Related papers: A Large Dimensional Analysis of Least Squares Supp…
This article proposes a performance analysis of kernel least squares support vector machines (LS-SVMs) based on a random matrix approach, in the regime where both the dimension of data $p$ and their number $n$ grow large at the same rate.…
Support vector machine (SVM) is a particularly powerful and flexible supervised learning model that analyzes data for both classification and regression, whose usual algorithm complexity scales polynomially with the dimension of data space…
The support vector machine (SVM) and minimum Euclidean norm least squares regression are two fundamentally different approaches to fitting linear models, but they have recently been connected in models for very high-dimensional data through…
The least-squares support vector machine is a frequently used kernel method for non-linear regression and classification tasks. Here we discuss several approximation algorithms for the least-squares support vector machine classifier. The…
The parameters of support vector machines (SVMs) such as the penalty parameter and the kernel parameters have a great impact on the classification accuracy and the complexity of the SVM model. Therefore, the model selection in SVM involves…
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…
Support vector machines (SVMs) are special kernel based methods and belong to the most successful learning methods since more than a decade. SVMs can informally be described as a kind of regularized M-estimators for functions and have…
We derive improved regression and classification rates for support vector machines using Gaussian kernels under the assumption that the data has some low-dimensional intrinsic structure that is described by the box-counting dimension. Under…
A general framework of least squares support vector machine with low rank kernels, referred to as LR-LSSVM, is introduced in this paper. The special structure of low rank kernels with a controlled model size brings sparsity as well as…
This paper investigates the asymptotic behavior of the soft-margin and hard-margin support vector machine (SVM) classifiers for simultaneously high-dimensional and numerous data (large $n$ and large $p$ with $n/p\to\delta$) drawn from a…
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 a supervised learning algorithm that finds a maximum-margin linear classifier, often after mapping the data to a high-dimensional feature space via the kernel trick. Recent work has demonstrated that in…
Multi Task Learning (MTL) efficiently leverages useful information contained in multiple related tasks to help improve the generalization performance of all tasks. This article conducts a large dimensional analysis of a simple but, as we…
Least squares support vector machines are a commonly used supervised learning method for nonlinear regression and classification. They can be implemented in either their primal or dual form. The latter requires solving a linear system,…
Support vector machine (SVM), is a popular kernel method for data classification that demonstrated its efficiency for a large range of practical applications. The method suffers, however, from some weaknesses including; time processing,…
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 show theoretical similarities between the Least Squares Support Vector Regression (LS-SVR) model with a Radial Basis Functions (RBF) kernel and maximum a posteriori (MAP) inference on Bayesian RBF networks with a specific Gaussian prior…
In the last few years, various types of machine learning algorithms, such as Support Vector Machine (SVM), Support Vector Regression (SVR), and Non-negative Matrix Factorization (NMF) have been introduced. The kernel approach is an…
The Support Vector Machine (SVM) of Vapnik (1998) has become widely established as one of the leading approaches to pattern recognition and machine learning. It expresses predictions in terms of a linear combination of kernel functions…
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…