# Optimal Bayes Classification of High Dimensional Data in Face Recognition

### Wissal Drira, Faouzi Ghorbel

#### Abstract

In the supervised context, we intend to introduce a system which is composed of a series of novel and efficient algorithms that is able to realize a non parametric Bayesian classifier for high dimension. The proposed system tries to search for the best discriminate sub space in the mean of the minimum of the probability error of classification which is computed by using a modified kernel estimate of the conditional probability density functions. Therefore, Bayesian classification rule is applied in the reduced sub space. Such heuristic consists of four tasks. First, we maximize a novel estimate of the quadratic measure of the probabilistic dependence in order to realize multivariate extractors resulting from a number of different initializations of a given numerical optimizing procedure. Second, an estimation of the miss classification error is computed for each solution by the kernel estimate of the conditional probability density functions with the optimal band-with parameter in the sense of the Mean Integrate Square Error (MISE) which is obtained with the Plug in algorithm. Third, the sub space which presents the minimum of the miss classification values is thus chosen. After that, the Bayesian classification rule is operated in the reduced sub space with the optimal MISE of the modified kernel estimate. Finally, different algorithms will be applied to a base of images in grayscale representing classes of faces, showing its interest in the case of real data.

#### References

- Devijver, P. A., Kittler, J., 1982. Pattern recognition: A statistical approach, Prentice-Hall, Englewood Cliffs, NJ.
- Drira, W., Neji, W. and Ghorbel F., 2012. Dimension reduction by an orthogonal series estimate of the probabilistic dependence measure. The International Conference on Pattern Recognition Applications and Methods ICPRAM 2012, Portugal, February, 2012.
- Drira, W., Ghorbel F., 2012. Non Parametric Feature Discriminate Analysis for High Dimension. The 16 International Conference on Image Processing, Computer Vision, and Pattern Recognition IPCV, Las Vegas USA, July 2012.
- Effron, B., 1983. Estimating the Error Rate of a Prediction Rule: Improvement on Cross-Validation. J. Am. Statistical Assoc.
- Fisher, R. A., 1936.The Use of Multiple Measurements in Taxonomic Problems. Annals of Eugenics, vol. 7, 179- 188.
- Hillion, A., Masson, P., Roux, C., 1988. A nonparametric approach to linear feature extraction; Application to classification of binary synthetic textures. 9th International Conference on Pattern Recognition, ICPR, 1036-1039.
- Jesorsky, O., Kirchberg, K., Frischholz, R. 2001.Robust Face Detection Using the Hausdorff Distance. In Proc. Third International Conference on Audio and Video based Person Authentication - AVBPA 2001, pp. 90- 95, https://support.bioid.com/downloads/facedb/ index.php.
- Loog, M., Duin R. P. W., Haeb-Umbach R., 2001. Multiclass Linear Dimension Reduction by Weighted Pairwise Fisher Criteria. IEEE transaction on PAMI, vol. 23, n° 7.
- Nenadic Z., 2007. Information Discriminant Analysis: Feature Extraction with an Information-Theoretic Objective. IEEE transactions on Pattern Analysis and Machine Intelligence, vol. 29, n° 8.
- Patrick, E. A., Fischer, F. P., 1969. Non parametric feature selection. IEEE Trans. On Inf. Theory, vol. IT-15, 577-584.

#### Paper Citation

#### in Harvard Style

Drira W. and Ghorbel F. (2013). **Optimal Bayes Classification of High Dimensional Data in Face Recognition** . In *Proceedings of the 2nd International Conference on Pattern Recognition Applications and Methods - Volume 1: BTSA, (ICPRAM 2013)* ISBN 978-989-8565-41-9, pages 641-646. DOI: 10.5220/0004345106410646

#### in Bibtex Style

@conference{btsa13,

author={Wissal Drira and Faouzi Ghorbel},

title={Optimal Bayes Classification of High Dimensional Data in Face Recognition},

booktitle={Proceedings of the 2nd International Conference on Pattern Recognition Applications and Methods - Volume 1: BTSA, (ICPRAM 2013)},

year={2013},

pages={641-646},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0004345106410646},

isbn={978-989-8565-41-9},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 2nd International Conference on Pattern Recognition Applications and Methods - Volume 1: BTSA, (ICPRAM 2013)

TI - Optimal Bayes Classification of High Dimensional Data in Face Recognition

SN - 978-989-8565-41-9

AU - Drira W.

AU - Ghorbel F.

PY - 2013

SP - 641

EP - 646

DO - 10.5220/0004345106410646