Title of Paper:多层感知器处理多分类问题的计算能力

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Date of Publication:2022-06-29

Journal:Numerical Mathematics A Journal of Chinese University

Volume:42

Issue:3

Page Number:277-288

ISSN No.:1000-081X

Key Words:"Multiple linear perceptron; multi-class classification problem; one-to-one approach; binary-coding approach; accuracies"

CN No.:32-1170/O1

Abstract:In this paper, we consider the design of output layer nodes of multiple linear perceptron network for solving $r$-class classification problems $\left( {r \ge 3} \right)$. 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 ${2^{q - 1}} < r \le {2^q}$ with $q \ge 2$ 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 $r \le 16$ by using r output nodes, while our binary-coding approach can solve the same problem by using $q\left( {q \le 4} \right)$ output nodes.

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