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
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
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.
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.
