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The performance of machine learning algorithms is affected by the imbalanced distribution of data among classes. This issue is crucial in various practical problem domains, for example, in medical diagnosis, network intrusion, fraud detection etc. Most efforts so far are mainly focused upon binary class imbalance problem. However, the class imbalance problem is also reported in multi-class scenario. The solutions proposed by the researchers for two-class scenario are not applicable to multi-class domains. So, in this paper, we have developed an effective Weighted Multi-class Least Squares Twin Support Vector Machine (WMLSTSVM) approach to address the problem of imbalanced data classification for multi class. This research work employs appropriate weight setting in loss function, e.g. it adjusts the cost of error for imbalanced data in order to control the sensitivity of the classifier. In order to prove the validity of the proposed approach, the experiment has been performed on fifteen benchmark datasets. The performance of proposed WMLSTSVM is analyzed and compared with some other SVMs and TWSVMs and it is observed that our proposed approach outperforms all of them. The proposed approach is statistically analyzed by using non-parametric Wilcoxon signed rank and Friedman tests.

  With the rapid development of human society, resource shortages and environmental degradation have become increasingly pressing issues. To address these challenges, solar energy has garnered significant attention due to its high efficiency, safety, and pollution-free nature. This paper proposes a novel short-term photovoltaic power prediction framework based on an integrated LMD-IPSO-LSVM approach. The model's key innovation lies in its hierarchical decomposition-optimization architecture: First, Local Mean Decomposition (LMD) addresses the non-stationary and nonlinear characteristics of PV power data by decomposing original signals into physically meaningful Product Functions (PFs). Second, an Improved Particle Swarm Optimization (IPSO) algorithm featuring an adaptive inertia weight mechanism is developed to optimize LSVM hyperparameters for each PF component. This strategic integration enables the model to simultaneously capture complex temporal patterns while maintaining superior generalization capability. Experimental validation demonstrates that our IPSO achieves significantly faster convergence (46.3% improvement in convergence speed) and enhanced optimization precision compared to standard PSO, providing a solid foundation for accurate power forecasting. In order to evaluate the proposed methodology, comparative models including standalone LSVM and PSO-LSVM are also established and tested on the same dataset. Experimental results demonstrate that the proposed hybrid model called LMD-IPSO-LSVM achieves high prediction accuracy and better performance compared with other algorithms.  

Support vector machines (SVMs) have been proved effective and promising techniques for classification problem. Recently, SVMs have been successfully applied to target diseases classification and prediction by using real-world data. In this paper, we propose a new quadratic kernel-free least squares support vector machine (QLSSVM) for binary classification problem. The model of QLSSVM is a convex quadratic programming problem with an advantage of kernel-free, compared with the existed least squares SVM. By using consensus technique, the decision variables of QLSSVM are split into local variable and global variable. Then the QLSSVM is converted into the consensus QLSSVM and solved by alternating direction method of multipliers with a Gaussian back substitution. Finally, our QLSSVM is illustrated in terms of numerical tests based on two types of training data sets. The first numerical test is implemented based on artificial data to certify the performance of our QLSSVM. To apply our QLSSVM to disease classification, the second one is implemented based on diseases data set from University of California, Irvine, Machine Learning Repository to demonstrates that our model has higher classification accuracy compared with several existed methods. In particularly, our numerical example is implemented based on a special heart disease data set provided by Hungarian heart disease database to illustrates the effectiveness of our QLSSVM for a particular disease diagnosis.

Hysteresis is a non−unique phenomenon known as a multi−valued mapping in different fields of science and engineering. Accurate identification of the hysteretic systems is a crucial step in hysteresis compensation and control. This study proposes a novel approach for simulating hysteresis with various features that combines the extreme learning machine (ELM) and least−squares support vector machine (LS−SVM). First, the hysteresis is converted into a single−valued mapping by deteriorating stop operators, a combination of stop and play hysteresis operators. Then, the converted mapping is learned by a LS−SVM model. This approach facilitates the training steps and provides more accurate results in contrast to the previous experimental studies. The proposed model is evaluated for several hystereses with various properties. These properties include rate−independent or rate−dependent, congruent or non-congruent, and symmetric or asymmetric problems. The results indicate the efficiency of the newly developed technique in terms of accuracy, computational cost, and convergence rate.

Support vector machine (SVM), as an effective method in classification problems, tries to find the optimal hyperplane that maximizes the margin between two classes and can be obtained by solving a constrained optimization criterion using quadratic programming (QP). This QP leads to higher computational cost. Least squares support vector machine (LS-SVM), as a variant of SVM, tries to avoid the above shortcoming and obtain an analytical solution directly from solving a set of linear equations instead of QP. Both SVM and LS-SVM operate directly on patterns represented by vector, i.e., before applying SVM or LS-SVM to a pattern, any non-vector pattern such as an image has to be first vectorized into a vector pattern by some techniques like concatenation. However, some implicit structural or local contextual information may be lost in this transformation. Moreover, as the dimension d of the weight vector in SVM or LS-SVM with the linear kernel is equal to the dimension d1 × d2 of the original input pattern, as a result, the higher the dimension of a vector pattern is, the more space is needed for storing it. In this paper, inspired by the method of feature extraction directly based on matrix patterns and the advantages of LS-SVM, we propose a new classifier design method based on matrix patterns, called MatLSSVM, such that the new method can not only directly operate on original matrix patterns, but also efficiently reduce memory for the weight vector (d) from d1 × d2 to d1 + d2. However like LS-SVM, MatLSSVM inherits LS-SVM’s existence of unclassifiable regions when extended to multi-class problems. Thus with the fuzzy version of LS-SVM, a corresponding fuzzy version of MatLSSVM (MatFLSSVM) is further proposed to remove unclassifiable regions effectively for multi-class problems. Experimental results on some benchmark datasets show that the proposed method is competitive in classification performance compared to LS-SVM, fuzzy LS-SVM (FLS-SVM), more-recent MatPCA and MatFLDA. In addition, more importantly, the idea used here has a possibility of providing a novel way of constructing learning model.

Aiming at the problem that the most existing fault diagnosis methods could not effectively recognize the early faults in the rotating machinery, the empirical mode decomposition, fuzzy information entropy, improved particle swarm optimization algorithm and least squares support vector machines are introduced into the fault diagnosis to propose a novel intelligent diagnosis method, which is applied to diagnose the faults of the motor bearing in this paper. In the proposed method, the vibration signal is decomposed into a set of intrinsic mode functions (IMFs) by using empirical mode decomposition method. The fuzzy information entropy values of IMFs are calculated to reveal the intrinsic characteristics of the vibration signal and considered as feature vectors. Then the diversity mutation strategy, neighborhood mutation strategy, learning factor strategy and inertia weight strategy for basic particle swarm optimization (PSO) algorithm are used to propose an improved PSO algorithm. The improved PSO algorithm is used to optimize the parameters of least squares support vector machines (LS-SVM) in order to construct an optimal LS-SVM classifier, which is used to classify the fault. Finally, the proposed fault diagnosis method is fully evaluated by experiments and comparative studies for motor bearing. The experiment results indicate that the fuzzy information entropy can accurately and more completely extract the characteristics of the vibration signal. The improved PSO algorithm can effectively improve the classification accuracy of LS-SVM, and the proposed fault diagnosis method outperforms the other mentioned methods in this paper and published in the literature. It provides a new method for fault diagnosis of rotating machinery.

The determination of epileptogenic area is a prime task in presurgical evaluation. The seizure activity can be prevented by operating the affected areas by clinical surgery. In this paper, an automatic approach has been presented to detect electroencephalogram (EEG) signals of non-focal and focal groups. The proposed approach can be used to determine the area linked to the focal epilepsy. In our method, the EEG signal is decomposed into rhythms using empirical wavelet transform technique. The two-dimensional (2D) projections of the reconstructed phase space (RPS) have been obtained for the rhythms. Area measures for various RPS plots are estimated using central tendency measure (CTM) parameter. The area parameters are used with least-squares support vector machine (LS-SVM) classifier to classify the focal and non-focal classes of EEG signals. In this work, we have achieved a maximum classification accuracy of 90%, sensitivity and specificity of 88 and 92%, respectively, using 50 pairs of focal and non-focal EEG signals. The same method has achieved maximum classification accuracy, sensitivity and specificity of 82.53, 81.60 and 83.46%, respectively, with 750 pairs of signals. The developed prototype can be used for the epileptic patients and aid the clinicians to confirm diagnosis.

In this study, a model is proposed by applying the least squares support vector machine (LSSVM). In addition, genetic algorithm is used for selection and optimization of hyperparameters that are embedded in the LSSVM model. In addition to temperature and concentration of nanoparticles, the parameters which are used in most of the modeling procedures for thermal conductivity, the effect of particle size is considered. By considering the size of nanoparticles as one of the input variables, a more comprehensive model is obtained which is applicable for wider ranges of influential factor on the thermal conductivity of the nanofluid. The coefficient of determination ( R 2 ) for the introduced model is equal to 0.9902, and the mean squared error is 8.64 × 10 −4 for the thermal conductivity ratio of Al 2 O 3 /EG.

Rapid and accurate crop aboveground biomass estimation is beneficial for high-throughput phenotyping and site-specific field management. This study explored the utility of high-definition digital images acquired by a low-flying unmanned aerial vehicle (UAV) and ground-based hyperspectral data for improved estimates of winter wheat biomass. To extract fine textures for characterizing the variations in winter wheat canopy structure during growing seasons, we proposed a multiscale texture extraction method (Multiscale_Gabor_GLCM) that took advantages of multiscale Gabor transformation and gray-level co-occurrency matrix (GLCM) analysis. Narrowband normalized difference vegetation indices (NDVIs) involving all possible two-band combinations and continuum removal of red-edge spectra (SpeCR) were also extracted for biomass estimation. Subsequently, non-parametric linear (i.e., partial least squares regression, PLSR) and nonlinear regression (i.e., least squares support vector machine, LSSVM) analyses were conducted using the extracted spectral features, multiscale textural features and combinations thereof. The visualization technique of LSSVM was utilized to select the multiscale textures that contributed most to the biomass estimation for the first time. Compared with the best-performing NDVI (1193, 1222 nm), the SpeCR yielded higher coefficient of determination (R2), lower root mean square error (RMSE), and lower mean absolute error (MAE) for winter wheat biomass estimation and significantly alleviated the saturation problem after biomass exceeded 800 g/m2. The predictive performance of the PLSR and LSSVM regression models based on SpeCR decreased with increasing bandwidths, especially at bandwidths larger than 11 nm. Both the PLSR and LSSVM regression models based on the multiscale textures produced higher accuracies than those based on the single-scale GLCM-based textures. According to the evaluation of variable importance, the texture metrics “Mean” from different scales were determined as the most influential to winter wheat biomass. Using just 10 multiscale textures largely improved predictive performance over using all textures and achieved an accuracy comparable with using SpeCR. The LSSVM regression model based on the combination of the selected multiscale textures, and SpeCR with a bandwidth of 9 nm produced the highest estimation accuracy with R2val = 0.87, RMSEval = 119.76 g/m2, and MAEval = 91.61 g/m2. However, the combination did not significantly improve the estimation accuracy, compared to the use of SpeCR or multiscale textures only. The accuracy of the biomass predicted by the LSSVM regression models was higher than the results of the PLSR models, which demonstrated LSSVM was a potential candidate to characterize winter wheat biomass during multiple growth stages. The study suggests that multiscale textures derived from high-definition UAV-based digital images are competitive with hyperspectral features in predicting winter wheat biomass.

Detecting pipeline leaks is an essential factor in maintaining the integrity of fluid transport systems. This paper introduces an advanced deep learning framework that uses continuous wavelet transform (CWT) images for precise detection of such leaks. Transforming acoustic signals from pipelines under various conditions into CWT scalograms, followed by signal processing by non-local means and adaptive histogram equalization, results in new enhanced leak-induced scalograms (ELIS) that capture detailed energy fluctuations across time-frequency scales. The fundamental approach takes advantage of a deep belief network (DBN) fine-tuned with a genetic algorithm (GA) and unified with a least squares support vector machine (LSSVM) to improve feature extraction and classification accuracy. The DBN-GA framework precisely extracts informative features, while the LSSVM classifier precisely distinguishes between leaky and non-leak conditions. By concentrating solely on the advanced capabilities of ELIS processed through an optimized DBN-GA-LSSVM model, this research achieves high detection accuracy and reliability, making a significant contribution to pipeline monitoring and maintenance. This innovative approach to capturing complex signal patterns can be applied to real-time leak detection and critical infrastructure safety in several industrial applications.