Fuzzy principal component analysis

Cundari, T.R., Sarbu, C. and Pop, H.F. (2002) Robust fuzzy principal component analysis (FPCA). A comparative study concerning interaction of carbon-hydrogen bonds with molybdenum—oxo bonds. /. Chem. Inf. Comp. Sci., 42, 1363. 

We compared fuzzy principal component analysis (FPCA) to classical PCA methods to characterize lanthanum, the 14 lanthanides, and the other... 

Fuzzy Principal Component Analysis was also performed on the structural features concerned with the interaction of carbon-hydrogen bonds and molyb-denum-oxo bonds. In addition to all possible atom-atom distances and the angles subtended thereof, several additional metrics were defined and tabu-lated. These include the distance R, p, and the angles ot, p, and y, as well as the dihedral MOCH, Scheme 1. Interactions between metal-oxo and carbon-hydrogen bonds are of importance with respect to microbial and industrial oxidation, and for these reasons molybdenum was the focus of this research. 

Fuzzy Principal Component Analysis (FPCA). A Comparative Study Concerning Interaction of Carbon-Hydrogen Bonds with Molybdenum-Oxo Bonds. 

Thus, multilinear models were introduced, and then a wide series of tools, such as nonlinear models, including artificial neural networks, fuzzy logic, Bayesian models, and expert systems. A number of reviews deal with the different techniques [4-6]. Mathematical techniques have also been used to keep into account the high number (up to several thousands) of chemical descriptors and fragments that can be used for modeling purposes, with the problem of increase in noise and lack of statistical robustness. Also in this case, linear and nonlinear methods have been used, such as principal component analysis (PCA) and genetic algorithms (GA) [6]. 

Fredericks et al. (1985) describe materials characterization by factor analysis of IR spectra . Wold et al. (1987) the principal component analysis , and Haaland and Thomas (1988) materials characterization using factor analyses of FT-IR spectra . Of special importance are the procedures using fuzzy logic and neural networks (Harrington, 1991 Zupan and Gasteiger, 1993). 

Ischemia in the forearm was studied by Mansfield et al. in 1997 [38], In this study, the workers used fuzzy C means clustering and principal component analysis (PCA) of time series from the NIR imaging of volunteers forearms. They attempted predictions of blood depletion and increase without a priori values for calibration. For those with a mathematical bent, this paper does a very nice job describing the theory behind the PCA and fuzzy C means algorithms. 

J. R. Mansfield et al., Fuzzy C-Means Clustering and Principal Component Analysis of Time Series from Near-Infrared Imaging of Forearm Ischemia, Computerized Med. Imaging and Graphics, 21(5), 299 (1997). 

LDA, linear discriminant analysis NN, neural nets P, principal component (PC-based) CCD, computerized consensus diagnosis N, normalized U, unnormalized R, subregion-based F, fuzzy. 

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