Primal-dual framework for feature selection using least squares support vector machines

Classical support vector machine (SVM) and its twin variant twin support vector machine (TWSVM) utilize the Hinge loss that shows linear behaviour, whereas the least squares version of SVM (LSSVM) and twin least squares support vector machine (LSTSVM) uses L2-norm of error which shows quadratic growth. The robust Huber loss function is considered as the generalization of Hinge loss and L2-norm loss that behaves like the quadratic L2-norm loss for closer error points and the linear Hinge loss after a specified distance. Three functional iterative approaches based on generalized Huber loss function are proposed in this paper to solve support vector classification problems of which one is based on SVM, i.e. generalized Huber support vector machine and the other two are in the spirit of TWSVM, namely generalized Huber twin support vector machine and regularization on generalized Huber twin support vector machine. The proposed approaches iteratively find the solutions and eliminate the requirements to solve any quadratic programming problem (QPP) as for SVM and TWSVM. The main advantages of the proposed approach are: firstly, utilize the robust Huber loss function for better generalization and for lesser sensitivity towards noise and outliers as compared to quadratic loss; secondly, it uses functional iterative scheme to find the solution that eliminates the need to solving QPP and also makes the proposed approaches faster. The efficacy of the proposed approach is established by performing numerical experiments on several real-world datasets and comparing the result with related methods, viz. SVM, TWSVM, LSSVM and LSTSVM. The classification results are convincing.

Utilization of SVM, LSSVM and GP for Predicting the Medical Waste Generation

The prediction of wastes generated in the hospital will help their management for several activities like storage, transport and disposing. This chapter adopts Support Vector Machine (SVM), Least Square Support Vector Machine (LSSVM) and Genetic Programming (GP) in order to estimate the rate of medical waste generation. In the event of predicting the rate, type of hospital, capacity and bed occupancy has been used as inputs of SVM, LSSVM and GP. SVM is based on statistical learning theory, which provides an elegant tool for nonlinear system modeling. LSSVM is the re-formulation to the general SVM. GP, a best part of evolutionary algorithm and also the specification of Genetic Algorithm (GA). These SVM, LSSVM and GP have been used as the regression techniques. The results show the performance of the developed SVM, LSSVM and GP models were elegant and outstanding.

The objective of this paper was to determine soluble solids content (SSC) of intact Gannan navel orange by a portable near-infrared (NIR) spectrometer with the optical fiber in the wavelength range of 551~950nm. The effective wavelength regions (EWs) were chosen from the spectra pro-processed by second derivative by interval partial least square (iPLS) and backward interval partial least square (Bipls). Then the partial least square (PLS) and least square support vector machine (LS-SVM) models were developed with EWs. 60 unknown samples were used to evaluate the performance of them. The LS-SVM model was better than others with EWs chosen by Bilps. The correlation coefficient (R) and root mean square error of prediction (RMSEP) for LS-SVM (Bipls) were 0.86 and 0.55°Brix. The results showed that the portable NIR combination with LS-SVM was a feasible method to determine SSC of intact Gannan navel orange nondestructively.

The prediction of wastes generated in the hospital will help their management for several activities like storage, transport and disposing. This chapter adopts Support Vector Machine (SVM), Least Square Support Vector Machine (LSSVM) and Genetic Programming (GP) in order to estimate the rate of medical waste generation. In the event of predicting the rate, type of hospital, capacity and bed occupancy has been used as inputs of SVM, LSSVM and GP. SVM is based on statistical learning theory, which provides an elegant tool for nonlinear system modeling. LSSVM is the re-formulation to the general SVM. GP, a best part of evolutionary algorithm and also the specification of Genetic Algorithm (GA). These SVM, LSSVM and GP have been used as the regression techniques. The results show the performance of the developed SVM, LSSVM and GP models were elegant and outstanding.

The minimal complexity support vector machine is a fusion of the support vector machine (SVM) and the minimal complexity machine (MCM), and results in maximizing the minimum margin and minimizing the maximum margin. It works to improve the generalization ability of the L1 SVM (standard SVM) and LP (Linear Programming) SVM. In this paper, we discuss whether it also works for the LS (Least Squares) SVM. The minimal complexity LS SVM (MLS SVM) is trained by minimizing the sum of squared margin errors and minimizing the maximum margin. This results in solving a set of linear equations and a quadratic program, alternatingly. According to the computer experiments for two-class and multiclass problems, the MLS SVM does not outperform the LS SVM for the test data although it does for the cross-validation data.

This article adopts three soft computing techniques including support vector machine (SVM), least square support vector machine (LSSVM) and relevance vector machine (RVM) for prediction of status of epimetemorphic rock slope. The input variables of SVM, LSSVM and RVM are bulk density, height, inclination, cohesion and internal friction angle. There are 53 datasets which have been used to develop the SVM, LSSVM and RVM models. The developed SVM, LSSVM and RVM give equations for prediction of status of epimetemorphic rock slope. The performance of SVM, LSSVM and RVM is 100%. A comparative study has been presented between the developed SVM, LSSVM and RVM. The results confirm that the developed SVM, LSSVM and RVM are effective tools for prediction of status of epimetemorphic rock slope.

This paper addresses processing of spectrophotometric array signals based on genetic algorithms (GA) least square support vector machines (LS-SVM) regression to provide a powerful model for machine learning and data mining. The key to complete LS-SVM regression is to choose its optimal parameters. Due to their outstanding ability in solving global optimization problems in complex multidimensional search space, GA are used in this study to obtain the optimal parameter combination of the LS-SVM model. Experimental results showed the GA-LS-SVM method to be successful for simultaneous multicomponent determination even where severe overlap of spectra was present. KeywordsLeast squares support vector machines; Genetic algorithms; Spectrophotometric array signals; Overlapping spectra; Artificial intelligence Nowadays, with the application of photometric diode array detector and computers, rapid scanning commercial spectrophotometers are capable of quickly generating huge data consisting of hundreds and even thousands of absorbance values per spectrum. The array data named fullspectrum contain sufficient information to be able to determine the contents of various compounds. The main drawback of ultraviolet-visible (UV-VIS) is its poor selectivity because in many cases UV-VIS spectra display strong overlaps, especially some less specific and selective chromagenic reagents often give rise to strongly overlapped spectra in many cases. The combination of artificial intelligence methods with the computer-controlled spectrophotometers was proven to be effective in overcoming this difficulty [1-3]. Artificial neural network (ANN) is a form of artificial intelligence that mathematically simulates biological nervous system [4, 5]. However, ANN often has slow convergence, is prone to the existence of many local minima during training, and has a tendency of overfitting. Recently, a promising technology called support vector machines (SVM) has been used for classification and regression problems. SVM pioneered by Vapnik is a kind of machine learning method based on modern statistical learning theory and has notable properties including absence of local minima and high generalization ability [6, 7]. Suykens and his coworkers [8] introduced a modified version of SVM called least square SVM (LS-SVM) , which requires solving a set of linear equations instead of a quadratic programming problem and is much easier and computationally simpler than SVM. SVM and LS-SVM represent relatively recent artificial intelligence method and have found some applications in image analysis, classification and disease diagnosis etc. [9, 10]. It is worth mentioning that the success of LS-SVM model is highly dependent on the optimum choice of two parameters, the relative weight of regression error γ and the kernel width σ of radial basis function (RBF). Genetic algorithms (GA) [11, 12] introduced by John Holland are probabilistic optimization techniques based on natural evolution and genetics and Darwin’s theory of survival of the best. With their efficient and robust global search ability, GA are used to search two optimal parameters for the LS-SVM model simultaneously and automatically. The LS-SVM model then performs the regression task using these optimal parameters.

Improving forecasts, particularly the accuracy, efficiency, and precision of time-series forecasts, is becoming critical for authorities to predict, monitor, and prevent the spread of the Coronavirus disease. However, the results obtained from the predictive models are imprecise and inefficient because the dataset contains linear and non-linear patterns, respectively. Linear models such as autoregressive integrated moving average cannot be used effectively to predict complex time series, so nonlinear approaches are better suited for such a purpose. Therefore, to achieve a more accurate and efficient predictive value of COVID-19 that is closer to the true value of COVID-19, a hybrid approach was implemented. Therefore, the objectives of this study are twofold. The first objective is to propose intelligence-based prediction methods to achieve better prediction results called autoregressive integrated moving average-least-squares support vector machine. The second objective is to investigate the performance of these proposed models by comparing them with the autoregressive integrated moving average, support vector machine, least-squares support vector machine, and autoregressive integrated moving average-support vector machine. Our investigation is based on three COVID-19 real datasets, i.e., daily new cases data, daily new death cases data, and daily new recovered cases data. Then, statistical measures such as mean square error, root mean square error, mean absolute error, and mean absolute percentage error were performed to verify that the proposed models are better than the autoregressive integrated moving average, support vector machine model, least-squares support vector machine, and autoregressive integrated moving average-support vector machine. Empirical results using three recent datasets of known the Coronavirus Disease-19 cases in Malaysia show that the proposed model generates the smallest mean square error, root mean square error, mean absolute error, and mean absolute percentage error values for training and testing datasets compared to the autoregressive integrated moving average, support vector machine, least-squares support vector machine, and autoregressive integrated moving average-support vector machine models. This means that the predicted value of the proposed model is closer to the true value. These results demonstrate that the proposed model can generate estimates more accurately and efficiently. Compared to the autoregressive integrated moving average, support vector machine, least-squares support vector machine, and autoregressive integrated moving average-support vector machine models, our proposed models perform much better in terms of percent error reduction for both training and testing all datasets. Therefore, the proposed model is possibly the most efficient and effective way to improve prediction for future pandemic performance with a higher level of accuracy and efficiency.

Fast discrimination of rice varieties plays a key role in the rice processing industry and benefits the management of rice in the supermarket. In order to discriminate rice varieties in a fast and nondestructive way, hyperspectral technology and several classification algorithms were used in this study. The hyperspectral data of 250 rice samples of 5 varieties were obtained using FieldSpec®3 spectrometer. Multiplication Scatter Correction (MSC) was used to preprocess the raw spectra. Principal Component Analysis (PCA) was used to reduce the dimension of raw spectra. To investigate the influence of different linear and non-linear classification algorithms on the discrimination results, K-Nearest Neighbors (KNN), Support Vector Machine (SVM) and Least Square Support Vector Machine (LS-SVM) were used to develop the discrimination models respectively. Then the performances of these three multivariate classification methods were compared according to the discrimination accuracy. The number of Principal Components (PCs) and K parameter of KNN, kernel function of SVM or LS-SVM, were optimized by cross-validation in corresponding models. One hundred and twenty five rice samples (25 of each variety) were chosen as calibration set and the remaining 125 rice samples were prediction set. The experiment results showed that, the optimal PCs was 8 and the cross-validation accuracy of KNN (K = 2), SVM, LS-SVM were 94.4, 96.8 and 100%, respectively, while the prediction accuracy of KNN (K = 2), SVM, LS-SVM were 89.6, 93.6 and 100%, respectively. The results indicated that LS-SVM performed the best in the discrimination of rice varieties.

Demand-side management (DSM) has been introduced and paid much effort in the electricity industry for such a long time, and become more and more focused in the most of the electricity markets recent years, because of its effect on the modification of consumer demand for energy through various methods especially financial incentives. But due to the complexity of the influence factors, the demand elasticity analysis on electric load is along one of focused and unsolved problems in the researches of electricity market. This paper presents a mathematical tool based on optimization models that is intended to be used to evaluate the load elasticity. Here one effective way of tackling the elasticity computation problem is proposed to simulate the accurate demand response for its influence factors, where least square support vector machine (LS-SVM) is generalized to build the simulation model. First to overcome the limitations of traditional parametric regression methods based on least square rule, load mapping model are accomplished by LS-SVM that is a strong nonlinear regression tool and outperforms standard support vector machine in the regression accuracy and modeling velocity by obtaining the solutions of a set of linear equations instead of solving a quadratic programming problem. Based on that model, numerical simulation is performed to simulate the changes in load and its influence factor in consistency with the latent mapping relationship. Then demand elasticity models are deduced, whose elasticity coefficients are computed by the generated samples. The method embodies clear concepts, so it can be easily understood theoretical and computationally realized. Case studies are used to test the proposed model. In this scenario, the goal is to show the response of demands to different influence signals. Alternative analyses based on assessing the elasticity of power to other input parameters could be also carried out.

Accurate electricity price prediction is key to the orderly operation of the electricity market. However, the uncertain, stochastic and fluctuant characteristics of electricity pricees make prediction difficult. With the aim of solving this issue, this investigation proposed a multi-stage intelligent model integrating the Beveridge–Nelson decomposition (B-N-D) model, the least square support vector machine (LSSVM), and a nature-inspired optimization model named the whale optimization algorithm (WOA). Firstly, the B-N-D model was utilized to decompose the hourly electricity price time series into determinacy component, periodic trend, and stochastic item. Secondly, the WOA–LSSVM model was proposed to forecast the future hourly data of three components respectively, of which the optimal parameters of LSSVM were determined by using WOA. Finally, the future hourly electricity price data were computed by multiplying the forecasted data of those terms. To verify the validity of the proposed electricity price prediction model in this paper, five comparison approaches based on the B-N-D approach were selected, which are auto-regressive integrated moving average (ARIMA), single LSSVM, LSSVM optimized by the fruit-fly optimization algorithm (FOA), LSSVM optimized by particle swarm optimization (PSO) models, and WOA–LSSVM without B-N-D. By comparatively analyzing the error criteria values of the above models through testing on the objective data of the Pennsylvania–New Jersey–Maryland (PJM) electricity market collected from 11 December 2017 to 18 December 2017, from 15 January 2018 to 22 January 2018, and from 1 February 2018 to 25 February 2018, we conclude that the constructed intelligent model in this paper can greatly enhance the prediction precision of electricity prices.

According to the current electricity price forecasting studies, it was very difficult to conclude whether support vector machine (SVM) or least squares support vector machine (LSSVM) is more suitable in solving highly non-linear regression problems with very large time horizon such as mid-term electricity market clearing price (MCP) forecasting. In this paper, a detailed evaluation process using price zones analysis technique is applied in evaluating single SVM and single LSSVM based mid-term electricity MCP forecasting models. Based on much more detailed performance evaluation results and consideration of requirements for machine learning techniques utilizing in longer time horizon and highly nonlinear questions, the proposed paper concluded that SVM is more suitable than LSSVM in mid-term electricity MCP forecasting. Numerical examples using PJM interconnection data are utilized to illustrate the conclusion.

In the practical implementation of control of electromyography (sEMG) driven devices, algorithms should recognize the human’s motion from sEMG with fast speed and high accuracy. This study proposes two feature engineering (FE) techniques, namely, feature-vector resampling and time-lag techniques, to improve the accuracy and speed of least square support vector machine (LSSVM) for wrist palmar angle estimation from sEMG feature. The root mean square error and correlation coefficients of LSSVM with FE are 9.50 2.32 degree and 0.971 0.018 respectively. The average training time and average execution time of LSSVM with FE in processing 12600 sEMG points are 0.016 s and 0.053 s respectively. To evaluate the proposed algorithm, its estimation results are compared with those of three other methods, namely, LSSVM, radial basis function (RBF) neural network, and RBF with FE. Experimental results verify that introduction of time-lag into feature vector can greatly improve the estimation accuracy of both RBF and LSSVM; meanwhile the application of feature-vector resampling technique can significantly increase the training and execution speed of RBF neural network and LSSVM. Among different algorithms applied in this study, LSSVM with FE techniques performed best in terms of training and execution speed, as well as estimation accuracy.

Least squares support vector machine (LS-SVM) is a modified version of traditional support vector machine (SVM). LS-SVM considers equality constraints, therefore it solves a set of linear equations instead of quadratic programming problem in SVM. However, the sparseness of LS-SVM is lost due to itpsilas isin-sensitive cost function. Sparseness can be obtained by applying a pruning method, which eliminates some vectors with smallest support values and retrains the remaining samples. But iterative retraining is a time-consuming process. Motivated by the fact that boundary samples are more significant for constructing a LS-SVM classifier, this paper proposes a method of using pulse coupled neural networks (PCNNs) to search boundary samples of original data sets. The original data sets are mapped into some PCNN neurons, and a firing algorithm is designed to determine which samples lie at boundary region. It gives a novel approach to impose sparsity for LS-SVM. Experiments show that the proposed method can effectively detect boundary samples and speed up LS-SVM classifiers.