Maxautofactors

Purpose

Maximum Autocorrelation Factors.

Synopsis

[model] = maxautofactors(x,ncomp,options)

Description

In it's default mode, MAXAUTOFACTORS uses a generalized eigenvalue decomposition to provide a model of data (x) which captures maximum spatially-correlated variance. An approximate solution is used to stabilize and speed up the algorithm (see options.varcap). The difference between MAF and PCA is that the loadings are determined to maximize spatial correlation (not based on capturing variance) and the loadings and scores are not orthogonal.

See Papers:

Green AA, Berman M, Switzer P, Craig MD (1988) IEEE Trans Geosci Remote Sens 26:65–74

Blake TA, Kelly, JF, Gallagher, NB, Gassman, PL, Johnson, TJ, Anal Bioanal Chem, 395(2), 337-348 (2009).

Keenan, MR, Smentkowski, VS, Surf. Interface Anal. (2011) DOI 10.1002/sia.3757

Inputs

• x = MxNxP image class 'dataset' or 'double'.
• ncomp = number of components (integer).

Outputs

• model: standard model structure containing the MAF model (see Standard Model Structure).
• options: options structure. (some fields may have been modified)

Options

options = a structure array with the following fields:

• display: [ 'off' | {'on'} ] governs level of display to command window.
• plots: [ 'none' | {'final'} ] governs level of plotting.
• algorithm: [ {'maf'} | 'paf' | 'mdf' | 'pdf' ]

if algorithm == 'maf' or 'paf' the options settings are for numerator and denomenator operators to be I and the first difference respectively.

if algorithm == 'mdf' or 'pdf' the options settings are for numerator and denomenator operators to be 1stD and the 2ndD respectively.

• varcap: [{0.999}] 0<varcap<1, specifies the variance of X to be captured when approximating the input X with a PCA model.

If (varcap) is an integer >=ncomp, this is the number of PCs used. The minimum number is (ncomp).

• smooth: [ ] smoothness penalty, based on the fraction of variance of the numerator (typical value might be 1e-3 to 0.05).

Smoothness is only available for MAF and MDF.

See Also

mcr, parafac, pca