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| A Geometrical Judgment Method for Linear Separability Based on Pseudo-Separating Hyperplane and Its Application |
| ZHANG Yin-Chuan, HAN Li-Xin, ZENG Xiao-Qin |
| Institute of Intelligence Science and Technology, College of Computer and Information, Hohai University, Nanjing 211100 |
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Abstract Aiming at the problem of linear separability in pattern classification, the patterns are taken as points in Euclidean space, the geometric properties including the relationship between points and planes in Euclidean space are studied, and the pseudo-separating hyperplane is defined based on the general separating hyperplane. By analyzing linear separability equivalence, the mapping from a higher dimensional space to a lower dimensional space is developed when spatial dimension reduction is required. The method for finding pseudo-separating hyperplane is studied and a judgment method for linear separability is presented with obvious geometric meaning. A classification complexity measure is proposed based on this method. The experimental results show that the proposed method reflects the complexity of data classification well.
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Received: 16 April 2013
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2014, Vol. 27 
