EM算法的参数分辨率

数学物理学报 ›› 2019, Vol. 39 ›› Issue (3): 638-648.

EM算法的参数分辨率

鲁纳纳(),余旌胡*()

武汉理工大学理学院武汉 430070

收稿日期:2018-07-16 出版日期:2019-06-26 发布日期:2019-06-27
通讯作者: 余旌胡 E-mail:1358242069@qq.com;yujh67@126.com
作者简介:鲁纳纳, 1358242069@qq.com
基金资助:
中央高校基本科研业务费专项资金(2017IVA073);中央高校基本科研业务费(2018IB016)

Research on Resolution Based on EM Algorithm

Nana Lu(),Jinghu Yu*()

Department of Mathematics, School of Science, Wuhan University of Technology, Wuhan 430070

Received:2018-07-16 Online:2019-06-26 Published:2019-06-27
Contact: Jinghu Yu E-mail:1358242069@qq.com;yujh67@126.com
Supported by:
the Fundamental Research Funds for the Central Universities(2017IVA073);the Fundamental Research Funds for the Central Universities(2018IB016)

摘要/Abstract

摘要：

参数分辨率是在给定噪声情况下，衡量两个相近信号能否区分开的一个标准，为敏感参数、有效精度以及准确度的衡量提供了评估的"尺子".该文以EM算法为基础，结合Fisher线性判别准则的思想，给出EM算法参数分辨率的定义，并以两正态混合模型为例进行验证.实验表明两个方差为0.1的正态分布其均值距离大于0.206时，EM算法在90%的置信度下可以区分这两个分布，通过构建实验结果和理论推导之间的联系，得到不同置信度下的比例因子图.参数分辨率的提出，为准确度的衡量提供一个定量指标，也为相近信号的区分提供新的解决方案.

关键词: EM算法, 分辨率, 判别准则, 变异系数

Abstract:

Parameter resolution is a criterion for measuring whether two adjacent signals can be distinguished under the given noise conditions, it provides an evaluation of the "ruler" for the measurement of sensitive parameters, effective precision and accuracy. This paper proposes a definition of the parameter resolution of EM algorithm, which is based on the EM algorithm, and the idea of Fisher linear discriminant criterion, two-component Gaussian mixed model is taken as an example to verify it. Experiments show that when two normal distributions with a variance of 0.1 have a mean distance greater than 0.206, the EM algorithm can tell the differences between the two distributions under a confidence of 90%, by constructing the connection between experimental results and theoretical derivation, the scale factor graphs with different confidence levels are obtained. The proposed resolution of the parameters provides a quantitative indicator for the accuracy measurement and also provides a new solution for the differentiation of similar signals.

Key words: EM algorithm, Resolution, Criterion, Coefficient of variation

中图分类号:

O213

鲁纳纳,余旌胡. EM算法的参数分辨率[J]. 数学物理学报, 2019, 39(3): 638-648.

Nana Lu,Jinghu Yu. Research on Resolution Based on EM Algorithm[J]. Acta mathematica scientia,Series A, 2019, 39(3): 638-648.

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固定$\mu$调整$\nu$	RE1	AE1	固定$\nu$调整$\mu$	RE2	$\delta$	CV1	CV2
$\mu=1.0, \nu=1.190$	0.1900	0.190	$\mu=0.814, \nu=1.0$	0.1860	0.1880	0.1840	0.2229
$\mu=1.2, \nu=1.391$	0.1592	0.191	$\mu=1.010, \nu=1.2$	0.1583	0.1588	0.1552	0.1823
$\mu=1.6, \nu=1.792$	0.1200	0.192	$\mu=1.407, \nu=1.6$	0.1206	0.1203	0.1183	0.1336
$\mu=1.8, \nu=1.991$	0.1061	0.191	$\mu=1.606, \nu=1.8$	0.1078	0.1070	0.1058	0.1178
$\mu=2.0, \nu=2.192$	0.0960	0.192	$\mu=1.806, \nu=2.0$	0.0970	0.0965	0.0956	0.1054
$\mu=3.0, \nu=3.192$	0.0640	0.192	$\mu=2.809, \nu=3.0$	0.0637	0.0639	0.0647	0.0689

固定$\mu$调整$\nu$	RE1	AE1	固定$\nu$调整$\mu$	RE2	$\delta$	CV1	CV2
$\mu=1.0, \nu=1.200$	0.2000	0.200	$\mu=0.798, \nu=1.0$	0.2020	0.2010	0.1833	0.2253
$\mu=1.2, \nu=1.400$	0.1667	0.200	$\mu=1.000, \nu=1.2$	0.1667	0.1667	0.1548	0.1833
$\mu=1.6, \nu=1.804$	0.1275	0.204	$\mu=1.395, \nu=1.6$	0.1281	0.1278	0.1179	0.1342
$\mu=1.8, \nu=2.005$	0.1139	0.205	$\mu=1.597, \nu=1.8$	0.1128	0.1134	0.1054	0.1182
$\mu=2.0, \nu=2.204$	0.1020	0.204	$\mu=1.795, \nu=2.0$	0.1025	0.1023	0.0954	0.1057
$\mu=3.0, \nu=3.206$	0.0687	0.206	$\mu=2.796, \nu=3.0$	0.0680	0.0684	0.0645	0.0691

固定$\mu$调整$\nu$	RE1	AE1	固定$\nu$调整$\mu$	RE2	$\delta$	CV1	CV2
$\mu=1.0, \nu=1.220$	0.2200	0.220	$\mu=0.780, \nu=1.0$	0.2200	0.2200	0.1820	0.2282
$\mu=1.2, \nu=1.420$	0.1833	0.220	$\mu=0.980, \nu=1.2$	0.1833	0.1833	0.1538	0.1854
$\mu=1.6, \nu=1.827$	0.1419	0.227	$\mu=1.376, \nu=1.6$	0.1400	0.1410	0.1172	0.1352
$\mu=1.8, \nu=2.025$	0.1250	0.225	$\mu=1.576, \nu=1.8$	0.1244	0.1247	0.1049	0.1190
$\mu=2.0, \nu=2.226$	0.1130	0.226	$\mu=1.778, \nu=2.0$	0.1110	0.1120	0.0949	0.1062
$\mu=3.0, \nu=3.224$	0.0747	0.224	$\mu=2.775, \nu=3.0$	0.0750	0.0749	0.0644	0.0694

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