基于非线性主成分分析的信用评估模型研究

传统的主成分分析（PCA）本质上是一种线性映射算法，无法有效处理非线性关系的数据。本文在分析自联想神经网络（AANN）的基础上，借鉴传统PCA方法中的序数主成分概念，提出了基于顺序自联想神经网络（SAANN）的非线性主成分分析法（NLPCA）。进一步，结合神经网络（NN）和Logisitic模型，以我国上市公司为研究对象，分别构建了基于NLPCA-NN和NLPCA-Logisitic的信用评估模型。实证结果及ROC曲线分析表明，本文构建的NLPCA相比传统的线性PCA方法能有效地实现数据的非线性特征提取与降维，提高模型预测性能。此外，实证结果还表明，在相同PCA方法处理数据的条件下，神经网络模型的信用评估效果要好于Logisitic模型。

Research on Credit Evaluation Model Based on Nonlinear Principal Component Analysis

The traditional Principal component analysis (PCA) is only a linear dimension reduction method, it cannot deal efficiently with nonlinearly correlated financial variables. This paper presents an improved approach of nonlinear principal component analysis (NLPCA) based on analysis of the auto-associate neural networks (AANN), sequential AANN, to realize the data reduction. Furthermore, two integrated models, NLPCA-NN and NLPCA-Logisitic models, are presented combined NLPCA with particle swarm optimization neural networks (NN) and Logisitic model respectively. The results in terms of predicting accuracy and receiver operating characteristic (ROC) curve indicate the proposed model can achieve a better performance than the model based traditional linear PCA approach, Furthermore, under the conditions of processing data in the same PCA, the forecasting result of NN model is better than one of Logisitic model.