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


imagery, transformation, PCA, principal components analysis


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

Normalize (center and scale) input maps
Default: center only

Output will be filtered input bands
Apply inverse PCA after PCA

Allow output files to overwrite existing files

Print usage summary

Verbose module output

Quiet module output

Force launching GUI dialog

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

Rescaling range for output maps
For no rescaling use 0,0
Default: 0,255

Cumulative percent importance for filtering
Options: 50-99
Default: 99


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


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.


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 \
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)

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