{"title":"Regularization method for reduced biquaternion neural network","authors":"","doi":"10.1016/j.asoc.2024.112206","DOIUrl":null,"url":null,"abstract":"<div><p>A reduced biquaternion neural network (RQNN) has achieved significant success in machine learning. However, as the reduced biquaternion algebra system contains infinite zero divisors, the RQNN can be easily trapped in a local minimum and overfitting. In this paper, we propose a new regularization scheme for the RQNN to address these issues. Firstly, we propose a new operation in the reduced biquaternion domain named the reduced biquaternion complex modulus (RQCM), which can extract the scale transformation of reduced biquaternions and decrease the unreasonable network constraints caused by constrained phases. Secondly, we mathematically analyse the properties of the reduced biquaternions and obtain the geometric meaning of the RQCM. Finally, we propose an improved weight decay method using the RQCM which can better project the reduced biquaternion in terms of the scale and phase. In addition, our proposed method can effectively solve the non-differentiability of reduced biquaternion matrix and overfitting problem in the process of network parameter updating. The experimental results demonstrate that the proposed method is effective in color image classification and denoising taskas, and outperforms the state of the arts.</p></div>","PeriodicalId":50737,"journal":{"name":"Applied Soft Computing","volume":null,"pages":null},"PeriodicalIF":7.2000,"publicationDate":"2024-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Soft Computing","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1568494624009803","RegionNum":1,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE","Score":null,"Total":0}
引用次数: 0
Abstract
A reduced biquaternion neural network (RQNN) has achieved significant success in machine learning. However, as the reduced biquaternion algebra system contains infinite zero divisors, the RQNN can be easily trapped in a local minimum and overfitting. In this paper, we propose a new regularization scheme for the RQNN to address these issues. Firstly, we propose a new operation in the reduced biquaternion domain named the reduced biquaternion complex modulus (RQCM), which can extract the scale transformation of reduced biquaternions and decrease the unreasonable network constraints caused by constrained phases. Secondly, we mathematically analyse the properties of the reduced biquaternions and obtain the geometric meaning of the RQCM. Finally, we propose an improved weight decay method using the RQCM which can better project the reduced biquaternion in terms of the scale and phase. In addition, our proposed method can effectively solve the non-differentiability of reduced biquaternion matrix and overfitting problem in the process of network parameter updating. The experimental results demonstrate that the proposed method is effective in color image classification and denoising taskas, and outperforms the state of the arts.
期刊介绍:
Applied Soft Computing is an international journal promoting an integrated view of soft computing to solve real life problems.The focus is to publish the highest quality research in application and convergence of the areas of Fuzzy Logic, Neural Networks, Evolutionary Computing, Rough Sets and other similar techniques to address real world complexities.
Applied Soft Computing is a rolling publication: articles are published as soon as the editor-in-chief has accepted them. Therefore, the web site will continuously be updated with new articles and the publication time will be short.