NONLINEAR PRINCIPAL COMPONENT ANALYSIS USING AUTOASSOCIATIVE NEURAL NETWORKS
NONLINEAR PRINCIPAL COMPONENT ANALYSIS USING AUTOASSOCIATIVE NEURAL NETWORKS
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DOI：
10.1002/aic.690370209
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发表时间：
1991-02-01
期刊：
影响因子：
3.7
通讯作者：
KRAMER, MA
中科院分区：
文献类型：
--
作者：
KRAMER, MA
非线性主成分分析是一种新的多元数据分析方法，类似于众所周知的主成分分析方法。NLPCA与PCA一样，用于识别和去除问题变量之间的相关性，以辅助降维、可视化和探索性数据分析。虽然PCA只识别变量之间的线性相关性，但NLPCA揭示了线性和非线性相关性，而不限制数据中存在的非线性特征。NLPCA通过训练前馈神经网络来执行身份映射，其中网络输入在输出层被复制。网络包含一个内部“瓶颈”层（包含比输入或输出层更少的节点），这迫使网络开发输入数据的紧凑表示，以及两个额外的隐藏层。NLPCA方法是用时间相关的，模拟批反应数据来证明的。结果表明，NLPCA成功地降低了维数，并生成了与底层系统参数实际分布相似的特征空间图。
Nonlinear principal component analysis is a novel technique for multivariate data analysis, similar to the well-known method of principal component analysis. NLPCA, like PCA, is used to identify and remove correlations among problem variables as an aid to dimensionality reduction, visualization, and exploratory data analysis. While PCA identifies only linear correlations between variables, NLPCA uncovers both linear and nonlinear correlations, without restriction on the character of the nonlinearities present in the data. NLPCA operates by training a feedforward neural network to perform the identity mapping, where the network inputs are reproduced at the output layer. The network contains an internal "bottleneck" layer (containing fewer nodes than input or output layers), which forces the network to develop a compact representation of the input data, and two additional hidden layers. The NLPCA method is demonstrated using time-dependent, simulated batch reaction data. Results show that NLPCA successfully reduces dimensionality and produces a feature space map resembling the actual distribution of the underlying system parameters.