Related papers: Multiplicative updates For Non-Negative Kernel SVM
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…
In this paper, we study the nonnegative matrix factorization problem under the separability assumption (that is, there exists a cone spanned by a small subset of the columns of the input nonnegative data matrix containing all columns),…
Nonnegative Matrix Factorization (NMF) is the problem of approximating a nonnegative matrix with the product of two low-rank nonnegative matrices and has been shown to be particularly useful in many applications, e.g., in text mining, image…
Quantum algorithms can enhance machine learning in different aspects. Here, we study quantum-enhanced least-square support vector machine (LS-SVM). Firstly, a novel quantum algorithm that uses continuous variable to assist matrix inversion…
This paper considers convex quadratic programs associated with the training of support vector machines (SVM). Exploiting the special structure of the SVM problem a new type of active set method with long cycles and stable rank-one-updates…
We address the problem of model selection for Support Vector Machine (SVM) classification. For fixed functional form of the kernel, model selection amounts to tuning kernel parameters and the slack penalty coefficient $C$. We begin by…
Using methods of Statistical Physics, we investigate the generalization performance of support vector machines (SVMs), which have been recently introduced as a general alternative to neural networks. For nonlinear classification rules, the…
We generalize the non-negative matrix factorization algorithm of Lee and Seung to accept a weighted norm, and to support ridge and Lasso regularization. We recast the Lee and Seung multiplicative update as an additive update which does not…
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…
We propose a method for support vector machine classification using indefinite kernels. Instead of directly minimizing or stabilizing a nonconvex loss function, our algorithm simultaneously computes support vectors and a proxy kernel matrix…
In nonparametric classification and regression problems, regularized kernel methods, in particular support vector machines, attract much attention in theoretical and in applied statistics. In an abstract sense, regularized kernel methods…
This article proposes new multiplicative updates for nonnegative matrix factorization (NMF) with the $\beta$-divergence objective function. Our new updates are derived from a joint majorization-minimization (MM) scheme, in which an…
The Support Vector Machine (SVM) is one of the most widely used classification methods. In this paper, we consider the soft-margin SVM used on data points with independent features, where the sample size $n$ and the feature dimension $p$…
Nonnegative (linear) least square problems are a fundamental class of problems that is well-studied in statistical learning and for which solvers have been implemented in many of the standard programming languages used within the machine…
Kernel-based support vector machines (SVMs) are supervised machine learning algorithms for classification and regression problems. We introduce a method to train SVMs on a D-Wave 2000Q quantum annealer and study its performance in…
Symmetric Nonnegative Matrix Factorization (SNMF) models arise naturally as simple reformulations of many standard clustering algorithms including the popular spectral clustering method. Recent work has demonstrated that an elementary…
Support vector machines (SVMs) with sparsity-inducing nonconvex penalties have received considerable attentions for the characteristics of automatic classification and variable selection. However, it is quite challenging to solve the…
Support Vector Machines (SVMs) are among the most fundamental tools for binary classification. In its simplest formulation, an SVM produces a hyperplane separating two classes of data using the largest possible margin to the data. The focus…
Support vector machine (SVM) is one of the most popular classification algorithms in the machine learning literature. We demonstrate that SVM can be used to balance covariates and estimate average causal effects under the unconfoundedness…
It is shown that bootstrap approximations of support vector machines (SVMs) based on a general convex and smooth loss function and on a general kernel are consistent. This result is useful to approximate the unknown finite sample…