# Optimal Conjugate Gradient Algorithm for Generalization of Linear Discriminant Analysis Based on L1 Norm

### Kanishka Tyagi, Nojun Kwak, Michael Manry

#### Abstract

This paper analyzes a linear discriminant subspace technique from an L1 point of view. We propose an efficient and optimal algorithm that addresses several major issues with prior work based on, not only the L1 based LDA algorithm but also its L2 counterpart. This includes algorithm implementation, effect of outliers and optimality of parameters used. The key idea is to use conjugate gradient to optimize the L1 cost function and to find an learning factor during the update of the weight vector in the subspace. Experimental results on UCI datasets reveal that the present method is a significant improvement over the previous work. Mathematical treatment for the proposed algorithm and calculations for learning factor are the main subject of this paper.

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#### Paper Citation

#### in Harvard Style

Tyagi K., Kwak N. and Manry M. (2014). **Optimal Conjugate Gradient Algorithm for Generalization of Linear Discriminant Analysis Based on L1 Norm** . In *Proceedings of the 3rd International Conference on Pattern Recognition Applications and Methods - Volume 1: ICPRAM,* ISBN 978-989-758-018-5, pages 207-212. DOI: 10.5220/0004825402070212

#### in EndNote Style

TY - CONF

JO - Proceedings of the 3rd International Conference on Pattern Recognition Applications and Methods - Volume 1: ICPRAM,

TI - Optimal Conjugate Gradient Algorithm for Generalization of Linear Discriminant Analysis Based on L1 Norm

SN - 978-989-758-018-5

AU - Tyagi K.

AU - Kwak N.

AU - Manry M.

PY - 2014

SP - 207

EP - 212

DO - 10.5220/0004825402070212

#### in Bibtex Style

@conference{icpram14,

author={Kanishka Tyagi and Nojun Kwak and Michael Manry},

title={Optimal Conjugate Gradient Algorithm for Generalization of Linear Discriminant Analysis Based on L1 Norm},

booktitle={Proceedings of the 3rd International Conference on Pattern Recognition Applications and Methods - Volume 1: ICPRAM,},

year={2014},

pages={207-212},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0004825402070212},

isbn={978-989-758-018-5},

}