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 present the basic idea of abstract principal component analysis(APCA)as a general approach that extends various popular data analysis techniques such as PCA and GPCA.We describe the mathematical theory behind APCA ...We present the basic idea of abstract principal component analysis(APCA)as a general approach that extends various popular data analysis techniques such as PCA and GPCA.We describe the mathematical theory behind APCA and focus on a particular application to mode extractions from a data set of mixed temporal and spatial signals.For illustration,algorithmic implementation details and numerical examples are presented for the extraction of a number of basic types of wave modes including,in particular,dynamic modes involving spatial shifts.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 National Science Foundation of USA(Grant No.DMS101607)
文摘We present the basic idea of abstract principal component analysis(APCA)as a general approach that extends various popular data analysis techniques such as PCA and GPCA.We describe the mathematical theory behind APCA and focus on a particular application to mode extractions from a data set of mixed temporal and spatial signals.For illustration,algorithmic implementation details and numerical examples are presented for the extraction of a number of basic types of wave modes including,in particular,dynamic modes involving spatial shifts.
