A Hierarchical Convex Optimization for Multiclass SVM Achieving Maximum Pairwise Margins with Least Empirical Hinge-Loss

“The use of multiple measurements in taxonomic problems,”

R. A. Fisher, · 1936

Earlier work this paper cites.

Estimation of Dependence Based on Empirical Data,

V. Vapnik, · 1982

Earlier work this paper cites.

“On the Douglas-Rachford splitting method and the proximal point algorithm for maximal monotone operators,”

J. Eckstein and D. P. Bertsekas, · 1992

Earlier work this paper cites.

“Support-vector networks,”

C. Cortes and V. Vapnik, · 1995

Earlier work this paper cites.

“Comparison of view-based object recognition algorithms using realistic 3D models,”

V. Blanz, B. Schölkopf, H. Bülthoff, C. Burges, V. Vapnik, and T. Vetter, · 1996

Earlier work this paper cites.

Projection Algorithms and Monotone Operators

H. H. Bauschke, · 1996

Earlier work this paper cites.

Statistical Learning Theory

V. Vapnik, · 1998

Earlier work this paper cites.

“Multi-class support vector machines,”

J. Weston and C. Watkins, · 1998

Earlier work this paper cites.

“Pairwise classification and support vector machines,”

U. H.-G. Kreßel, · 1999

Cited alongside, same era.

“The hybrid steepest descent method for the variational inequality problem over the intersection of fixed point sets of nonexpansive mappings,”

I. Yamada, · 2001

Cited alongside, same era.

“On the algorithmic implementation of multiclass kernel-based vector machines,”

K. Crammer and Y. Singer, · 2001

Cited alongside, same era.

“Combining discriminant models with new multi-class svms,”

Y. Guermeur, · 2002

Cited alongside, same era.

“Non-strictly convex minimization over the bounded fixed point set of a nonexpansive mapping,”

N. Ogura and I. Yamada, · 2003

Cited alongside, same era.

“Multicategory ψ \psi -learning,”

Y. Liu and X. Shen, · 2006

“Multiobjective multiclass support vector machines maximizing geometric margins,”

K. Tatsumi, K. Hayashida, R. Kawauchi, and T. Tanino, · 2010

Later among the works it cites.

“Minimizing the Moreau envelope of nonsmooth convex functions over the fixed point set of certain quasi-nonexpansive mappings,”

I. Yamada, M. Yukawa, and M. Yamagishi, · 2011

Later among the works it cites.

“A splitting algorithm for dual monotone inclusions involving cocoercive operators,”

B. C. Vũ, · 2013

Later among the works it cites.

“A primal-dual splitting method for convex optimization involving Lipschitzian, proximable and linear composite terms,”

L. Condat, · 2013

Later among the works it cites.

“A proximal approach for sparse multiclass SVM,”

Original

G. Chierchia, N. Pustelnik, J.-C. Pesquet, and B. Pesquet-Popescu, · 2015

Later among the works it cites.