However, optimizing hinge loss yields more nuanced behavior. We give experimental evidence and theoretical arguments that, for a class of problems that arises frequently in natural-language processing, both L1- and L2-regularized hinge loss lead to sparser models than L2-regularized log loss, but ...
It considers L1 loss (hinge loss) in a complicated optimization problem. In SVM, squared hinge loss (L2 loss) is a common alternative to L1 loss, but surprisingly we have not seen any paper studying the details of Crammer and Singer's method using L2 loss. In this letter, we conduct a...
Sparsity-inducing penalties are useful tools to design multiclass support vector machines (SVMs). In this paper, we propose a convex optimization approach for efficiently and exactly solving the multiclass SVM learning problem involving a sparse regularization and the multiclass hinge loss formulated ...
Support vector machine (SVM) model is one of most successful machine learning methods and has been successfully applied to solve numerous real-world application. Because the SVM methods use the hinge loss or squared hinge loss functions for classifications, they usually outperform other classification ...
6.Pillai, I, Fumera, G, Roli, F. Multi-label classification with a reject option.Pattern Recognhttps://doi.org/10.1016/j.patcog.2013.01.035Search in Google Scholar 7.Bartlett, P, Wegkamp, M. Classification with a reject option using a hinge loss.J Mach Learn Res2008;9:1823–40.Sear...
samples from class +1, one can solve the regularization problem based on the weighted hinge loss min f∈F n −1 (1 −π) y i =1 H 1 {y i f(x i )} +π y i =−1 H 1 {y i f(x i )} +λJ(f), (2) where 0 ≤π≤ 1. Wang et al. (2008) showed that the ...
In this paper, we propose a novel direct multiclass formulation specifically designed for large-scale and high-dimensional problems such as document classification. Based on a multiclass extension of the squared hinge loss, our formulation employs l(1)/l(2) regularization so as to force weights ...
The IEstimator<TTransformer> to predict a target using a linear multiclass classifier model trained with a coordinate descent method. Depending on the used loss function, the trained model can be, for example, maximum entropy classifier or multi-cl
cation is to solve a minimization problem of a risk based on a convex lossφ.Main examples ofφinclude the exponential lossφ(x)=e−x used in AdaBoost,the logit lossφ(x)=ln(1+e−x)and the hinge lossφ(x)=(1−x)+used in support vector machine,where(u)+=max{0,u}for a ...
(3) A theorem that transforms the multiclass hinge loss minimization problem using the l_2,1-norm and l_p-norm regularizations to a previous solvable optimization problem and its proof are given. Additionally, it is theoretically proved that the optimization process converges to the global ...