Title: A deeper Newton descent direction with generalised Hessian matrix for SVMs: an application to face detection

Authors: Abdessamad Amir; Korichi Mokhtar El Amine

Addresses: Laboratory of Pure and Applied Mathematics, Mostaganem University, Algeria ' Laboratory of Pure and Applied Mathematics, Mostaganem University, Algeria

Abstract: By formulating the generalised Newton descent direction according to the parameter resulting from the calculation of the subgradient of the max function, a new version of NSVM (Fung and Mangasarian, 2004) is presented in this paper. This descent direction ensures even more the precision of the solution in a fast time. Associated with a good features extraction technique like Gabor's wavelets, the application of the proposed method in the context of facial detection shows that either the direction is calculated as an optimal solution of a one-dimensional problem or by a heuristic approach, manages to detect faces not detected by advanced methods.

Keywords: support vector machines; quadratic programming; Newton method; face detection.

DOI: 10.1504/IJMMNO.2021.114485

International Journal of Mathematical Modelling and Numerical Optimisation, 2021 Vol.11 No.2, pp.196 - 208

Received: 05 Jun 2020
Accepted: 29 Jul 2020

Published online: 10 Feb 2021 *

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