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Note: A new GRASS GIS stable version has been released: GRASS GIS 7.4, available here.
Updated manual page: here

NAME

i.pca - Principal components analysis (PCA) for image processing.

KEYWORDS

imagery, transformation, PCA, principal components analysis

SYNOPSIS

i.pca
i.pca --help
i.pca [-nf] input=name[,name,...] output=basename [rescale=min,max] [percent=integer] [--overwrite] [--help] [--verbose] [--quiet] [--ui]

Flags:

-n
Normalize (center and scale) input maps
Default: center only
-f
Output will be filtered input bands
Apply inverse PCA after PCA
--overwrite
Allow output files to overwrite existing files
--help
Print usage summary
--verbose
Verbose module output
--quiet
Quiet module output
--ui
Force launching GUI dialog

Parameters:

input=name[,name,...] [required]
Name of two or more input raster maps or imagery group
output=basename [required]
Name for output basename raster map(s)
A numerical suffix will be added for each component map
rescale=min,max
Rescaling range for output maps
For no rescaling use 0,0
Default: 0,255
percent=integer
Cumulative percent importance for filtering
Options: 50-99
Default: 99

Table of contents

DESCRIPTION

i.pca is an image processing program based on the algorithm provided by Vali (1990), that processes n (n >= 2) input raster map layers and produces n output raster map layers containing the principal components of the input data in decreasing order of variance ("contrast"). The output raster map layers are assigned names with .1, .2, ... .n suffixes. The numbers used as suffix correspond to percent importance with .1 being the scores of the principal component with the highest importance.

The current geographic region definition and MASK settings are respected when reading the input raster map layers. When the rescale option is used, the output files are rescaled to fit the min,max range.

The order of the input bands does not matter for the output maps (PC scores), but does matter for the vectors (loadings), since each loading refers to a specific input band.

If the output is not rescaled (rescale=0,0, the output raster maps will be of type DCELL, otherwise the output raster maps will be of type CELL.

By default, the values of the input raster maps are centered for each map separately with x - mean. With -n, the input raster maps are normalized for each map separately with (x - mean) / stddev. Normalizing is highly recommended when the input raster maps have different units, e.g. represent different environmental parameters.

The -f flag, together with the percent option, can be used to remove noise from input bands. Input bands will be recalculated from a subset of the principal components (inverse PCA). The subset is selected by using only the most important (highest eigenvalue) principal components which explain together percent percent variance observed in the input bands.

NOTES

Richards (1986) gives a good example of the application of principal components analysis (PCA) to a time series of LANDSAT images of a burned region in Australia.

Eigenvalue and eigenvector information is stored in the output maps' history files. View with r.info.

EXAMPLE

PCA calculation using Landsat7 imagery in the North Carolina sample dataset: 
g.region raster=lsat7_2002_10 -p
i.pca in=lsat7_2002_10,lsat7_2002_20,lsat7_2002_30,lsat7_2002_40,lsat7_2002_50,lsat7_2002_70 \
    out=lsat7_2002_pca

r.info -h lsat7_2002_pca.1
   Eigen values, (vectors), and [percent importance]:
   PC1   4334.35 ( 0.2824, 0.3342, 0.5092,-0.0087, 0.5264, 0.5217) [83.04%]
   PC2    588.31 ( 0.2541, 0.1885, 0.2923,-0.7428,-0.5110,-0.0403) [11.27%]
   PC3    239.22 ( 0.3801, 0.3819, 0.2681, 0.6238,-0.4000,-0.2980) [ 4.58%]
   PC4     32.85 ( 0.1752,-0.0191,-0.4053, 0.1593,-0.4435, 0.7632) [ 0.63%]
   PC5     20.73 (-0.6170,-0.2514, 0.6059, 0.1734,-0.3235, 0.2330) [ 0.40%]
   PC6      4.08 (-0.5475, 0.8021,-0.2282,-0.0607,-0.0208, 0.0252) [ 0.08%]

d.mon wx0
d.rast lsat7_2002_pca.1
# ...
d.rast lsat7_2002_pca.6
In this example, the first two PCAs (PCA1 and PCA2) already explain 94.31% of the variance in the six input channels.

PCA result
Resulting PCA maps calculated from the Landsat7 imagery (NC, USA)

SEE ALSO

Richards, John A., Remote Sensing Digital Image Analysis, Springer-Verlag, 1986.

Vali, Ali R., Personal communication, Space Research Center, University of Texas, Austin, 1990.

i.cca, g.gui.iclass, i.fft, i.ifft, m.eigensystem, r.covar, r.mapcalc

Principal Components Analysis article (GRASS Wiki)

AUTHORS

David Satnik, GIS Laboratory

Major modifications for GRASS 4.1 were made by
Olga Waupotitsch and Michael Shapiro, U.S.Army Construction Engineering Research Laboratory

Rewritten for GRASS 6.x and major modifications by
Brad Douglas

Last changed: $Date: 2015-09-14 10:06:52 -0700 (Mon, 14 Sep 2015) $

SOURCE CODE

Available at: i.pca source code (history)

Note: A new GRASS GIS stable version has been released: GRASS GIS 7.4, available here.
Updated manual page: here

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