基于概率核主成分分析的属性优化方法及其应用

Attribute optimization based on the probability kernel principal component analysis

主成分分析(PCA)是最常用的属性优化分析技术,但存在缺少概率模型和缺失高阶统计量信息的不足。本文基于贝叶斯理论和核主成分分析(KPCA)法,研究了可同时克服PCA两个缺点的方法———概率核主成分分析(PKPCA)。即首先将样本数据映射到高维特征空间,继而在特征空间定义数据的概率模型,最后应用期望最大(EM)估计最佳结果。该方法兼具概率分析和核主成分分析的优点,能有效地适应更复杂储层情况,实现非线性概率分析。实际数据的应用结果表明,基于贝叶斯理论的属性概率优化法提高了属性优化的精度,同时增强了储层预测的准确性和可靠性。

The principal component analysis(PCA)is the most common attribute optimization analysis techniques,but with lack of probability model and the absence of higher-order statistics information.In order to overcome its shortcomings,this paper proposes the probability kernel principal component analysis(PKPCA)based on Bayesian theory and kernel principal component analysis(KPCA).First,we map the sample data to the high dimensional feature space,then define probability model of the data in high-dimensional space,and finally,use expectation maximization(EM)estimated to get the best results.This method has both the advantage of the probability analysis and the kernel principal component analysis(KPCA),and can realize the non-linear probability analysis in more complex reservoir conditions.The probability of kernel principal component analysis(PKPCA)is applied to reservoir prediction of an oilfield.The predicted results show that the method not only improves the precision of attribute optimization,but also the accuracy of reservoir prediction.