In this study, a nonlinear dimension reduction based low-order neural model identification approach is proposed for nonlinear distributed parameter processes.
Locally linear embedding (LLE), as a representative manifold learning technique, is a nonlinear dimension reduction method by mapping the high-dimensional data to a lower dimensional space while preserving the essential properties of the raw data.
In order to find the intrinsic manifold structure of data samples, researchers also proposed some nonlinear dimension reduction methods, such as the locally linear embedding (LLE) (Roweis and Saul 2000) and the Laplacian eigenmap (LE) (Belkin and Niyogi 2003).
Wilkinson [12] points out that not only MDS and hierarchical clustering may be used for matrix reordering, but also singular values decomposition (SVD), nonlinear dimension reduction, and entropy minimization.
First, a nonlinear principal component analysis (NL-PCA) network is designed for the nonlinear dimension reduction, which can transform the high-dimensional spatio-temporal data into a low-dimensional time domain.
Numerical experiments indicate that FTGA can efficiently and reliably achieve more accurate global optima of complex, nonlinear, high-dimension and multimodal optimization problems subject to nonlinear constraints.
As described above, the GDA is a nonlinear data dimension reduction method based on kernel function learning technique, which will be used to deal with the normalized feature vectors.
However, dynamical behavior of neural networks in response to external stimuli is less well studied due to the difficulty of the mathematical description of nonlinear high dimension dynamical system [7], [8].
Results: We propose a joint association test strategy based on two key components: a nonlinear supervised dimension reduction approach for effective SNP information aggregation and a novel kernel specially designed for qualitative genotype data.
With the help of simulations, the control strategy based on direct RBFNN model reference adaptive control can not only make the multi-dimension nonlinear plants track multi-dimension reference signals quickly, but also endow the control systems with satisfying robustness.
