Principal component analysis coupled with nonlinear regression for chemistry reduction

Nonlinear Principal Component Analysis

A. Two quite different forms of nonlinear principal component analysis have been proposed in the literature. The first one is associated with the names of Guttman, Burt, Hayashi, Benzécri, McDonald, De Leeuw, Hill, Nishisato. We call itmultiple correspondence analysis. The second form has been discussed by Kruskal, Shepard, Roskam, Takane, Young, De Leeuw, Winsberg, Ramsay. We call it no...

Nonlinear principal component analysis

We study the extraction of nonlinear data models in high dimensional spaces with modi ed self organizing maps We present a general algorithm which maps low dimensional lattices into high dimensional data manifolds without violation of topology The approach is based on a new principle exploiting the speci c dynamical properties of the rst order phase tran sition induced by the noise of the data ...

Projection techniques for nonlinear principal component analysis

Sketching for Principal Component Regression

Principal component regression (PCR) is a useful method for regularizing linear regression. Although conceptually simple, straightforward implementations of PCR have high computational costs and so are inappropriate when learning with large scale data. In this paper, we propose efficient algorithms for computing approximate PCR solutions that are, on one hand, high quality approximations to the...

Nonlinear identification of a gasoline HCCI engine using neural networks coupled with principal component analysis

Homogeneous charge compression ignition (HCCI) is a futuristic combustion technology that operates with high efficiency and reduced emissions. HCCI combustion is characterized by complex nonlinear dynamics which necessitates the use of a predictive model in controller design. Developing a physics based model for HCCI involves significant development times and associated costs arising from devel...