i.pca(1grass) GRASS GIS User's Manual i.pca(1grass)
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
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 pro-
duces n output raster map layers containing the principal components of
the input data in decreasing order of variance ("contrast"). The out-
put raster map layers are assigned names with .1, .2, ... .n suffixes.
The numbers used as suffix correspond to percent importance with .1 be-
ing the scores of the principal component with the highest importance.
The current geographic region definition and MASK settings are re-
spected when reading the input raster map layers. When the rescale op-
tion 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 nor-
malized 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.
Resulting PCA maps calculated from the Landsat7 imagery (NC, USA)
SEE ALSO
Richards, John A., Remote Sensing Digital Image Analysis, Springer-Ver-
lag, 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
SOURCE CODE
Available at: i.pca source code (history)
Accessed: unknown
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