@CONFERENCE\{IMM2005-03883,
author = "R. Larsen and A. A. Nielsen",
title = "Functional Maximum Autocorrelation Factors",
year = "2005",
month = "aug",
booktitle = "9th Scandinavian Conference on Chemometrics, Reykjavik, Iceland",
volume = "",
series = "",
editor = "",
publisher = "University of Iceland",
organization = "",
address = "",
url = "http://www2.compute.dtu.dk/pubdb/pubs/3883-full.html",
abstract = "Purpose.
We aim at data where samples of an underlying function are observed in a spatial or temporal layout. Examples of underlying functions are reflectance spectra and biological shapes. We apply functional models based on smoothing splines and generalize the functional {PCA} in\verb+~+\$\backslash\$cite\{ramsay97\} to functional maximum autocorrelation factors (MAF)\verb+~+\$\backslash\$cite\{switzer85,larsen2001d\}. We apply the method to biological shapes as well as reflectance spectra.
\{\$\backslash\$bf Methods\}. {MAF} seeks linear combination of the original variables that maximize autocorrelation between (temporally or spatially) neighbouring observations. This is useful when 'noise' components have higher variance than the interesting signal components. We adapt the multivariate {MAF} transform to the functional setting. It is assumed that relevant signal components exhibit correlation across the layout of observations. Where the functional {PCA} can be solved as an eigenvalue problem functional {MAF} becomes a generalized eigenvalue problem.
Results
We apply the methods to temporally varying outlines of the cardiac wall as observed in {MR} scans as well as to reflectance spectra in earth observations. The functional {MAF} outperforms the functional {PCA} in concentrating the interesting' spectra/shape variation in one end of the eigenvalue spectrum and
allows for easier interpretation of effects.
Conclusions.
Functional {MAF} analysis is a useful methods for extracting low dimensional models of temporally or spatially varying phenomena."
}