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In this paper, we introduce novel Twin Parametric Margin Support Vector Machine (TPMSVM) models designed to address multiclass classification tasks under feature uncertainty. To handle data perturbations, we construct bounded-by-norm…
Support vector machines (SVMs) are a standard method in the machine learning toolbox, in particular for tabular data. Non-linear kernel SVMs often deliver highly accurate predictors, however, at the cost of long training times. That problem…
Several supermodular losses have been shown to improve the perceptual quality of image segmentation in a discriminative framework such as a structured output support vector machine (SVM). These loss functions do not necessarily have the…
The support vector machine (SVM) is a widely used machine learning tool for classification based on statistical learning theory. Given a set of training data, the SVM finds a hyperplane that separates two different classes of data points by…
The Support Vector Machine (SVM) is a popular classification paradigm in machine learning and has achieved great success in real applications. However, the standard SVM can not select variables automatically and therefore its solution…
Support vector machines (SVMs) are powerful supervised learning tools developed to solve classification problems. However, SVMs are likely to perform poorly in the classification of imbalanced data. The rough set theory presents a…
The kernel support vector machine (SVM) is one of the most widely used classification methods; however, the amount of computation required becomes the bottleneck when facing millions of samples. In this paper, we propose and analyze a novel…
Recent advance on linear support vector machine with the 0-1 soft margin loss ($L_{0/1}$-SVM) shows that the 0-1 loss problem can be solved directly. However, its theoretical and algorithmic requirements restrict us extending the linear…
Localized support vector machines solve SVMs on many spatially defined small chunks and one of their main characteristics besides the computational benefit compared to global SVMs is the freedom of choosing arbitrary kernel and…
Real-world data such as digital images, MRI scans and electroencephalography signals are naturally represented as matrices with structural information. Most existing classifiers aim to capture these structures by regularizing the regression…
Using a support vector machine requires to set two types of hyperparameters: the soft margin parameter C and the parameters of the kernel. To perform this model selection task, the method of choice is cross-validation. Its leave-one-out…
This chapter describes componentwise Least Squares Support Vector Machines (LS-SVMs) for the estimation of additive models consisting of a sum of nonlinear components. The primal-dual derivations characterizing LS-SVMs for the estimation of…
The support vector machine (SVM) is one of the most successful learning methods for solving classification problems. Despite its popularity, SVM has a serious drawback, that is sensitivity to outliers in training samples. The penalty on…
Kernel-free quadratic surface support vector machines (QSVM) have recently gained traction due to their flexibility in modeling nonlinear decision boundaries without relying on kernel functions. However, the introduction of a full quadratic…
Training a Support Vector Machine (SVM) requires the solution of a quadratic programming problem (QP) whose computational complexity becomes prohibitively expensive for large scale datasets. Traditional optimization methods cannot be…
This paper presents a novel framework for designing support vector machines (SVMs), which does not impose restriction on the SVM kernel to be positive-definite and allows the user to define memory constraint in terms of fixed template…
Neural Networks and related Deep Learning methods are currently at the leading edge of technologies used for classifying objects. However, they generally demand large amounts of time and data for model training; and their learned models can…
Support vector machines (SVM) and other kernel techniques represent a family of powerful statistical classification methods with high accuracy and broad applicability. Because they use all or a significant portion of the training data,…
Expectile regression is a nice tool for investigating conditional distributions beyond the conditional mean. It is well-known that expectiles can be described with the help of the asymmetric least square loss function, and this link makes…
Support vector machine (SVM) has achieved many successes in machine learning, especially for a small sample problem. As a famous extension of the traditional SVM, the $\nu$ support vector machine ($\nu$-SVM) has shown outstanding…