Related papers: Algebraic multigrid support vector machines
The numerical simulation of structural mechanics applications via finite elements usually requires the solution of large-size and ill-conditioned linear systems, especially when accurate results are sought for derived variables interpolated…
Inspired by multigrid methods for linear systems of equations, multilevel optimization methods have been proposed to solve structured optimization problems. Multilevel methods make more assumptions regarding the structure of the…
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…
This paper introduces a novel approach to algebraic multigrid methods for large systems of linear equations coming from finite element discretizations of certain elliptic second order partial differential equations. Based on a discrete…
The support vector clustering algorithm is a well-known clustering algorithm based on support vector machines using Gaussian or polynomial kernels. The classical support vector clustering algorithm works well in general, but its performance…
We investigate the performance of algebraic multigrid methods for the solution of the linear system of equations arising from a Virtual Element discretization. We provide numerical experiments on very general polygonal meshes for a 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…
Machine learning techniques always aim to reduce the generalized prediction error. In order to reduce it, ensemble methods present a good approach combining several models that results in a greater forecasting capacity. The Random Machines…
Support Vector Machine (SVM) is a powerful tool in binary classification, known to attain excellent misclassification rates. On the other hand, many realworld classification problems, such as those found in medical diagnosis, churn or fraud…
Support vector machines (SVM) can classify data sets along highly non-linear decision boundaries because of the kernel-trick. This expressiveness comes at a price: During test-time, the SVM classifier needs to compute the kernel…
Although multigrid is asymptotically optimal for solving many important partial differential equations, its efficiency relies heavily on the careful selection of the individual algorithmic components. In contrast to recent approaches that…
Efficient numerical solvers for sparse linear systems are crucial in science and engineering. One of the fastest methods for solving large-scale sparse linear systems is algebraic multigrid (AMG). The main challenge in the construction of…
Support Vector Machines (SVM), a popular machine learning technique, has been applied to a wide range of domains such as science, finance, and social networks for supervised learning. Whether it is identifying high-risk patients by…
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,…
In this paper, we study the support vector machine and introduced the notion of generalized support vector machine for classification of data. We show that the problem of generalized support vector machine is equivalent to the problem of…
Topology optimization for large scale problems continues to be a computational challenge. Several works exist in the literature to address this topic, and all make use of iterative solvers to handle the linear system arising from the Finite…
Recently, decision trees (DT) have been used as an explainable representation of controllers (a.k.a. strategies, policies, schedulers). Although they are often very efficient and produce small and understandable controllers for discrete…
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,…
The use of multigrid and related preconditioners with the finite element method is often limited by the difficulty of applying the algorithm effectively to a problem, especially when the domain has a complex shape or adaptive refinement. We…
In order to fully utilize "big data", it is often required to use "big models". Such models tend to grow with the complexity and size of the training data, and do not make strong parametric assumptions upfront on the nature of the…