Related papers: Tropical Support Vector Machines: Evaluations and …
This paper proposes a robust classification model, based on support vector machine (SVM), which simultaneously deals with outliers detection and feature selection. The classifier is built considering the ramp loss margin error and it…
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.…
We introduce a notion of tropical vector bundle on a tropical toric variety which is a tropical analogue of a torus equivariant vector bundle on a toric variety. Alternatively it can be called a toric matroid bundle. We define equivariant…
The Support Vector Machine (SVM) method has been widely used in numerous classification tasks. The main idea of this algorithm is based on the principle of the margin maximization to find an hyperplane which separates the data into two…
Support Vector Machine (SVM) has been one of the most successful machine learning techniques for binary classification problems. The key idea is to maximize the margin from the data to the hyperplane subject to correct classification on…
We provide a formulation for Local Support Vector Machines (LSVMs) that generalizes previous formulations, and brings out the explicit connections to local polynomial learning used in nonparametric estimation literature. We investigate the…
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…
Support Vector Machines (SVMs) are a cornerstone of supervised learning, widely used for data classification. A central component of their success lies in kernel functions, which enable efficient computation of inner products in…
In this paper, we extend the methodology developed for Support Vector Machines (SVM) using $\ell_2$-norm ($\ell_2$-SVM) to the more general case of $\ell_p$-norms with $p\ge 1$ ($\ell_p$-SVM). The resulting primal and dual problems are…
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 show that super Gromov-Witten invariants can be defined and computed by methods of tropical geometry. When the target is a point, the super invariants are descendant invariants on the moduli space of curves, which can be computed…
Extreme value statistics is the max analogue of classical statistics, while tropical geometry is the max analogue of classical geometry. In this paper, we review recent work where insights from tropical geometry were used to develop new,…
An unsolved issue in widely used methods such as Support Vector Data Description (SVDD) and Small Sphere and Large Margin SVM (SSLM) for anomaly detection is their nonconvexity, which hampers the analysis of optimal solutions in a manner…
Distance metric learning aims to learn from the given training data a valid distance metric, with which the similarity between data samples can be more effectively evaluated for classification. Metric learning is often formulated as a…
Support Vector Machine (SVM) is a state-of-the-art classification method widely used in science and engineering due to its high accuracy, its ability to deal with high dimensional data, and its flexibility in modeling diverse sources of…
Support vector classification (SVC) is a classical and well-performed learning method for classification problems. A regularization parameter, which significantly affects the classification performance, has to be chosen and this is usually…
Recent work in metric learning has significantly improved the state-of-the-art in k-nearest neighbor classification. Support vector machines (SVM), particularly with RBF kernels, are amongst the most popular classification algorithms that…
Support vector machine (SVM) has been one of the most popular learning algorithms, with the central idea of maximizing the minimum margin, i.e., the smallest distance from the instances to the classification boundary. Recent theoretical…
This paper addresses the problem of efficiently classifying high-dimensional data over decentralized networks. Penalized support vector machines (SVMs) are widely used for high-dimensional classification tasks. However, the double…
Support Vector Machines (SVMs) based on hinge loss have been extensively discussed and applied to various binary classification tasks. These SVMs achieve a balance between margin maximization and the minimization of slack due to outliers.…