Traditional PCA is a linear method, but most engineering problems are nonlinear. Using the linear PCA in nonlinear problems may bring distorted and misleading results. Therefore, an approach of nonlinear principal com...Traditional PCA is a linear method, but most engineering problems are nonlinear. Using the linear PCA in nonlinear problems may bring distorted and misleading results. Therefore, an approach of nonlinear principal component analysis (NLPCA) using radial basis function (RBF) neural network is developed in this paper. The orthogonal least squares (OLS) algorithm is used to train the RBF neural network. This method improves the training speed and prevents it from being trapped in local optimization. Results of two experiments show that this NLPCA method can effectively capture nonlinear correlation of nonlinear complex data, and improve the precision of the classification and the prediction.展开更多
We compared nonlinear principal component analysis(NLPCA) with linear principal component analysis(LPCA) with the data of sea surface wind anomalies(SWA),surface height anomalies(SSHA),and sea surface temperature anom...We compared nonlinear principal component analysis(NLPCA) with linear principal component analysis(LPCA) with the data of sea surface wind anomalies(SWA),surface height anomalies(SSHA),and sea surface temperature anomalies(SSTA),taken in the South China Sea(SCS) between 1993 and 2003.The SCS monthly data for SWA,SSHA and SSTA(i.e.,the anomalies with climatological seasonal cycle removed) were pre-filtered by LPCA,with only three leading modes retained.The first three modes of SWA,SSHA,and SSTA of LPCA explained 86%,71%,and 94% of the total variance in the original data,respectively.Thus,the three associated time coefficient functions(TCFs) were used as the input data for NLPCA network.The NLPCA was made based on feed-forward neural network models.Compared with classical linear PCA,the first NLPCA mode could explain more variance than linear PCA for the above data.The nonlinearity of SWA and SSHA were stronger in most areas of the SCS.The first mode of the NLPCA on the SWA and SSHA accounted for 67.26% of the variance versus 54.7%,and 60.24% versus 50.43%,respectively for the first LPCA mode.Conversely,the nonlinear SSTA,localized in the northern SCS and southern continental shelf region,resulted in little improvement in the explanation of the variance for the first NLPCA.展开更多
State reconstruction approach is very useful for sensor fault isolation, reconstruction of faulty measurement and the determination of the number of components retained in the principal components analysis （PCA） mod...State reconstruction approach is very useful for sensor fault isolation, reconstruction of faulty measurement and the determination of the number of components retained in the principal components analysis （PCA） model. An extension of this approach based on a Nonlinear PCA （NLPCA） model is described in this paper. The NLPCA model is obtained using five layer neural network. A simulation example is given to show the performances of the proposed approach.展开更多
Dimensionality reduction and data visualization are useful and important processes in pattern recognition. Many techniques have been developed in the recent years. The self-organizing map （SOM） can be an efficient m...Dimensionality reduction and data visualization are useful and important processes in pattern recognition. Many techniques have been developed in the recent years. The self-organizing map （SOM） can be an efficient method for this purpose. This paper reviews recent advances in this area and related approaches such as multidimensional scaling （MDS）, nonlinear PC A, principal manifolds, as well as the connections of the SOM and its recent variant, the visualization induced SOM （ViSOM）, with these approaches. The SOM is shown to produce a quantized, qualitative scaling and while the ViSOM a quantitative or metric scaling and approximates principal curve/surface. The SOM can also be regarded as a generalized MDS to relate two metric spaces by forming a topological mapping between them. The relationships among various recently proposed techniques such as ViSOM, Isomap, LLE, and eigenmap are discussed and compared.展开更多
文摘Traditional PCA is a linear method, but most engineering problems are nonlinear. Using the linear PCA in nonlinear problems may bring distorted and misleading results. Therefore, an approach of nonlinear principal component analysis (NLPCA) using radial basis function (RBF) neural network is developed in this paper. The orthogonal least squares (OLS) algorithm is used to train the RBF neural network. This method improves the training speed and prevents it from being trapped in local optimization. Results of two experiments show that this NLPCA method can effectively capture nonlinear correlation of nonlinear complex data, and improve the precision of the classification and the prediction.
基金Supported by the Knowledge Innovation Program of the Chinese Academy of Sciences (No.KZCX1-YW-12)the National Natural Science Foundation of China (No.40706011)the Open Foundation of Key Laboratory of Marine Science and Numerical Modeling (MASNUM)
文摘We compared nonlinear principal component analysis(NLPCA) with linear principal component analysis(LPCA) with the data of sea surface wind anomalies(SWA),surface height anomalies(SSHA),and sea surface temperature anomalies(SSTA),taken in the South China Sea(SCS) between 1993 and 2003.The SCS monthly data for SWA,SSHA and SSTA(i.e.,the anomalies with climatological seasonal cycle removed) were pre-filtered by LPCA,with only three leading modes retained.The first three modes of SWA,SSHA,and SSTA of LPCA explained 86%,71%,and 94% of the total variance in the original data,respectively.Thus,the three associated time coefficient functions(TCFs) were used as the input data for NLPCA network.The NLPCA was made based on feed-forward neural network models.Compared with classical linear PCA,the first NLPCA mode could explain more variance than linear PCA for the above data.The nonlinearity of SWA and SSHA were stronger in most areas of the SCS.The first mode of the NLPCA on the SWA and SSHA accounted for 67.26% of the variance versus 54.7%,and 60.24% versus 50.43%,respectively for the first LPCA mode.Conversely,the nonlinear SSTA,localized in the northern SCS and southern continental shelf region,resulted in little improvement in the explanation of the variance for the first NLPCA.
文摘State reconstruction approach is very useful for sensor fault isolation, reconstruction of faulty measurement and the determination of the number of components retained in the principal components analysis （PCA） model. An extension of this approach based on a Nonlinear PCA （NLPCA） model is described in this paper. The NLPCA model is obtained using five layer neural network. A simulation example is given to show the performances of the proposed approach.
文摘Dimensionality reduction and data visualization are useful and important processes in pattern recognition. Many techniques have been developed in the recent years. The self-organizing map （SOM） can be an efficient method for this purpose. This paper reviews recent advances in this area and related approaches such as multidimensional scaling （MDS）, nonlinear PC A, principal manifolds, as well as the connections of the SOM and its recent variant, the visualization induced SOM （ViSOM）, with these approaches. The SOM is shown to produce a quantized, qualitative scaling and while the ViSOM a quantitative or metric scaling and approximates principal curve/surface. The SOM can also be regarded as a generalized MDS to relate two metric spaces by forming a topological mapping between them. The relationships among various recently proposed techniques such as ViSOM, Isomap, LLE, and eigenmap are discussed and compared.
