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 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.

       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 19:06:52 +0200 (Mon, 14 Sep 2015) $

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       © 2003-2016 GRASS Development Team, GRASS GIS 7.0.3 Reference Manual

GRASS 7.0.3                                                                                        i.pca(1grass)