Research on stereographic projection and it's application on feed forward neural network

  • Authors:
  • Zhenya Zhang;Hongmei Cheng;Xufa Wang

  • Affiliations:
  • Institute of Architecture & Industry (AIAI), Computer and Information Engineering Department of Anhui, Hefei, China;Management Engineering Department of AIAI, Hefei, China;Computer Science Department of USTC, Hefei, China

  • Venue:
  • ICNC'06 Proceedings of the Second international conference on Advances in Natural Computation - Volume Part I
  • Year:
  • 2006

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Abstract

Feed forward neural network for classification instantly requires that the modular length of input vector is 1. On the other hand, Stereographic projection can map a point in n dimensional real space into the surface of unit sphere in (n+1) dimensional real space. Because the modular length of any point in the unit sphere of (n+1) dimensional real surface is 1 and stereographic projection is a bijective mapping, Stereographic projection can be treated as an implementation for the normalization of vector in n dimensional real space. Experimental results shown that feed forward neural network can classify data instantly and accurately if stereographic projection is used to normalized input vector for feed forward network.