<p>Based on principal component analysis (PCA) and and Bayesian theory, a mix probabilistic kernel principal component analysis (MPKPCA) technique is proposed. It overcomes the problem of lack of probability model and high-order statistics information in PCA analysis. At the same time, it uses the probability structure to establish the mixed mode of probability kernel principal component analysis function(MPKPCA). Thus it can simultaneously apply multiple probability models and kernel functions to simulate reservoir types with different data rules, and has high generalization ability. In the extraction of complex nonlinear features, firstly, the number of kernel functions and probability models is selected, and the initial mixed probability model coefficients are given. Then, under the constraint of the defined probability model, the sample data with different characteristics are mapped to different high-dimensional kernel spaces to realize the characterization of different types of reservoirs. Finally, the expected maximum (EM) estimation is used to obtain the final probability model coefficients and the best reservoir feature extraction results. Using a small number of sample data, this technology can accurately capture the characteristics of nonlinear substructure data contained in nonlinear high-dimensional data, realize the extraction of complex reservoir characteristics, and complete the intelligent classification and prediction of reservoirs. The application results of practical data show that the mix probability kernel principal component analysis technology improves the accuracy of reservoir feature extraction and reservoir prediction.</p>

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Reservoir prediction and mixed probability kernel principal component analysis based on Small-Sample Data

  • Jing-jing Zheng,
  • Naiguo Wang,
  • Chun Yang,
  • Yun Wang

摘要

Based on principal component analysis (PCA) and and Bayesian theory, a mix probabilistic kernel principal component analysis (MPKPCA) technique is proposed. It overcomes the problem of lack of probability model and high-order statistics information in PCA analysis. At the same time, it uses the probability structure to establish the mixed mode of probability kernel principal component analysis function(MPKPCA). Thus it can simultaneously apply multiple probability models and kernel functions to simulate reservoir types with different data rules, and has high generalization ability. In the extraction of complex nonlinear features, firstly, the number of kernel functions and probability models is selected, and the initial mixed probability model coefficients are given. Then, under the constraint of the defined probability model, the sample data with different characteristics are mapped to different high-dimensional kernel spaces to realize the characterization of different types of reservoirs. Finally, the expected maximum (EM) estimation is used to obtain the final probability model coefficients and the best reservoir feature extraction results. Using a small number of sample data, this technology can accurately capture the characteristics of nonlinear substructure data contained in nonlinear high-dimensional data, realize the extraction of complex reservoir characteristics, and complete the intelligent classification and prediction of reservoirs. The application results of practical data show that the mix probability kernel principal component analysis technology improves the accuracy of reservoir feature extraction and reservoir prediction.