This paper describes a novel means for creating a nonlinear extension of principal component analysis (PCA) using radial basis function (RBF) networks. This algorithm comprises two distinct stages: projection and self-consistency. The projection stage contains a single network, trained to project data from a high- to a low-dimensional space. Training requires solution of a generalized eigenvector equation. The second stage, trained using a novel hybrid nonlinear optimization algorithm, then performs the inverse transformation. Issues relating to the practical implementation of the procedure are discussed, and the algorithm is demonstrated on a nonlinear test problem. An example of the application of the algorithm to data from a benchmark simulation of an industrial overheads condenser and reflux drum rig is also included. This shows the usefulness of the procedure in detecting and isolating both sensor and process faults. Pointers for future research in this area are also given.
Summary We address the problem of dimension reduction for time series of functional data (Xt:t∈Z). Such functional time series frequently arise, for example, when a continuous t...
Abstract A new projection pursuit algorithm for exploring multivariate data is presented that has both statistical and computational advantages over previous methods. A number o...
Abstract A new projection pursuit algorithm for exploring multivariate data is presented that has both statistical and computational advantages over previous methods. A number o...
The Support Vector (SV) machine is a novel type of learning machine, based on statistical learning theory, which contains polynomial classifiers, neural networks, and radial bas...
Most existing multiobjective evolutionary algorithms aim at approximating the Pareto front (PF), which is the distribution of the Pareto-optimal solutions in the objective space...
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