一种基于混合Gamma分布的自动目标识别混合EM算法
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摘要
提出一种基于高分辨距离像的混合EM算法用于自动目标识别,采用混合Gamma分布对目标主要散射点的特征进行建模。混合Gamma分布的参数分为两类:1)可以通过EM算法进行更新Gamma分布的混合系数和尺度参数;2)不存在解析更新表达式的Gamma分布的形状参数。提出的算法可为两部分:1)原始EM算法的加速算法;2)利用共轭梯度法估计Gamma分布的形状参数,并对更新表达式进行推导。数值仿真结果验证了提出方法的有效性。
For automatic target recognition,a mixed EM algorithm based on high resolution range profile( HRRP) is proposed. Mixed Gamma distribution is used to model the characteristics of the target's primary scattering point. The parameters of the mixed Gamma distribution are divided into two categories: 1) Mixed coefficient and scale parameters,which can be updated by EM algorithm. 2)Shape parameters,the analytic updating expression of which does not exist. Therefore,we present a two-step algorithm: first,the original EM algorithm is accelerated; second,the shape parameters of the Gamma distribution are estimated by a conjugate gradient method,and the updating expression is derived.The empirical studies show the efficiency and effectiveness of our method.
For automatic target recognition,a mixed EM algorithm based on high resolution range profile( HRRP) is proposed. Mixed Gamma distribution is used to model the characteristics of the target's primary scattering point. The parameters of the mixed Gamma distribution are divided into two categories: 1) Mixed coefficient and scale parameters,which can be updated by EM algorithm. 2)Shape parameters,the analytic updating expression of which does not exist. Therefore,we present a two-step algorithm: first,the original EM algorithm is accelerated; second,the shape parameters of the Gamma distribution are estimated by a conjugate gradient method,and the updating expression is derived.The empirical studies show the efficiency and effectiveness of our method.
引文
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[17]MINGJIN Y,YE K.Determining the number of clusters using the weighted gap statistic[J].Biometrics,2007,63(4):1031-1037.
[18]LAN D,LIU H W,BAO Z.Radar HRRP statistical recognition:parametric model and model selection[J].IEEE Transactions on Signal Processing,2008,56(5):1931-1944.
[19]KEITH C,WEBB A.Bayesian gamma mixture model approach to radar target recognition[J].IEEE Transactions on Aerospace and Electronic System,2003,39(4):1201-1217.
[20]SUGAR C A,JAMES G M.Finding the number of clusters in a dataset[J].Journal of the American Statistical Association,2003,463(98):750-763.
[2]DOUGLAS R A,QUATIERI T F,DUNN R B.Speaker verification using adapted Gaussian mixture models[J].Digital signal processing,2000,10(1):19-41.
[3]YANHUA R,HONG L.Feature extraction by Gaussian mixture with rigidity constraint[J].IEEE Transactions on Automatic Control,2007,52(10):1899-1907.
[4]KEITH C,WEBB A.Bayesian gamma mixture model approach to radar target recognition[J].IEEE Transactions on Aerospace and Electronic Systems,2003,39(4):1201-1217.
[5]WEBB A R.Gamma mixture models for target recognition[J].Pattern Recognition,2000,33(12):2045-2054.
[6]SKOLNIK M I.Radar Handbook[M].New York:Mc GrawHill Publishing Company,1962.
[7]DEMPSTER A P,LAIRD N M,RUBIN D B.Maximum likelihood from incomplete data via the EM algorithm[J].Journal of the Royal Statistical Society,1977,39(1):1-38.
[8]RAVI V,ROLAND C.Simple and globally convergent methods for accelerating the convergence of any EM algorithm[J].Scandinavian Journal of Statistics,2008,35(2):335-353.
[9]TZIKAS D G,LIKAS C L,GALATSANOS N P.The variational approximation for bayesian inference[J].Signal Processing Magazine,2008,25(6):131-146.
[10]LANGE K.A quasi-Newton acceleration of the EM algorithm[J].Statistica Sinica,1995,5(1):1-18.
[11]CHUANHAI L,RUBIN D B,WU Y N.Parameter expansion to accelerate EM:the PX-EM algorithm[J].Biometrika,1998,85(4):755-770.
[12]HU L,et al.Compressed sensing of complex sinusoids:an approach based on dictionary refinement[J].IEEE Transactions on Signal Processing,2012,60(7):3809-3822.
[13]WANG J,DOGANDZIC A,NEHORAI A.Maximum likelihood estimation of compound-Gaussian clutter and target parameters[J].IEEE Transactions on Signal Processing,2006,54(10):3884-3898.
[14]ZHOU H,ALEXANDER D,LANGE K.A quasi-Newton acceleration for high-dimensional optimization algorithms[J].Statistics and computing,2011,21(2):261-273.
[15]MORTAZA J,JENNRICH R I.Conjugate gradient acceleration of the EM algorithm[J].Journal of the American Statistical Association,1993,421(88):221-228.
[16]CHRISTOPHE B,CELEUX G,GOVAERT G R.Assessing a mixture model for clustering with the integrated completed likelihood[J].IEEE Transactions on Pattern Analysis and Machine Intelligence,2000,22(7):719-725.
[17]MINGJIN Y,YE K.Determining the number of clusters using the weighted gap statistic[J].Biometrics,2007,63(4):1031-1037.
[18]LAN D,LIU H W,BAO Z.Radar HRRP statistical recognition:parametric model and model selection[J].IEEE Transactions on Signal Processing,2008,56(5):1931-1944.
[19]KEITH C,WEBB A.Bayesian gamma mixture model approach to radar target recognition[J].IEEE Transactions on Aerospace and Electronic System,2003,39(4):1201-1217.
[20]SUGAR C A,JAMES G M.Finding the number of clusters in a dataset[J].Journal of the American Statistical Association,2003,463(98):750-763.