Time Series Forecasting Using Wavelet-Least Squares Support Vector Machines and Wavelet Regression Models for Monthly Stream Flow Data

This study explores the least square support vector and wavelet technique (WLSSVM) in the monthly stream flow forecasting. This is a new hybrid technique. The 30 days periodic predicting statistics used in this study are derived from the subjection of this model to the river flow data of the Jhelum and Chenab rivers. The root mean square error (RMSE), mean absolute error (RME) and correlation (R) statistics are used for evaluating the accuracy of the WLSSVM and WR models. The accuracy of the WLSSVM model is compared with LSSVM, WR and LR models. The two rivers surveyed are in the Republic of Pakistan and cover an area encompassing 39,200 km2 for the Jhelum River and 67,515 km2 for the Chenab River. Using discrete wavelets, the observed data has been decomposed into sub-series. These have then appropriately been used as inputs in the least square support vector machines for forecasting the hydrological variables. The resultant observation from this comparison indicates the WLSSVM is more accurate than the LSSVM, WR and LR models in river flow forecasting.

ONLINE PARSIMONIOUS LEAST SQUARES SUPPORT VECTOR REGRESSION AND ITS APPLICATION

A simple and effective mechanism is proposed to realize the parsimoniousness of the online least squares support vector regression （LS-SVR）, and the approach is called the OPLS-SVR for short. Hence, the response time is curtailed. Besides, an OPLS-SVR based analytical redundancy technique is presented to cope with the sensor failure and drift problems to guarantee that the provided signals for the aeroengine controller are correct and acceptable. Experiments on the sensor failure and drift show the effectiveness and the validity of the proposed analytical redundancy.

BOOSTING SPARSE LEAST SQUARES SUPPORT VECTOR REGRESSION (BSLSSVR) AND ITS APPLICATION TO THRUST ESTIMATION

In order to realize direct thrust control instead of conventional sensors-based control for aero-engine, a thrust estimator with high accuracy is designed by using the boosting technique to improve the performance of least squares support vector regression （LSSVR）. There exist two distinct features compared with the conven- tional boosting technique： （1） Sampling without replacement is used to avoid numerical instability for modeling LSSVR. （2） To realize the sparseness of LSSVR and reduce the computational complexity, only a subset of the training samples is used to construct LSSVR. Thus, this boosting method for LSSVR is called the boosting sparse LSSVR （BSLSSVR）. Finally, simulation results show that BSLSSVR-based thrust estimator can satisfy the requirement of direct thrust control, i.e. , maximum absolute value of relative error of thrust estimation is not more than 5‰.

Resting-state functional magnetic resonance imaging and support vector machines for the diagnosis of major depressive disorder in adolescents

BACKGROUND Research has found that the amygdala plays a significant role in underlying pathology of major depressive disorder(MDD).However,few studies have explored machine learning-assisted diagnostic biomarkers based on amygdala functional connectivity(FC).AIM To investigate the analysis of neuroimaging biomarkers as a streamlined approach for the diagnosis of MDD in adolescents.METHODS Forty-four adolescents diagnosed with MDD and 43 healthy controls were enrolled in the study.Using resting-state functional magnetic resonance imaging,the FC was compared between the adolescents with MDD and the healthy controls,with the bilateral amygdala serving as the seed point,followed by statistical analysis of the results.The support vector machine(SVM)method was then applied to classify functional connections in various brain regions and to evaluate the neurophysiological characteristics associated with MDD.RESULTS Compared to the controls and using the bilateral amygdala as the region of interest,patients with MDD showed significantly lower FC values in the left inferior temporal gyrus,bilateral calcarine,right lingual gyrus,and left superior occipital gyrus.However,there was an increase in the FC value in Vermis-10.The SVM analysis revealed that the reduction in the FC value in the right lingual gyrus could effectively differentiate patients with MDD from healthy controls,achieving a diagnostic accuracy of 83.91%,sensitivity of 79.55%,specificity of 88.37%,and an area under the curve of 67.65%.CONCLUSION The results showed that an abnormal FC value in the right lingual gyrus was effective as a neuroimaging biomarker to distinguish patients with MDD from healthy controls.

Temperature prediction control based on least squares support vector machines

A prediction control algorithm is presented based on least squares support vector machines (LS-SVM) model for a class of complex systems with strong nonlinearity. The nonlinear off-line model of the controlled plant is built by LS-SVM with radial basis function (RBF) kernel. In the process of system running, the off-line model is linearized at each sampling instant, and the generalized prediction control (GPC) algorithm is employed to implement the prediction control for the controlled plant. The obtained algorithm is applied to a boiler temperature control system with complicated nonlinearity and large time delay. The results of the experiment verify the effectiveness and merit of the algorithm.

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。

Prediction of chaotic systems with multidimensional recurrent least squares support vector machines

In this paper, we propose a multidimensional version of recurrent least squares support vector machines （MDRLS- SVM） to solve the problem about the prediction of chaotic system. To acquire better prediction performance, the high-dimensional space, which provides more information on the system than the scalar time series, is first reconstructed utilizing Takens＇s embedding theorem. Then the MDRLS-SVM instead of traditional RLS-SVM is used in the high- dimensional space, and the prediction performance can be improved from the point of view of reconstructed embedding phase space. In addition, the MDRLS-SVM algorithm is analysed in the context of noise, and we also find that the MDRLS-SVM has lower sensitivity to noise than the RLS-SVM.

Sparse representation based on projection method in online least squares support vector machines

A sparse approximation algorithm based on projection is presented in this paper in order to overcome the limitation of the non-sparsity of least squares support vector machines （LS-SVM）. The new inputs are projected into the subspace spanned by previous basis vectors （BV） and those inputs whose squared distance from the subspace is higher than a threshold are added in the BV set, while others are rejected. This consequently results in the sparse approximation. In addition, a recursive approach to deleting an exiting vector in the BV set is proposed. Then the online LS-SVM, sparse approximation and BV removal are combined to produce the sparse online LS-SVM algorithm that can control the size of memory irrespective of the processed data size. The suggested algorithm is applied in the online modeling of a pH neutralizing process and the isomerization plant of a refinery, respectively. The detailed comparison of computing time and precision is also given between the suggested algorithm and the nonsparse one. The results show that the proposed algorithm greatly improves the sparsity just with little cost of precision.

New predictive control algorithms based on Least Squares Support Vector Machines

Used for industrial process with different degree of nonlinearity, the two predictive control algorithms presented in this paper are based on Least Squares Support Vector Machines (LS-SVM) model. For the weakly nonlinear system, the system model is built by using LS-SVM with linear kernel function, and then the obtained linear LS-SVM model is transformed into linear input-output relation of the controlled system. However, for the strongly nonlinear system, the off-line model of the controlled system is built by using LS-SVM with Radial Basis Function (RBF) kernel. The obtained nonlinear LS-SVM model is linearized at each sampling instant of system running, after which the on-line linear input-output model of the system is built. Based on the obtained linear input-output model, the Generalized Predictive Control (GPC) algorithm is employed to implement predictive control for the controlled plant in both algorithms. The simulation results after the presented algorithms were implemented in two different industrial processes model; respectively revealed the effectiveness and merit of both algorithms.

Application of least squares vector machines in modelling water vapor and carbon dioxide fluxes over a cropland

Least squares support vector machines (LS-SVMs), a nonlinear kemel based machine was introduced to investigate the prospects of application of this approach in modelling water vapor and carbon dioxide fluxes above a summer maize field using the dataset obtained in the North China Plain with eddy covariance technique. The performances of the LS-SVMs were compared to the corresponding models obtained with radial basis function (RBF) neural networks. The results indicated the trained LS-SVMs with a radial basis function kernel had satisfactory performance in modelling surface fluxes; its excellent approximation and generalization property shed new light on the study on complex processes in ecosystem.

Estimating Military Aircraft Cost Using Least Squares Support Vector Machines

A multi-layer adaptive optimizing parameters algorithm is developed forimproving least squares support vector machines (LS-SVM) , and a military aircraft life-cycle-cost(LCC) intelligent estimation model is proposed based on the improved LS-SVM. The intelligent costestimation process is divided into three steps in the model. In the first step, a cost-drive-factorneeds to be selected, which is significant for cost estimation. In the second step, militaryaircraft training samples within costs and cost-drive-factor set are obtained by the LS-SVM. Thenthe model can be used for new type aircraft cost estimation. Chinese military aircraft costs areestimated in the paper. The results show that the estimated costs by the new model are closer to thetrue costs than that of the traditionally used methods.

Design of Ballistic Consistency Based on Least Squares Support Vector Machine and Particle Swarm Optimization

In order to improve the firing efficiency of projectiles,it is required to use the universal firing table for gun weapon system equipped with a variety of projectiles.Moreover,the foundation of sharing the universal firing table is the ballistic matching for two types of projectiles.Therefore,a method is proposed in the process of designing new type of projectile.The least squares support vector machine is utilized to build the ballistic trajectory model of the original projectile,thus it is viable to compare the two trajectories.Then the particle swarm optimization is applied to find the combination of trajectory parameters which meet the criterion of ballistic matching best.Finally,examples show the proposed method is valid and feasible.

MULTI-RESOLUTION LEAST SQUARES SUPPORT VECTOR MACHINES

The Least Squares Support Vector Machines (LS-SVM) is an improvement to the SVM. Combined the LS-SVM with the Multi-Resolution Analysis (MRA),this letter proposes the Multi-resolution LS-SVM (MLS-SVM).The proposed algorithm has the same theoretical framework as MRA but with better approximation ability.At a fixed scale MLS-SVM is a classical LS-SVM,but MLS-SVM can gradually approximate the target function at different scales.In experiments,the MLS-SVM is used for nonlinear system identification,and achieves better identification accuracy.

NOISE REDUCTION FOR FAST FADING CHANNEL BY RECURRENT LEAST SQUARES SUPPORT VECTOR MACHINES IN EMBEDDING PHASE SPACES

A new strategy for noise reduction of fast fading channel is presented. Firstly, more information is acquired utilizing the reconstructed embedding phase space. Then, based on the Recurrent Least Squares Sup-port Vector Machines (RLS-SVM), noise reduction of the fast fading channel is realized. This filtering tech-nique does not make use of the spectral contents of the signal. Based on the stability and the fractal of the cha-otic attractor, the RLS-SVM algorithm is a better candidate for the nonlinear time series noise-reduction. The simulation results shows that better noise-reduction performance is acquired when the signal to noise ratio is 12dB.

NOVEL WEIGHTED LEAST SQUARES SUPPORT VECTOR REGRESSION FOR THRUST ESTIMATION ON PERFORMANCE DETERIORATION OF AERO-ENGINE

A thrust estimator with high precision and excellent real-time performance is needed to mitigate perfor- mance deterioration for future aero-engines. A weight least squares support vector regression is proposed using a novel weighting strategy. Then a thrust estimator based on the proposed regression is designed for the perfor- mance deterioration. Compared with the existing weighting strategy, the novel one not only satisfies the require- ment of precision but also enhances the real-time performance. Finally, numerical experiments demonstrate the effectiveness and feasibility of the proposed weighted least squares support vector regression for thrust estimator. Key words ： intelligent engine control; least squares ; support vector machine ; performance deterioration

Semi-supervised least squares support vector machine algorithm:application to offshore oil reservoir

At the early stages of deep-water oil exploration and development, fewer and further apart wells are drilled than in onshore oilfields. Supervised least squares support vector machine algorithms are used to predict the reservoir parameters but the prediction accuracy is low. We combined the least squares support vector machine （LSSVM） algorithm with semi-supervised learning and established a semi-supervised regression model, which we call the semi-supervised least squares support vector machine （SLSSVM） model. The iterative matrix inversion is also introduced to improve the training ability and training time of the model. We use the UCI data to test the generalization of a semi-supervised and a supervised LSSVM models. The test results suggest that the generalization performance of the LSSVM model greatly improves and with decreasing training samples the generalization performance is better. Moreover, for small-sample models, the SLSSVM method has higher precision than the semi-supervised K-nearest neighbor （SKNN） method. The new semi- supervised LSSVM algorithm was used to predict the distribution of porosity and sandstone in the Jingzhou study area.

NEW HYBRID AI-SVM ALGORITHM: COMBINATION OF SUPPORT VECTOR MACHINES AND ARTIFICIAL IMMUNE NETWORKS

Support vector machines （SVMs） are combined with the artificial immune network （aiNet）, thus forming a new hybrid ai-SVM algorithm. The algorithm is used to reduce the number of samples and the training time of SVM on large datasets, aiNet is an artificial immune system （AIS） inspired method to perform the automatic data compression, extract the relevant information and retain the topology of the original sample distribution. The output of aiNet is a set of antibodies for representing the input dataset in a simplified way. Then the SVM model is built in the compressed antibody network instead of the original input data. Experimental results show that the ai-SVM algorithm is effective to reduce the computing time and simplify the SVM model, and the accuracy is not decreased.

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.

Differentially Private Support Vector Machines with Knowledge Aggregation

With the widespread data collection and processing,privacy-preserving machine learning has become increasingly important in addressing privacy risks related to individuals.Support vector machine(SVM)is one of the most elementary learning models of machine learning.Privacy issues surrounding SVM classifier training have attracted increasing attention.In this paper,we investigate Differential Privacy-compliant Federated Machine Learning with Dimensionality Reduction,called FedDPDR-DPML,which greatly improves data utility while providing strong privacy guarantees.Considering in distributed learning scenarios,multiple participants usually hold unbalanced or small amounts of data.Therefore,FedDPDR-DPML enables multiple participants to collaboratively learn a global model based on weighted model averaging and knowledge aggregation and then the server distributes the global model to each participant to improve local data utility.Aiming at high-dimensional data,we adopt differential privacy in both the principal component analysis(PCA)-based dimensionality reduction phase and SVM classifiers training phase,which improves model accuracy while achieving strict differential privacy protection.Besides,we train Differential privacy(DP)-compliant SVM classifiers by adding noise to the objective function itself,thus leading to better data utility.Extensive experiments on three high-dimensional datasets demonstrate that FedDPDR-DPML can achieve high accuracy while ensuring strong privacy protection.

Comparison of debris flow susceptibility assessment methods:support vector machine,particle swarm optimization,and feature selection techniques

The selection of important factors in machine learning-based susceptibility assessments is crucial to obtain reliable susceptibility results.In this study,metaheuristic optimization and feature selection techniques were applied to identify the most important input parameters for mapping debris flow susceptibility in the southern mountain area of Chengde City in Hebei Province,China,by using machine learning algorithms.In total,133 historical debris flow records and 16 related factors were selected.The support vector machine(SVM)was first used as the base classifier,and then a hybrid model was introduced by a two-step process.First,the particle swarm optimization(PSO)algorithm was employed to select the SVM model hyperparameters.Second,two feature selection algorithms,namely principal component analysis(PCA)and PSO,were integrated into the PSO-based SVM model,which generated the PCA-PSO-SVM and FS-PSO-SVM models,respectively.Three statistical metrics(accuracy,recall,and specificity)and the area under the receiver operating characteristic curve(AUC)were employed to evaluate and validate the performance of the models.The results indicated that the feature selection-based models exhibited the best performance,followed by the PSO-based SVM and SVM models.Moreover,the performance of the FS-PSO-SVM model was better than that of the PCA-PSO-SVM model,showing the highest AUC,accuracy,recall,and specificity values in both the training and testing processes.It was found that the selection of optimal features is crucial to improving the reliability of debris flow susceptibility assessment results.Moreover,the PSO algorithm was found to be not only an effective tool for hyperparameter optimization,but also a useful feature selection algorithm to improve prediction accuracies of debris flow susceptibility by using machine learning algorithms.The high and very high debris flow susceptibility zone appropriately covers 38.01%of the study area,where debris flow may occur under intensive human activities and heavy rainfall events.