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 classifi-cation 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 pro-mise of faster algorithmic processing of data.However,FSVM and quantum com-puting 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 deter-mine whether a sample belongs to the positive or negative class while also achiev-ing 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 expo-nentially with the number of training samples.

Improved Twin Support Vector Machine Algorithm and Applications in Classification Problems

The distribution of data has a significant impact on the results of classification.When the distribution of one class is insignificant compared to the distribution of another class,data imbalance occurs.This will result in rising outlier values and noise.Therefore,the speed and performance of classification could be greatly affected.Given the above problems,this paper starts with the motivation and mathematical representing of classification,puts forward a new classification method based on the relationship between different classification formulations.Combined with the vector characteristics of the actual problem and the choice of matrix characteristics,we firstly analyze the orderly regression to introduce slack variables to solve the constraint problem of the lone point.Then we introduce the fuzzy factors to solve the problem of the gap between the isolated points on the basis of the support vector machine.We introduce the cost control to solve the problem of sample skew.Finally,based on the bi-boundary support vector machine,a twostep weight setting twin classifier is constructed.This can help to identify multitasks with feature-selected patterns without the need for additional optimizers,which solves the problem of large-scale classification that can’t deal effectively with the very low category distribution gap.

A new hybrid approach to assessing soil quality using neutrosophic fuzzy-AHP and support vector machine algorithm in sub-humid ecosystem

Soil quality determination and estimation is an important issue not only for terrestrial ecosystems but also for sustainable management of soils.In this study,soil quality was determined by linear and nonlinear standard scoring function methods integrated with a neutrosophic fuzzy analytic hierarchy process in the micro catchment.In addition,soil quality values were estimated using a support vector machine(SVM)in machine learning algorithms.In order to generate spatial distribution maps of soil quality indice values,different interpolation methods were evaluated to detect the most suitable semivariogram model.While the soil quality index values obtained by the linear method were determined between 0.458-0.717,the soil quality index with the nonlinear method showed variability at the levels of 0.433-0.651.There was no statistical difference between the two methods,and they were determined to be similar.In the estimation of soil quality with SVM,the normalized root means square error(NRMSE)values obtained in the linear and nonlinear method estimation were determined as 0.057 and 0.047,respectively.The spherical model of simple kriging was determined as the interpolation method with the lowest RMSE value in the actual and predicted values of the linear method while,in the nonlinear method,the lowest error in the distribution maps was determined with exponential of the simple kriging.

Fuzzy smooth support vector machine with different smooth functions

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）.

Fault Diagnosis Based on Fuzzy Support Vector Machine with Parameter Tuning and Feature Selection

This study describes a classification methodology based on support vector machines(SVMs),which offer superior classification performance for fault diagnosis in chemical process engineering.The method incorporates an efficient parameter tuning procedure(based on minimization of radius/margin bound for SVM's leave-one-out errors)into a multi-class classification strategy using a fuzzy decision factor,which is named fuzzy support vector machine(FSVM).The datasets generated from the Tennessee Eastman process(TEP)simulator were used to evaluate the clas-sification performance.To decrease the negative influence of the auto-correlated and irrelevant variables,a key vari-able identification procedure using recursive feature elimination,based on the SVM is implemented,with time lags incorporated,before every classifier is trained,and the number of relatively important variables to every classifier is basically determined by 10-fold cross-validation.Performance comparisons are implemented among several kinds of multi-class decision machines,by which the effectiveness of the proposed approach is proved.

Fuzzy least squares support vector machine soft measurement model based on adaptive mutative scale chaos immune algorithm

In order to enhance measuring precision of the real complex electromechanical system,complex industrial system and complex ecological & management system with characteristics of multi-variable,non-liner,strong coupling and large time-delay,in terms of the fuzzy character of this real complex system,a fuzzy least squares support vector machine(FLS-SVM) soft measurement model was established and its parameters were optimized by using adaptive mutative scale chaos immune algorithm.The simulation results reveal that fuzzy least squares support vector machines soft measurement model is of better approximation accuracy and robustness.And application results show that the relative errors of the soft measurement model are less than 3.34%.

Chaotic time series prediction using fuzzy sigmoid kernel-based support vector machines

Support vector machines （SVM） have been widely used in chaotic time series predictions in recent years. In order to enhance the prediction efficiency of this method and implement it in hardware, the sigmoid kernel in SVM is drawn in a more natural way by using the fuzzy logic method proposed in this paper. This method provides easy hardware implementation and straightforward interpretability. Experiments on two typical chaotic time series predictions have been carried out and the obtained results show that the average CPU time can be reduced significantly at the cost of a small decrease in prediction accuracy, which is favourable for the hardware implementation for chaotic time series prediction.

A Multiple Model Approach to Modeling Based on Fuzzy Support Vector Machines

A new multiple models(MM) approach was proposed to model complex industrial process by using Fuzzy Support Vector Machines(F -SVMs). By applying the proposed approach to a pH neutralization titration experiment, F -SVMs MM not only provides satisfactory approximation and generalization property, but also achieves superior performance to USOCPN multiple modeling method and single modeling method based on standard SVMs.

A soft-sensing model on hydraulic excavator's backhoe vibratory excavating resistance based on fuzzy support vector machine

In order to measure the backhoe vibratory excavating resistance of a hydraulic excavator fast and precisely,the influences of vibratory excavating depth,angle,vibratory frequency,amplitude,bucket inserting velocity and soil type on the vibratory excavating resistance were analyzed.Simulation analysis was carded out to establish the bucket inserting velocity,amplitude and vibratory frequency considered as secondary variables and excavating resistance as primary variable.A fttzzy membership function was introduced to improve the anti-noise capacity of support vector machine,which is a soft-sensing model on the hydraulic excavator＇s backhoe vibratory excavating resistance based on fuzzy support vector machine.The simulation result reveals that its maximum relative training and testing error are nearly 0.68% and-0.47%,respectively.It is concluded that the model has quite high modeling precision and generalization capacity,and it can measure the vibratory excavating resistance accurately,reliably and fast in an indirect way.

Generating Fuzzy Rule-based Systems from Examples Based on Robust Support Vector Machine

This paper firstly proposes a new support vector machine regression (SVR) with a robust loss function, and designs a gradient based algorithm for implementation of the SVR, then uses the SVR to extract fuzzy rules and designs fuzzy rule-based system. Simulations show that fuzzy rule-based system technique based on robust SVR achieves superior performance to the conventional fuzzy inference method, the proposed method provides satisfactory performance with excellent approximation and generalization property than the existing algorithm.

Fault Identification of Internal Combustion Engine based on Support Vector Machine and Fuzzy Neural Network

The internal combustion engine is the main power source of current large⁃scale machinery and equipment.Overhaul and maintenance of its faults are important conditions for ensuring the safe and stable operation of machinery and equipment,and the identification of faults is a prerequisite.Therefore,the fault identification of internal combustion engines is one of the important directions of current research.In order to further improve the accuracy of the fault recognition of internal combustion engines,this paper takes a certain type of internal combustion engine as the research object,and constructs a support vector machine and a fuzzy neural network fault recognition model.The binary tree multi⁃class classification algorithm is used to determine the priority,and then the fuzzy neural network is verified.The feasibility of the model is proved through experiments,which can quickly identify the failure of the internal combustion engine and improve the failure processing efficiency.

Fuzzy-support vector machine geotechnical risk analysis method based on Bayesian network

Machine learning method has been widely used in various geotechnical engineering risk analysis in recent years. However, the overfitting problem often occurs due to the small number of samples obtained in history. This paper proposes the FuzzySVM(support vector machine) geotechnical engineering risk analysis method based on the Bayesian network. The proposed method utilizes the fuzzy set theory to build a Bayesian network to reflect prior knowledge, and utilizes the SVM to build a Bayesian network to reflect historical samples. Then a Bayesian network for evaluation is built in Bayesian estimation method by combining prior knowledge with historical samples. Taking seismic damage evaluation of slopes as an example, the steps of the method are stated in detail. The proposed method is used to evaluate the seismic damage of 96 slopes along roads in the area affected by the Wenchuan earthquake. The evaluation results show that the method can solve the overfitting problem, which often occurs if the machine learning methods are used to evaluate risk of geotechnical engineering, and the performance of the method is much better than that of the previous machine learning methods. Moreover,the proposed method can also effectively evaluate various geotechnical engineering risks in the absence of some influencing factors.

Fault Diagnosis Model Based on Fuzzy Support Vector Machine Combined with Weighted Fuzzy Clustering

A fault diagnosis model is proposed based on fuzzy support vector machine (FSVM) combined with fuzzy clustering (FC).Considering the relationship between the sample point and non-self class,FC algorithm is applied to generate fuzzy memberships.In the algorithm,sample weights based on a distribution density function of data point and genetic algorithm (GA) are introduced to enhance the performance of FC.Then a multi-class FSVM with radial basis function kernel is established according to directed acyclic graph algorithm,the penalty factor and kernel parameter of which are optimized by GA.Finally,the model is executed for multi-class fault diagnosis of rolling element bearings.The results show that the presented model achieves high performances both in identifying fault types and fault degrees.The performance comparisons of the presented model with SVM and distance-based FSVM for noisy case demonstrate the capacity of dealing with noise and generalization.

Convective clouds detection in satellite cloud image using fast fuzzy support vector machine

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.

A Support Vector Machine-based Evaluation Model of Customer Satisfaction Degree in Logistics

This paper presents a novel evaluation model of the customer satisfaction degree （CSD） in logistics based on support vector machine （SVM）. Firstly, the relation between the suppliers and the customers is analyzed. Seondly, the evaluation index system and fuzzy quantitative methods are provided. Thirdly, the CSD evaluation system including eight indexes and three ranks based on one-against-one mode of SVM is built, last simulation experint is presented to illustrate the theoretical results.

Classification of the Priority of Auditing XBRL Instance Documents with Fuzzy Support Vector Machines Algorithm

Concluding the conformity of XBRL(eXtensible Business Reporting Language)instance documents law to the Benford's law yields different results before and after a company's financial distress.A new idea of applying the machine learning technique to redefine the way conventional auditors work is therefore proposed since the unacceptable conformity implies a large likelihood of a fraudulent document.Fuzzy support vector machines models are developed to implement such an idea.The dependent variable is a fuzzy variable quantifying the conformity of an XBRL instance document to the Benford's law;whereas,independent variables are financial ratios.The interval factor method is introduced to express the fuzziness in input data.It is found the range of a fuzzy support vector machines model is controlled by maximum and minimum dependent and independent variables.Therefore,defining any member function to describe the fuzziness in input data is unnecessary.The results of this study indicate that the price-to-book ratio versus equity ratio is suitable to classify the priority of auditing XBRL instance documents with the less than 30%misclassification rate.In conclusion,the machine learning technique may be used to redefine the way conventional auditors work.This study provides the main evidence of applying a future project of training smart auditors.

Classification using wavelet packet decomposition and support vector machine for digital modulations

To make the modulation classification system more suitable for signals in a wide range of signal to noise rate （SNR）, a feature extraction method based on signal wavelet packet transform modulus maxima matrix （WPTMMM） and a novel support vector machine fuzzy network （SVMFN） classifier is presented. The WPTMMM feature extraction method has less computational complexity, more stability, and has the preferable advantage of robust with the time parallel moving and white noise. Further, the SVMFN uses a new definition of fuzzy density that incorporates accuracy and uncertainty of the classifiers to improve recognition reliability to classify nine digital modulation types （i.e. 2ASK, 2FSK, 2PSK, 4ASK, 4FSK, 4PSK, 16QAM, MSK, and OQPSK）. Computer simulation shows that the proposed scheme has the advantages of high accuracy and reliability （success rates are over 98% when SNR is not lower than 0dB）, and it adapts to engineering applications.

Adaptive support vector machine decision feedback equalizer

An adaptive support vector machine decision feedback equalizer（ASVM-DFE） based on the least square support vector machine（LS-SVM） is proposed,it solves linear system iteratively with less computational intensity.An adaptive non-singleton fuzzy support vector machine decision feedback equalizer（ANSFSVMDFE） is also presented,it adopts the non-singleton fuzzy Gaussian kernel function with similar characteristic of pre-filter and is modified with a space transformation based approach.Simulations under nonlinear time variant channels show that ASVM-DFE and ANSFSVM-DFE perform very well on nonlinear equalization and ANSFSVM-DFE acts especially well in resisting abrupt interference.

Generalized Predictive Control with Online Least Squares Support Vector Machines

这份报纸基于能有效地处理非线性的系统的联机最少的广场支持向量机器(LS-SVM ) 建议一个实际概括预兆的控制(GPC ) 算法。在每个采样时期，算法递归地由增加新数据对并且在实时性质上从考虑删除最不重要的修改模型。删除的数据对被 lagrange 的绝对值从最后一个采样时期更多样地决定。当增加新数据对并且删除存在的时，纸给模型参数的递归的算法分别地，一个大矩阵的倒置被避免，存储器能被算法完全控制。非线性的 LS-SVM 模型在每个采样时期在 GPC 算法被使用。抵销过程的 pH 上的概括预兆的控制的实验显示出建议算法的有效性和实物。

Learning Vector Quantization-Based Fuzzy Rules Oversampling Method

Imbalanced datasets are common in practical applications,and oversampling methods using fuzzy rules have been shown to enhance the classification performance of imbalanced data by taking into account the relationship between data attributes.However,the creation of fuzzy rules typically depends on expert knowledge,which may not fully leverage the label information in training data and may be subjective.To address this issue,a novel fuzzy rule oversampling approach is developed based on the learning vector quantization(LVQ)algorithm.In this method,the label information of the training data is utilized to determine the antecedent part of If-Then fuzzy rules by dynamically dividing attribute intervals using LVQ.Subsequently,fuzzy rules are generated and adjusted to calculate rule weights.The number of new samples to be synthesized for each rule is then computed,and samples from the minority class are synthesized based on the newly generated fuzzy rules.This results in the establishment of a fuzzy rule oversampling method based on LVQ.To evaluate the effectiveness of this method,comparative experiments are conducted on 12 publicly available imbalance datasets with five other sampling techniques in combination with the support function machine.The experimental results demonstrate that the proposed method can significantly enhance the classification algorithm across seven performance indicators,including a boost of 2.15%to 12.34%in Accuracy,6.11%to 27.06%in G-mean,and 4.69%to 18.78%in AUC.These show that the proposed method is capable of more efficiently improving the classification performance of imbalanced data.