Online least squares support vector machine regression based on rectangular window with forgetting factor algorithm

This article adopts least square support vector machine (LSSVM) and multivariate adaptive regression spline (MARS) for prediction of lateral load capacity (Q) of pile foundation. LSSVM is firmly based on the theory of statistical learning, uses regression technique. MARS is a nonparametric regression technique that models complex relationships. Diameter of pile (D), depth of pile embedment (L), eccentricity of load (e), and undrained shear strength of soil (Su) have been used as input parameters of LSSVM and MARS. Equations have been presented from the developed MARS and LSSVM. This study also presents a comparative study between the developed MARS and LSSVM.

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.

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.

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.

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.

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.

Application of least square support vector machine and multivariate adaptive regression spline models in long term prediction of river water pollution

Error tolerance based support vector machine for regression

Due to the growth prospect of analog circuit fault diagnosis, this paper tends to introduce a novel arithmetic model based on least squares support vector machine (LSSVM) and the semi-supervised learning (SSL) scheme which is adept at cost-saving. The proposed method contains two steps. Firstly, the fact that large deviation may emerge as a result of the empirical risk inspires the idea of an improved transductive least square support vector machine (T-LSSVM) which aims at obtaining the best hyperplane that equipped with the maximum margin to the support vectors no matter whether the samples are labeled or unlabeled. Secondly, to overcome the drawback of typical T-LSSVM, i.e., sensitivity to local minima, a laplcian-transductive least squares support vector machine (Lap-T-LSSVM) is proposed which can perform the fault diagnosis via a laplcian. The experiment adopts band-pass filter circuit as diagnosis object. Simulation results verify that the proposed method is superior to previous SVM in accuracy.

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.

Wind speed is an important data in the research of the output power in wind farm, but the measured wind speed data have the problem of missing data, meanwhile, the wind speed data also have the characteristics of nonlinearity. Least squares support vector machines (LSSVM) model has strong ability of nonlinear fitting, so LSSVM model is used as the model of interpolating missing wind speed data in this paper, and optimal interpolation model of missing wind speed data is established by using comprehensive learning particle swarm optimization (CLPSO) that has good global search ability to optimize hyper-parameters of LSSVM model. The simulation results indicate: the precision of interpolating tested data by optimized LSSVM model is better, the results of interpolating missing wind speed data fit with the variation of wind speed data at adjacent level, the effectiveness of the interpolation model is verified.

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.