的问题,提出了一种鲁棒的模糊最小二乘双参数间隔支持向量机算法(RFLSTPMSVM).该算法利用松弛变量的2范数使得优化问题具有强凸性,再根据隶属度为每个样本分配相应的权重,有效降低异常值带来的影响.同时,在目标函数中引入K-近邻加权,考虑样本之间的局部信息,提高模型的分类准确率.此外,通过求解简单的线性方程组来优化该算法,而不是求解二次规划问题,使模型具有较快的计算速度.在UCI(university of California irvine)数据集上对该算法进行性能评估,并与TWSVM、LSTSVM、LSTPMSVM和ULSTPMSVM 4种算法进行比较.数值实验结果表明,该算法具有更好的泛化性能.展开更多
针对模糊C均值算法(fuzzy C-means algorithm,简称FCM)在入侵检测中需要预先指定聚类数的问题,提出了一种自动决定聚类数算法(fuzzy C-means and support vector machine algorithm,简称F-CMSVM).它首先用模糊C均值算法把目标数据集分...针对模糊C均值算法(fuzzy C-means algorithm,简称FCM)在入侵检测中需要预先指定聚类数的问题,提出了一种自动决定聚类数算法(fuzzy C-means and support vector machine algorithm,简称F-CMSVM).它首先用模糊C均值算法把目标数据集分为两类,然后使用带有模糊成员函数的支持向量机(support vector machihe,简称SVM)算法对结果进行评估以确定目标数据集是否可分,再迭代计算,最终得到聚类结果.支持向量机算法引入模糊C均值算法得出的隶属矩阵作为模糊成员函数,使得不同的输入样本可以得到不同的惩罚值,从而得到最优的分类超平面.该算法既不需要对训练数据集进行标记,也不需要指定聚类数,因此是一种真正的无监督算法.在对KDD CUP 1999数据集的仿真实验结果表明,该算法不仅能够得到最佳聚类数,而且对入侵有较好的检测效果.展开更多
文摘The multiobjective group decision-making problem under risk is common in reality. This paper focuses on the study about risky multiobjective group decision-making problem where the index value is not certain. We give indexes classifying method and index normalizing formula of this type problem. By building objective function that minimizes general weighted distance from every alternative to the relatively best and worst alternative, the optimal membership degree of every decision-maker to every alternative can be obtained, and by building another objective function that minimizes general weighted distance from the optimal membership degree of every decision-maker to every alternative to the group optimal alternative and the group inferior alternative, the optimal membership degree of every decision-maker to every alternative can be obtained, which are both based on probability theory and fuzzy theory. Aftermost a model is established which collects group preferences. This method provides a new idea and approach for solving multiobjective decision-making problem among uncertain system, which is applicable for practical problem. Finally a case study shows a satisfactory result.
文摘提出了一种模糊最优间隔分布矩阵分类器(Fuzzy Optimal-margin Distribution Matrix Classifier,FODMC)。该模型通过整合模糊隶属度理论与间隔分布优化机制,实现了矩阵结构信息的有效提取与异常值的鲁棒处理。具体而言,FODMC采用基于间隔分布的损失函数来优化分类边界,结合核范数正则化策略保持矩阵的低秩特性,并利用交替方向乘子法(Alternating Direction Method of Multipliers,ADMM)实现模型的高效训练。在多个基准数据集上的实验结果表明:与现有方法相比,FODMC在分类准确率、鲁棒性和泛化能力等方面均展现出显著优势,为矩阵数据分类问题提供了一种有效的解决方案。
基金supported by the National Natural Science Foundation of China (60974082)
文摘Smooth support vector machine （SSVM） changs the normal support vector machine （SVM） into the unconstrained op- timization by using the smooth sigmoid function. The method can be solved under the Broyden-Fletcher-Goldfarb-Shanno （BFGS） algorithm and the Newdon-Armijio （NA） algorithm easily, however the accuracy of sigmoid function is not as good as that of polyno- mial smooth function. Furthermore, the method cannot reduce the influence of outliers or noise in dataset. A fuzzy smooth support vector machine （FSSVM） with fuzzy membership and polynomial smooth functions is introduced into the SVM. The fuzzy member- ship considers the contribution rate of each sample to the optimal separating hyperplane and makes the optimization problem more accurate at the inflection point. Those changes play a positive role on trials. The results of the experiments show that those FSSVMs can obtain a better accuracy and consume the shorter time than SSVM and lagrange support vector machine （LSVM）.
基金supported in part by the National Natural Science Foundation of China under Grants (61471212)Natural Science Foundation of Zhejiang Province under Grants (LY16F010001)+1 种基金Science and Technology Program of Zhejiang Meteorological Bureau under Grants (2016YB01)Natural Science Foundation of Ningbo under Grants(2016A610091,2017A610297)
文摘Support vector machine(SVM)is easily affected by noises and outliers,and its training time dramatically increases with the growing in number of training samples.Satellite cloud image may easily be deteriorated by noises and intensity non-uniformity with a huge amount of data needs to be processed regularly,so it is hard to detect convective clouds in satellite image using traditional SVM.To deal with this problem,a novel method for detection of convective clouds was proposed based on fast fuzzy support vector machine(FFSVM).FFSVM was constructed by eliminating feeble samples and designing new membership function as two aspects.Firstly,according to the distribution characteristics of fuzzy inseparable sample set and the fact that the classification hyper-plane is only determined by support vectors,this paper uses SVDD,Gaussian model and border vector extraction model comprehensively to design a sample selection method in three steps,which can eliminate most of redundant samples and keep possible support vectors.Then,by defining adaptive parameters related to attenuation rate and critical membership on the basis of the distribution characteristics of training set,an adaptive membership function is designed.Finally,the FFSVM is trained by the remaining samples using adaptive membership function to detect convective clouds.The experiments on FY-2D satellite images show that the proposed method,compared with traditional FSVM,not only remarkably reduces training time,but also further improves the accuracy of convective clouds detection.
基金supported by the National Natural Science Foundation of China (7083100170821061)
文摘A new fuzzy support vector machine algorithm with dual membership values based on spectral clustering method is pro- posed to overcome the shortcoming of the normal support vector machine algorithm, which divides the training datasets into two absolutely exclusive classes in the binary classification, ignoring the possibility of ＂overlapping＂ region between the two training classes. The proposed method handles sample ＂overlap＂ effi- ciently with spectral clustering, overcoming the disadvantages of over-fitting well, and improving the data mining efficiency greatly. Simulation provides clear evidences to the new method.
文摘针对最小二乘双参数间隔支持向量机(LSTPMSVM)对噪声敏感且在分类过程中易受异常值影响的问题,提出了一种鲁棒的模糊最小二乘双参数间隔支持向量机算法(RFLSTPMSVM).该算法利用松弛变量的2范数使得优化问题具有强凸性,再根据隶属度为每个样本分配相应的权重,有效降低异常值带来的影响.同时,在目标函数中引入K-近邻加权,考虑样本之间的局部信息,提高模型的分类准确率.此外,通过求解简单的线性方程组来优化该算法,而不是求解二次规划问题,使模型具有较快的计算速度.在UCI(university of California irvine)数据集上对该算法进行性能评估,并与TWSVM、LSTSVM、LSTPMSVM和ULSTPMSVM 4种算法进行比较.数值实验结果表明,该算法具有更好的泛化性能.
文摘针对模糊C均值算法(fuzzy C-means algorithm,简称FCM)在入侵检测中需要预先指定聚类数的问题,提出了一种自动决定聚类数算法(fuzzy C-means and support vector machine algorithm,简称F-CMSVM).它首先用模糊C均值算法把目标数据集分为两类,然后使用带有模糊成员函数的支持向量机(support vector machihe,简称SVM)算法对结果进行评估以确定目标数据集是否可分,再迭代计算,最终得到聚类结果.支持向量机算法引入模糊C均值算法得出的隶属矩阵作为模糊成员函数,使得不同的输入样本可以得到不同的惩罚值,从而得到最优的分类超平面.该算法既不需要对训练数据集进行标记,也不需要指定聚类数,因此是一种真正的无监督算法.在对KDD CUP 1999数据集的仿真实验结果表明,该算法不仅能够得到最佳聚类数,而且对入侵有较好的检测效果.
