多层感知器处理多分类问题的计算能力  

COMPUTATIONAL ABILITY OF MULTIPLE LINEAR PERCEPTRON NETWORKS FOR MULTI-CLASS CLASSIFICATION PROBLEMS

作　　者：杨思博 包园 罗金铭 吴微[1] 张超[1] Yang Sibo;Bao Yuan;Luo Jinming;Wu Wei;Zhang Chao(School of Mathematical Sciences,Dalian University of Technology,Dalian 116024)

机构地区：[1]大连理工大学数学科学学院,大连116024

出　　处：《高等学校计算数学学报》2020年第3期277-288,共12页Numerical Mathematics A Journal of Chinese Universities

基　　金：Supported by NNSFC:61473059,11401076 and 61473328.

摘　　要：In this paper,we consider the design of output layer nodes of multiple linear perception network for solving r-class classification problems(r≥ 3).In general,the output layer is designed in an "one-to-one" approach.Instead,we will adopt a "binary-coding" approach to build the output layer,which contains q nodes such that 2q-1 <r ≤2 q with q≥ 2 and outputs a binary code of the number i if an input belongs to the i-th class.In particular,for multiple linear perceptrons with four hidden nodes,we prove the following result:One-to-one approach can solve an r-class classification problem with r≤16 by using r output nodes,while our binary-coding approach can solve the same problem by using q(q≤4) output nodes.

关 键 词：Multiple linear perception multi-class classification problem one-to-one approach binary-coding approach accuracies 

分 类 号：O244[理学—计算数学]