Maxautofactors: Difference between revisions

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===Purpose===
===Purpose===


Maximum / Principal Autocorrelation Factors.
Maximum Autocorrelation Factors for hyperspectral images.


===Synopsis===
===Synopsis===
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In it's default mode, MAXAUTOFACTORS uses a generalized eigenvalue decomposition to provide a model of data (x) which captures maximum spatially-correlated variance.
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 stabelize and speed up the algorithm (see options.varcap).
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====
====Inputs====
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====Outputs====
====Outputs====
The resulting scores (scores), loadings (loads), and mean spectrum (mn) can be used to reconstruct the mean-centered data matrix X_mn
* '''model''': standard model structure containing the MAF model (see [[Standard Model Structure]]).
:<tt>X_mn = scores*loads</tt>
* '''options''': options structure. (some fields may have been modified)
The difference between PCA and MAF is that MAF extracts loadings which are highly correlated in the spatial dimension of an image. In addition, MAF always returns the entire set of components up to the rank of the data matrix. Input X is either a Image DataSet object or a three-way double matrix (first two dimensions are spatial, last is variable). Output ssq is an experimental sum of squares captured table but because of the nature of the decomposition, this table is only approximate. It includes the component number (column 1), estimated eigenvalue (column 2), and the estimated % captured per variable and total (columns 3 and 4, respectively).


===Options===
===Options===
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* '''display''': [ 'off' | {'on'} ]      governs level of display to command window.
* '''display''': [ 'off' | {'on'} ]      governs level of display to command window.
* '''plots''': [ 'none' | {'final'} ]  governs level of plotting.
* '''plots''': [ 'none' | {'final'} ]  governs level of plotting.
* '''algorithm''': [ {'maf'} | 'paf' | 'mdf' | 'pdf' | 'manual']
* '''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===
===See Also===


[[mcr]], [[parafac]], [[pca]]
[[mcr]], [[parafac]], [[pca]]

Latest revision as of 16:49, 24 October 2013

Purpose

Maximum Autocorrelation Factors for hyperspectral images.

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

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