Subset selection in noise based on diversity measure minimization
Subset selection in noise based on diversity measure minimization
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DOI：
10.1109/tsp.2002.808076
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发表时间：
2003-03
期刊：
影响因子：
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通讯作者：
B. Rao;K. Engan;S. Cotter;J. Palmer;K. Kreutz-Delgado
中科院分区：
文献类型：
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作者：
B. Rao;K. Engan;S. Cotter;J. Palmer;K. Kreutz-Delgado
我们提出了基于最小化多样性度量的子集选择的稳健方法。贝叶斯框架用于解释数据中的噪声，最大后验概率(MAP)估计过程导致迭代过程，该迭代过程是焦点欠确定系统解算器(FOCUSS)算法的正则化版本。证明了正则化FOCUSS算法的收敛性，证明了该算法的稳定不动点是稀疏的。我们研究了三种不同的正则化参数选择准则：拟合质量准则、稀疏性准则和L曲线。针对L曲线法在子集选择问题中的健壮性问题，提出了一种新的改进的L曲线法。每种正则化FOCUSS算法都通过检测问题的仿真进行了评估，并将结果与使用称为正交匹配追踪(OMP)的顺序前向选择算法所获得的结果进行了比较。在每种情况下，正则化的FOCUSS算法在噪声环境下都优于OMP算法。
We develop robust methods for subset selection based on the minimization of diversity measures. A Bayesian framework is used to account for noise in the data and a maximum a posteriori (MAP) estimation procedure leads to an iterative procedure which is a regularized version of the focal underdetermined system solver (FOCUSS) algorithm. The convergence of the regularized FOCUSS algorithm is established and it is shown that the stable fixed points of the algorithm are sparse. We investigate three different criteria for choosing the regularization parameter: quality of fit; sparsity criterion; L-curve. The L-curve method, as applied to the problem of subset selection, is found not to be robust, and we propose a novel modified L-curve procedure that solves this problem. Each of the regularized FOCUSS algorithms is evaluated through simulation of a detection problem, and the results are compared with those obtained using a sequential forward selection algorithm termed orthogonal matching pursuit (OMP). In each case, the regularized FOCUSS algorithm is shown to be superior to the OMP in noisy environments.