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In this paper, we present new optimization models for Support Vector Machine (SVM), with the aim of separating data points in two or more classes. The classification task is handled by means of nonlinear classifiers induced by kernel…
The accuracy and complexity of kernel learning algorithms is determined by the set of kernels over which it is able to optimize. An ideal set of kernels should: admit a linear parameterization (tractability); be dense in the set of all…
Improvement of statistical learning models in order to increase efficiency in solving classification or regression problems is still a goal pursued by the scientific community. In this way, the support vector machine model is one of the…
Sparse data models, where data is assumed to be well represented as a linear combination of a few elements from a dictionary, have gained considerable attention in recent years, and their use has led to state-of-the-art results in many…
In this article, a large dimensional performance analysis of kernel least squares support vector machines (LS-SVMs) is provided under the assumption of a two-class Gaussian mixture model for the input data. Building upon recent advances in…
The paper presents a new framework for complex Support Vector Regression as well as Support Vector Machines for quaternary classification. The method exploits the notion of widely linear estimation to model the input-out relation for…
This study introduces a novel formulation to enhance Support Vector Machines (SVMs) in handling class imbalance and noise. Unlike the conventional Soft Margin SVM, which penalizes the magnitude of constraint violations, the proposed model…
Support Vector Machines (SVMs) with various kernels have played dominant role in machine learning for many years, finding numerous applications. Although they have many attractive features interpretation of their solutions is quite…
Least Squares Twin Support Vector Machine (LST-SVM) has been shown to be an efficient and fast algorithm for binary classification. It combines the operating principles of Least Squares SVM (LS-SVM) and Twin SVM (T-SVM); it constructs two…
The computational complexity of solving nonlinear support vector machine (SVM) is prohibitive on large-scale data. In particular, this issue becomes very sensitive when the data represents additional difficulties such as highly imbalanced…
We compare two quantum approaches that use support vector machines for multi-class classification on a reduced Sloan Digital Sky Survey (SDSS) dataset: the quantum kernel-based QSVM and the Harrow-Hassidim-Lloyd least-squares SVM (HHL…
In functional data analysis, binary classification with one functional covariate has been extensively studied. We aim to fill in the gap of considering multivariate functional covariates in classification. In particular, we propose an…
This paper proposes a frequent pattern data mining algorithm based on support vector machine (SVM), aiming to solve the performance bottleneck of traditional frequent pattern mining algorithms in high-dimensional and sparse data…
A wide variety of machine learning algorithms such as support vector machine (SVM), minimax probability machine (MPM), and Fisher discriminant analysis (FDA), exist for binary classification. The purpose of this paper is to provide a…
Support vector machine (SVM) has attracted great attentions for the last two decades due to its extensive applications, and thus numerous optimization models have been proposed. To distinguish all of them, in this paper, we introduce a new…
Conventional algorithms for sparse signal recovery and sparse representation rely on $l_1$-norm regularized variational methods. However, when applied to the reconstruction of $\textit{sparse images}$, i.e., images where only a few pixels…
The support vector machine (SVM) is a popular machine learning classification method which produces a nonlinear decision boundary in a feature space by constructing linear boundaries in a transformed Hilbert space. It is well known that…
We introduce a principal support vector machine (PSVM) approach that can be used for both linear and nonlinear sufficient dimension reduction. The basic idea is to divide the response variables into slices and use a modified form of support…
We propose a data-driven approach to quantify the uncertainty of models constructed by kernel methods. Our approach minimizes the needed distributional assumptions, hence, instead of working with, for example, Gaussian processes or…
Supervised machine learning is the classification of new data based on already classified training examples. In this work, we show that the support vector machine, an optimized binary classifier, can be implemented on a quantum computer,…