EM算法的参数分辨率

Abstract

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

CLC Number:

O213

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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Figures/Tables 8

References 18

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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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Research on Resolution Based on EM Algorithm

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