The Open Cybernetics & Systemics Journal

2008, 2 : 101-105
Published online 2008 April 23. DOI: 10.2174/1874110X00802010101
Publisher ID: TOCSJ-2-101

New Criteria for the Linear Binary Separability in the Euclidean Normed Space

Yeong-Jeu Sun
Department of Electrical Engineering, I-Shou University, Kaohsiung, Taiwan 840, Republic of China.

ABSTRACT

In this paper, the classical binary classification problem is investigated. Necessary and sufficient criterion is presented to guarantee the linear binary separability of the training data in the Euclidean normed space. A suitable hyperplane that correctly classifies the training data is also constructed provided that the necessary and sufficient is satisfied. Based on the main result, we offer an easy-to-check criterion for the linear binary separability of the training set. Finally, a numerical example is provided to illustrate the feasibility and effectiveness of the obtained result.

Keywords:

Binary classification, necessary and sufficient criterion, pattern recognition.