Generalization Error of Linear Discriminant Analysis in Spatially-Correlated Sensor Networks
Generalization Error of Linear Discriminant Analysis in Spatially-Correlated Sensor Networks
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DOI：
10.1109/tsp.2012.2190063
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发表时间：
2012-06
影响因子：
5.4
通讯作者：
Kush R. Varshney
中科院分区：
文献类型：
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作者：
Kush R. Varshney
泛化误差，即从训练样本中学习到的检测规则在新的未见过的样本上出错的概率，是一个需要描述的基本量。然而，统计学习理论文献中对泛化误差的描述往往很宽松，在实际优化检测系统时无法使用。在这项工作中，重点关注从空间相关的传感器测量中学习线性判别分析检测规则，开发了一种紧密的泛化误差近似方法，可用于优化传感器网络检测系统的参数。因此，该近似方法被用于优化网络设置。该近似方法还被用于推导检测误差指数并选择已部署传感器节点的最优子集。在分析中，使用高斯 - 马尔可夫随机场来模拟相关性，并运用几何概率中的弱大数定律。
Generalization error, the probability of error of a detection rule learned from training samples on new unseen samples, is a fundamental quantity to be characterized. However, characterizations of generalization error in the statistical learning theory literature are often loose and practically unusable for optimizing detection systems. In this work, focusing on learning linear discriminant analysis detection rules from spatially-correlated sensor measurements, a tight generalization error approximation is developed that can be used to optimize the parameters of a sensor network detection system. As such, the approximation is used to optimize network settings. The approximation is also used to derive a detection error exponent and select an optimal subset of deployed sensor nodes. A Gauss-Markov random field is used to model correlation and weak laws of large numbers in geometric probability are employed in the analysis.