Parametric Minimum Error Entropy Criterion: A Case Study in Blind Sensor Fusion and Regression Problems

IF 4.6 2区 工程技术 Q1 ENGINEERING, ELECTRICAL & ELECTRONIC
Carlos Alejandro Lopez;Jaume Riba
{"title":"Parametric Minimum Error Entropy Criterion: A Case Study in Blind Sensor Fusion and Regression Problems","authors":"Carlos Alejandro Lopez;Jaume Riba","doi":"10.1109/TSP.2024.3488554","DOIUrl":null,"url":null,"abstract":"The purpose of this article is to present the Parametric Minimum Error Entropy (PMEE) principle and to show a case study of the proposed criterion in a blind sensor fusion and regression problem. This case study consists on the estimation of a temporal series with a certain temporal invariance, which is measured from multiple independent sensors with unknown variances and unknown mutual correlations of the measurement errors. In this setting, we show that a particular case of the PMEE criterion is obtained from the Conditional Maximum Likelihood (CML) principle of the measurement model, leading to a \n<italic>semi-data-driven</i>\n solution. Despite the fact that Information Theoretic Criteria (ITC) are inherently robust, they often result in difficult non-convex optimization problems. Our proposal is to address the non-convexity by means of a Majorization-Minimization (MM) based algorithm. We prove the conditions in which the resulting solution of the proposed algorithm reaches a stationary point of the original problem. In fact, the aforementioned global convergence of the proposed algorithm is possible thanks to a reformulation of the original cost function in terms of a variable constrained in the Grassmann manifold. As shown in this paper, the latter procedure is possible thanks to a homogeneity property of the PMEE cost function.","PeriodicalId":13330,"journal":{"name":"IEEE Transactions on Signal Processing","volume":"72 ","pages":"5091-5106"},"PeriodicalIF":4.6000,"publicationDate":"2024-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"IEEE Transactions on Signal Processing","FirstCategoryId":"5","ListUrlMain":"https://ieeexplore.ieee.org/document/10738454/","RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"ENGINEERING, ELECTRICAL & ELECTRONIC","Score":null,"Total":0}
引用次数: 0

Abstract

The purpose of this article is to present the Parametric Minimum Error Entropy (PMEE) principle and to show a case study of the proposed criterion in a blind sensor fusion and regression problem. This case study consists on the estimation of a temporal series with a certain temporal invariance, which is measured from multiple independent sensors with unknown variances and unknown mutual correlations of the measurement errors. In this setting, we show that a particular case of the PMEE criterion is obtained from the Conditional Maximum Likelihood (CML) principle of the measurement model, leading to a semi-data-driven solution. Despite the fact that Information Theoretic Criteria (ITC) are inherently robust, they often result in difficult non-convex optimization problems. Our proposal is to address the non-convexity by means of a Majorization-Minimization (MM) based algorithm. We prove the conditions in which the resulting solution of the proposed algorithm reaches a stationary point of the original problem. In fact, the aforementioned global convergence of the proposed algorithm is possible thanks to a reformulation of the original cost function in terms of a variable constrained in the Grassmann manifold. As shown in this paper, the latter procedure is possible thanks to a homogeneity property of the PMEE cost function.
参数最小误差熵准则:盲传感器融合与回归问题案例研究
本文旨在介绍参数最小误差熵(PMEE)原理,并展示在盲传感器融合和回归问题中对所提标准的案例研究。该案例研究包括对具有一定时间不变性的时间序列进行估计,该时间序列由多个独立传感器测量,测量误差的方差和相互关系未知。在这种情况下,我们展示了 PMEE 准则的一个特殊情况,即从测量模型的条件最大似然 (CML) 原则中获得,从而得到一个半数据驱动的解决方案。尽管信息论准则(ITC)本质上是稳健的,但它们往往会导致困难的非凸优化问题。我们的建议是通过基于大数最小化(MM)的算法来解决非凸问题。我们证明了所提算法的解达到原始问题静止点的条件。事实上,由于用格拉斯曼流形中的受限变量重新表述了原始成本函数,拟议算法的上述全局收敛才成为可能。正如本文所示,后一种方法之所以可行,得益于 PMEE 成本函数的同质性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 求助全文
来源期刊
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing 工程技术-工程:电子与电气
CiteScore
11.20
自引率
9.30%
发文量
310
审稿时长
3.0 months
期刊介绍: The IEEE Transactions on Signal Processing covers novel theory, algorithms, performance analyses and applications of techniques for the processing, understanding, learning, retrieval, mining, and extraction of information from signals. The term “signal” includes, among others, audio, video, speech, image, communication, geophysical, sonar, radar, medical and musical signals. Examples of topics of interest include, but are not limited to, information processing and the theory and application of filtering, coding, transmitting, estimating, detecting, analyzing, recognizing, synthesizing, recording, and reproducing signals.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信