Soft-margin Support Vector Machine Research Articles

Abstract PO4-08-07: Background parenchymal enhancement (BPE) on breast magnetic resonance imaging as a biomarker of breast cancer risk among BRCA1/2 carriers

Abstract Introduction: BRCA1/2 carriers are recommended to undergo dynamic contrast enhanced magnetic resonance imaging (DCE-MRI) screening of the breasts annually. Fibroglandular tissue (FGT) may enhance with MRI contrast agent termed background parenchymal enhancement (BPE). BPE is believed to be a marker of hormonally responsive breast tissue, as BPE is impacted by aromatase inhibition and by oophorectomy. BPE has been shown to be more strongly associated with breast cancer risk than breast density. We hypothesize that BPE may serve as a useful dynamic marker of breast cancer risk among BRCA1/2 mutation carriers, given their frequent MRI screening. Methods: We identified female BRCA1/2 carriers from the University of Pennsylvania Cancer Risk Evaluation Program with no personal history of breast or ovarian cancer at the time of breast MRI. Patients diagnosed within 6 months were excluded to remove prevalent cancer cases at MRI. Among 421 eligible patients, 42 were diagnosed with breast cancer. BPE was quantified from all available breast MRIs using a validated, fully automated method to segment fibroglandular tissue (FGT) and quantify BPE. For preprocessing, the N4ITK algorithm was used for bias-field artifact correction and FGT was segmented using a soft-margin support vector machine classifier using the T1-weighted nonfat-saturated breast MRI. FGT was segmented and quantified in 3D. For BPE quantification, the T1-weighted nonfat-saturated image and the derived FGT mask were registered to the pre-contrast DCE-MRI. The first post contrast DCE-MRI and FGT mask were used to compute the relative enhancement map compared to the pre-contrast image. We calculated BPE metrics in two ways. First, the median BPE enhancement was calculated as the median enhancement of all voxels within the FGT mask. Second the BPE enhancement ratio was calculated as the proportion of voxels enhancing at ≥20%. We performed Cox proportional hazards regression to estimate the hazard ratios for breast cancer per standard deviation unit increase in each BPE metric, with first MRI as the time origin and censoring upon bilateral mastectomy, ovarian cancer diagnosis, death, or loss to follow-up and adjustment for age at MRI, menopause status, volumetric breast density (VBD), body mass index (BMI), and BRCA1 vs. BRCA2 mutation. BPE, VBD, BMI, and menstrual status were included as time varying covariates, enabling inclusion of multiple BPE measurements per woman. Results: The mean age at first MRI was 39 for cases and 41 for non-cases, and the mean number of MRIs was 4. There were no significant differences in median BPE (14% vs. 14%, p=0.965) or BPE ratio (34% vs. 36%, p=0.769) between cases and non-cases. In regression analyses adjusted for age and menstrual status, median BPE was significantly associated with breast cancer risk (HR=1.12, p=0.025). The HR was similar in the fully adjusted model, though did not reach statistical significance (HR=1.11, p=0.055). Higher BPE ratio was significantly associated with increased breast cancer risk in both minimally (HR=1.21, p=0.005) and fully adjusted models (HR=1.21, p=0.012). Conclusions: Our results suggest that BPE is significantly associated with breast cancer diagnosis among BRCA1/2 carriers undergoing breast MRI screening. Both median BPE and BPE ratio metrics were associated with breast cancer risk, even after adjusting for breast density and when accounting for multiple measurements of BPE over time, suggesting that BPE may provide additional risk information for BRCA1/2 carriers. Table 1: Results of Cox proportional hazards regression with time varying covariates Citation Format: Anne Marie McCarthy, Alex Anh-Tu Nguyen, Walter Mankowski, Eric Cohen, Sarah Ehsan, Rhonda Gillette, Lauren Pantalone, Susan Weinstein, Emily Conant, Susan Domchek, Despina Kontos. Background parenchymal enhancement (BPE) on breast magnetic resonance imaging as a biomarker of breast cancer risk among BRCA1/2 carriers [abstract]. In: Proceedings of the 2023 San Antonio Breast Cancer Symposium; 2023 Dec 5-9; San Antonio, TX. Philadelphia (PA): AACR; Cancer Res 2024;84(9 Suppl):Abstract nr PO4-08-07.

Cluster-Based Toxicity Estimation of Osteoradionecrosis Via Unsupervised Machine Learning: Moving Beyond Single Dose-Parameter Normal Tissue Complication Probability by Using Whole Dose-Volume Histograms for Cohort Risk Stratification

PurposeGiven the limitations of extant models for normal tissue complication probability estimation for osteoradionecrosis (ORN) of the mandible, the purpose of this study was to enrich statistical inference by exploiting structural properties of data and provide a clinically reliable model for ORN risk evaluation through an unsupervised-learning analysis that incorporates the whole radiation dose distribution on the mandible. Materials and MethodsThe analysis was conducted on retrospective data of 1,259 head and neck cancer (HNC) patients treated at XXX between 2005 and 2015. During a minimum 12-month post-therapy follow-up period, 173 patients in this cohort (13.7%) developed ORN (grades I to IV). The (structural) clusters of mandibular dose-volume histograms (DVHs) for these patients were identified using the K-means clustering method. A soft-margin support vector machine (SVM) was used to determine the cluster borders and partition the dose-volume space. The risk of ORN for each dose-volume region was calculated based on incidence rates and other clinical risk factors. ResultsThe K-means clustering method identified six clusters among the DVHs. Based on the first five clusters, the dose-volume space was partitioned by the soft-margin SVM into distinct regions with different risk indices. The sixth cluster entirely overlapped with the others; the region of this cluster was determined by its envelopes. For each region, the ORN incidence rate per pre-radiation dental extraction status (a statistically significant, non-dose related risk factor for ORN) was reported as the corresponding risk index. ConclusionThis study presents an unsupervised-learning analysis of a large-scale data set to evaluate the risk of mandibular ORN among HNC patients. The results provide a visual risk-assessment tool for ORN (based on the whole DVH and pre-radiation dental extraction status) as well as a range of constraints for dose optimization under different risk levels.

Enhancing Adaboost performance in the presence of class-label noise: A comparative study on EEG-based classification of schizophrenic patients and benchmark datasets

The performance of Adaboost is highly sensitive to noisy and outlier samples. This is therefore the weights of these samples are exponentially increased in successive rounds. In this paper, three novel schemes are proposed to hunt the corrupted samples and eliminate them through the training process. The methods are: I) a hybrid method based on K-means clustering and K-nearest neighbor, II) a two-layer Adaboost, and III) soft margin support vector machines. All of these solutions are compared to the standard Adaboost on thirteen Gunnar Raetsch’s datasets under three levels of class-label noise. To test the proposed method on a real application, electroencephalography (EEG) signals of 20 schizophrenic patients and 20 age-matched control subjects, are recorded via 20 channels in the idle state. Several features including autoregressive coefficients, band power and fractal dimension are extracted from EEG signals of all participants. Sequential feature subset selection technique is adopted to select the discriminative EEG features. Experimental results imply that exploiting the proposed hunting techniques enhance the Adaboost performance as well as alleviating its robustness against unconfident and noisy samples over Raetsch benchmark and EEG features of the two groups.

G-Induced Loss of Consciousness Prediction Using a Support Vector Machine.

INTRODUCTION: Gravity-induced loss of consciousness (G-LOC) is a major threat to fighter pilots and may result in fatal accidents. The brain has a period of 5-6 s from the onset of high +Gz exposure, called the functional buffer period, during which transient ischemia is tolerated without loss of consciousness. We tried to establish a method for predicting G-LOC within the functional buffer period by using machine learning. We used a support vector machine (SVM), which is a popular classification algorithm in machine learning.METHODS: The subjects were 124 flight course students. We used a linear soft-margin SVM, a nonlinear SVM Gaussian kernel function (GSVM), and a polynomial kernel function, for each of which 10 classifiers were built every 0.5 s from the onset of high +Gz exposure (Classifiers 0.5-5.0) to predict G-LOC. Explanatory variables used for each SVM were age, height, weight, with/without anti-G suit, +Gz level, cerebral oxyhemoglobin concentration, and deoxyhemoglobin concentration.RESULTS: The performance of GSVM was better than that of other SVMs. The accuracy of each classifier of GSVM was as follows: Classifier 0.5, 58.1%; 1.0, 54.8%; 1.5, 57.3%; 2.0, 58.1%; 2.5, 64.5%; 3.0, 63.7%; 3.5, 65.3%; 4.0, 64.5%; 4.5, 64.5%; and 5.0, 64.5%.CONCLUSION: We could predict G-LOC with an accuracy rate of approximately 65% from 2.5 s after the onset of high +Gz exposure by using GSVM. Analysis of a larger number of cases and factors to enhance accuracy may be needed to apply those classifiers in centrifuge training and actual flight.Ohrui N, Iino Y, Kuramoto K, Kikukawa A, Okano K, Takada K, Tsujimoto T. G-induced loss of consciousness prediction using a support vector machine. Aerosp Med Hum Perform. 2024; 95(1):29-36.

Margin Maximization of Text Classification based on Support Vector Machine

Abstract: This project focuses on developing a margin maximization model for topic categorization using Support Vector Machines (SVM). Topic categorization aims to classify text documents into predefined topic categories. The proposed model leverages SVM's ability to create a hyperplane with maximum margin between different topics, enhancing the classification performance. The project begins with dataset preparation, where a labeled dataset covering a wide range of topics is gathered. The text data undergoes preprocessing, including cleaning, normalization, and conversion into numerical representations. Feature extraction techniques such as TF-IDF or word embeddings are employed to capture important features related to topics. The dataset is split into training and testing sets, with the training set used to train the SVM model. The SVM model is trained with a focus on maximizing the margin, utilizing techniques like soft-margin SVM or the kernel trick to handle non-linear separable data. Hyperparameters of the SVM model are tuned to optimize its performance. The trained SVM model is then used to predict the topics of the testing data, and its performance is evaluated using standard metrics such as accuracy, precision, recall, and F1 score. The findings of this project demonstrate the effectiveness of the margin maximization model for topic categorization using SVM

Design of Primal Soft-margin SVM Leveraging Piecewise Linear Approximation based Linear Programming Technique

This research introduces a new approach for training soft-margin Support Vector Machines (SVMs) using the primal formulation. The method, called soft-margin Piecewise Linear Approximation based SVM (Soft-margin PLA-SVM), streamlining the optimization of soft-margin SVM hyperparameters in linear programming framework using well-known GUROBI Optimizer Solver. It eliminates the need for an initial hyperparameter guess and uses an adaptable initial search domain. The study uses the Wisconsin Breast Cancer Original dataset from UCI machine learning to validate the effectiveness of proposed soft-margin PLA-SVM. Comparative analysis shows that proposed PLA-SVM outperforms other classifiers in terms of training speed, accuracy, precision, and ROC-AUC scores. The scalability and computational efficiency of soft-margin PLA-SVM make it suitable for high-dimensional and large-scale datasets. The research demonstrates the effectiveness of the primal perspective in solving the soft-margin SVM design problem.

Comparative of machine learning classification strategies for electron energy loss spectroscopy: Support vector machines and artificial neural networks

Machine Learning (ML) strategies applied to Scanning and conventional Transmission Electron Microscopy have become a valuable tool for analyzing the large volumes of data generated by various S/TEM techniques. In this work, we focus on Electron Energy Loss Spectroscopy (EELS) and study two ML techniques for classifying spectra in detail: Support Vector Machines (SVM) and Artificial Neural Networks (ANN). Firstly, we systematically analyze the optimal configurations and architectures for ANN classifiers using random search and the tree-structured Parzen estimator methods. Secondly, a new kernel strategy is introduced for the soft-margin SVMs, the cosine kernel, which offers a significant advantage over the previously studied kernels and other ML classification strategies. This kernel allows us to bypass the normalization of EEL spectra, achieving accurate classification. This result is highly relevant for the EELS community since we also assess the impact of common normalization techniques on our spectra using Uniform Manifold Approximation and Projection (UMAP), revealing a strong bias introduced in the spectra once normalized. In order to evaluate and study both classification strategies, we focus on determining the oxidation state of transition metals through their EEL spectra, examining which feature is more suitable for oxidation state classification: the oxygen K peak or the transition metal white lines. Subsequently, we compare the resistance to energy loss shifts for both classifiers and present a strategy to improve their resistance. The results of this study suggest the use of soft-margin SVMs for simpler EELS classification tasks with a limited number of spectra, as they provide performance comparable to ANNs while requiring lower computational resources and reduced training times. Conversely, ANNs are better suited for handling complex classification problems with extensive training data.

High-speed train localization algorithm via cooperative multi-classifier network using distributed heterogeneous signals

Long-distance high-speed train localization based on distributed optical fiber sensors (DOFS) has been a challenging issue due to the large-scale heterogeneous sensor nodes. It requires a competent localization algorithm to be capable of strong generalization and quick response. This paper proposes a cooperative multi-classifier network (CMCN) for locating HSTs based on heterogeneous DOFS signals by adaptive modeling of the local characteristics. The proposed CMCN is composed of adaptive feature extraction, lightweight base classifiers and spatial boostrap aggregating (SBA). First, the heterogeneous signals are adaptively transformed to an optimal intrinsic mode function for extracting the statistical features of base classifiers. The base classifiers are constructed based on dynamic soft-margin support vector machine to model local characteristics without computationally burdensome kernel functions by introducing a dynamic penalty factor. The factor is automatically initialized by evaluating the regional consistency before training. Furthermore, the SBA estimates the location of HSTs based on the local states of nodes. It can cooperate with base classifiers for enhanced accuracy by searching for the interval with maximum regional consistency. Finally, a trial is conducted in a high-speed railway in China in long-term running of 92 days. The results prove feasibility and accuracy of the proposed algorithm.

An Inexact Feasible Quantum Interior Point Method for Linearly Constrained Quadratic Optimization.

Quantum linear system algorithms (QLSAs) have the potential to speed up algorithms that rely on solving linear systems. Interior point methods (IPMs) yield a fundamental family of polynomial-time algorithms for solving optimization problems. IPMs solve a Newton linear system at each iteration to compute the search direction; thus, QLSAs can potentially speed up IPMs. Due to the noise in contemporary quantum computers, quantum-assisted IPMs (QIPMs) only admit an inexact solution to the Newton linear system. Typically, an inexact search direction leads to an infeasible solution, so, to overcome this, we propose an inexact-feasible QIPM (IF-QIPM) for solving linearly constrained quadratic optimization problems. We also apply the algorithm to ℓ1-norm soft margin support vector machine (SVM) problems, and demonstrate that our algorithm enjoys a speedup in the dimension over existing approaches. This complexity bound is better than any existing classical or quantum algorithm that produces a classical solution.

Deep convolutional cross-connected kernel mapping support vector machine based on SelectDropout

Deep neural mapping support vector machine (DNMSVM) has achieved good results in numerous tasks by mapping the input from a low-dimensional space to a high-dimensional space and then using support vector machine for classification. However, it did not consider the connection of different spaces and increased the model parameters. To improve the classification performance while reducing the number of model parameters, we propose a deep Convolutional Cross-connected Kernel Mapping Support Vector Machine framework based on SelectDropout (CCKMSVM-SD). It consists of a feature extraction module and a classification module. The feature extraction module maps the data from low-dimensional to high-dimensional space by fusing the representations of different dimensional spaces through convolutional layers with cross-connections. For some convolutional layers, we use the depthwise separable convolution to replace the original convolution to reduce the number of parameters. Besides, we use SelectDropout to improve its generalization capability. The classification module uses a soft margin support vector machine for classification. The results on three tasks with ten different datasets indicate that CCKMSVM-SD obtains higher classification accuracy than other models with fewer parameters, demonstrating its effectiveness.

A majorization penalty method for SVM with sparse constraint

Support vector machine (SVM) is an important and fundamental technique in machine learning. Soft-margin SVM models have stronger generalization performance compared with the hard-margin SVM. Most existing works use the hinge-loss function which can be regarded as an upper bound of the 0–1 loss function. However, it cannot explicitly control the number of misclassified samples. In this paper, we use the idea of soft-margin SVM and propose a new SVM model with a sparse constraint. Our model can strictly limit the number of misclassified samples, expressing the soft-margin constraint as a sparse constraint. By constructing a majorization function, a majorization penalty method can be used to solve the sparse-constrained optimization problem. We apply Conjugate-Gradient (CG) method to solve the resulting subproblem. Extensive numerical results demonstrate the impressive performance of the proposed majorization penalty method.

Deep Learning-Based Sign Language Recognition for Hearing and Speaking Impaired People

Sign language is mainly utilized in communication with people who have hearing disabilities. Sign language is used to communicate with people having developmental impairments who have some or no interaction skills. The interaction via Sign language becomes a fruitful means of communication for hearing and speech impaired persons. A Hand gesture recognition system finds helpful for deaf and dumb people by making use of human computer interface (HCI) and convolutional neural networks (CNN) for identifying the static indications of Indian Sign Language (ISL). This study introduces a shark smell optimization with deep learning based automated sign language recognition (SSODL-ASLR) model for hearing and speaking impaired people. The presented SSODL-ASLR technique majorly concentrates on the recognition and classification of sign language provided by deaf and dumb people. The presented SSODL-ASLR model encompasses a two stage process namely sign language detection and sign language classification. In the first stage, the Mask Region based Convolution Neural Network (Mask RCNN) model is exploited for sign language recognition. Secondly, SSO algorithm with soft margin support vector machine (SM-SVM) model can be utilized for sign language classification. To assure the enhanced classification performance of the SSODL-ASLR model, a brief set of simulations was carried out. The extensive results portrayed the supremacy of the SSODL-ASLR model over other techniques.

Comparing two SVM models through different metrics based on the confusion matrix

Support Vector Machines (SVM) are an efficient alternative for supervised classification. In the soft margin SVM model, two different objectives are optimized and the set of alternative solutions represent a Pareto-front of points, each one of them representing a different classifier. The performance of these classifiers can be evaluated and compared through some performance metrics that follow from the confusion matrix. Moreover, when the SVM includes feature selection, the model becomes hard to solve. In this paper, we present an alternative SVM model with feature selection and the performance of the new classifiers is compared to those of the classical soft margin model through some performance metrics based on the confusion matrix: the area under the ROC curve, Cohen’s Kappa coefficient and the F-Score. Both the classical soft margin SVM model with feature selection and our proposal have been implemented by metaheuristics, given the complexity of the models to solve.

Real-time and high precision feature matching between blur aerial images.

When aerial cameras get aerial remote sensing images, the defocus will occur because of reasons such as air pressure, temperature and ground elevation changes, resulting in different image sharpness of continual aerial remote sensing images. Nowadays, the rapidly developing feature matching algorithm will rapidly reduce the registration rate between images with different image sharpness. Therefore, in order to enable aerial cameras to get image sharpness parameters according to the locations of aerial image feature points with inconsistent sharpness, this paper proposes a feature matching algorithm between aerial images with different sharpness by using DEM data and multiple constraints. In this paper, the feature matching range is extended according to the modified aerial imaging model and the nonlinear soft margin support vector machine. Then the relative moving speed and its variation of the feature points in the image are obtained by using the extended L-k optical flow, and finally the epipolar geometric constraint is introduced. To locate the feature points is obtained under multiple constraints, there is no need to calculate the feature point descriptors, and some mismatched point pairs are corrected, which improves the matching efficiency and precision. The experimental results show the feature matching precision of this algorithm is more than 90%, and the running time and matching precision can meet various application needs of aerial cameras.

Bacterial Vaginosis Monitoring with Carbon Nanotube Field-Effect Transistors.

The ability to rapidly and reliably screen for bacterial vaginosis (BV) during pregnancy is of great significance for maternal health and pregnancy outcomes. In this proof-of-concept study, we demonstrated the potential of carbon nanotube field-effect transistors (NTFET) in the rapid diagnostics of BV with the sensing of BV-related factors such as pH and biogenic amines. The fabricated sensors showed good linearity to pH changes with a linear correlation coefficient of 0.99. The pH sensing performance was stable after more than one month of sensor storage. In addition, the sensor was able to classify BV-related biogenic amine-negative/positive samples with machine learning, utilizing different test strategies and algorithms, including linear discriminant analysis (LDA), support vector machine (SVM), and principal component analysis (PCA). The biogenic amine sample status could be well classified using a soft-margin SVM model with a validation accuracy of 87.5%. The accuracy could be further improved using a gold gate electrode for measurement, with accuracy higher than 90% in both LDA and SVM models. We also explored the sensing mechanisms and found that the change in NTFET off current was crucial for classification. The fabricated sensors successfully detect BV-related factors, demonstrating the competitive advantage of NTFET for point-of-care diagnostics of BV.

A Framework of Lightweight Deep Cross-Connected Convolution Kernel Mapping Support Vector Machines

Deep kernel mapping support vector machines have achieved good results in numerous tasks by mapping features from a low-dimensional space to a high-dimensional space and then using support vector machines for classification. However, the depth kernel mapping support vector machine does not take into account the connection of different dimensional spaces and increases the model parameters. To further improve the recognition capability of deep kernel mapping support vector machines while reducing the number of model parameters, this paper proposes a framework of Lightweight Deep Convolutional Cross-Connected Kernel Mapping Support Vector Machines (LC-CKMSVM). The framework consists of a feature extraction module and a classification module. The feature extraction module first maps the data from low-dimensional to high-dimensional space by fusing the representations of different dimensional spaces through cross-connections; then, it uses depthwise separable convolution to replace part of the original convolution to reduce the number of parameters in the module; The classification module uses a soft margin support vector machine for classification. The results on 6 different visual datasets show that LC-CKMSVM obtains better classification accuracies on most cases than the other five models.

Privacy-Preserving Online Medical Prediagnosis Training Model Based on Soft-Margin SVM

Online medical prediagnosis systems have already shown great achievement in providing the guidance of healthcare services with lower time and cost. Achieving a high-precision medical primary diagnosis system faces many severe challenges on the privacy of individual health information, the distributed storage of medical data and the diversity of the disease. In this paper, we propose an efficient and privacy-preserving framework for obtaining a pre-clinical guide model, which allows an authorized data analysis center to train a disease classifier using a combination of medical data gathered from different entities. Our proposed scheme is based on soft-margin support vector machine (SVM) which takes Taylor polynomial of exponential-loss as penalty. Our scheme achieves the following advantages: the trained model can tolerate some abnormal samples therefore has higher generalization ability, and the training process can constraint the inefficient operations in the encrypted domain thus leads to the availability of partial homomorphic encryption system. Lately, we prove that the proposed scheme achieves the goal of medical prediagnosis system construction and data without privacy leakage to data analysis center and model parameters without exposure to data providers, as well as demonstrating its utility and efficiency using real-world medical datasets.

Face Mask Wearing Detection Using Support Vector Machine (SVM)

As an effort to prevent the spread of the Covid-19, various countries have implemented health protocol policies such as work-from-home, social distancing, and face mask-wearing in public places. However, monitoring compliance with the policy is still difficult, especially for the face mask policy. It is still managed by humans and is costly. Thus, this research proposes a face mask-wearing detection using a soft-margin Support Vector Machine (SVM). There are three main stages: feature selection and preprocessing, model training, and evaluation. During the first stage, the dataset of 3833 images (1915 images with face masks and 1918 images without face masks) was prepared to be used in the training stage. The training stage was conducted using SVM added with the soft-margin objective to overcome images that could not be separated linearly. At the final stage, evaluation was conducted using a confusion matrix with 10 folds cross-validation. Based on the experiments, the proposed method shows a performance accuracy of 91.7%, a precision of 90.3%, recall of 93.5%, and an F-measure of 91.8%. Our method also worked fast, taking only 0.025 seconds to process a new image. It is 7.12 times faster than Deep Learning which requires 0.18 seconds for one classification.

S3UCA: Soft-Margin Support Vector Machine-Based Social Network User Credibility Assessment Method

Among the algorithms used to assess user credibility in social networks, most of them quantify user information and then calculate the user credibility measure by linear summation. The algorithm above, however, ignores the aliasing of user credibility results under the linear summation dimension, resulting in a low evaluation accuracy. To solve this problem, we propose a user credibility evaluation method based on a soft-margin support-vector machine (SVM). This method transforms the user credibility evaluation dimension from a linear summation dimension to a plane coordinate dimension, which reduces the evaluation errors caused by user aliasing in the classification threshold interval. In the quantization of user information, the ladder assignment method is used to process the user text information and numeric information, and the weight assignment method of information entropy is used to calculate the weight assignment among different feature items, which reduces the errors caused by the inconsistency of the order of magnitude among different types of user information. Simulation results demonstrate the superiority of the proposed method in the user’s credibility evaluation results.

The soft-margin Support Vector Machine with ordered weighted average

This paper deals with a cost sensitive extension of the standard Support Vector Machine (SVM) using an ordered weighted sum of the deviations of misclassified individuals with respect to their corresponding supporting hyperplanes. In contrast with previous heuristic approaches, an exact method that applies the ordered weighted average operator in the classical SVM model is proposed. Specifically, when weights are sorted in non-decreasing order, a quadratic continuous formulation is developed. For general weights, a mixed integer quadratic formulation is proposed. In addition, our results prove that nonlinear kernel functions can be also applied to these new models extending its applicability beyond the linear case. Extensive computational results reported in the paper show that the predictive performance provided by the proposed exact solution approaches are better than the ones provided by the classical models (linear and nonlinear kernel) and similar or better than the previous ones provided by the heuristic solution by Maldonado et al. (2018).