[GRASS-user] Creating PCA Plot

[Michael Barton]

After creating PCA images, you can do a bivariate plot of 2 of them in the scatterplot tool in GRASS 7.

You can do multiple bivariate scatter plots (i.e., bi-plots of each pair of component images) in a single graph.

Michael
____________________
C. Michael Barton
Director, Center for Social Dynamics & Complexity 
Professor of Anthropology, School of Human Evolution & Social Change
Arizona State University

voice: 	480-965-6262 (SHESC), 480-727-9746 (CSDC)
fax:          480-965-7671 (SHESC),  480-727-0709 (CSDC)
www: http://www.public.asu.edu/~cmbarton, http://csdc.asu.edu




On Feb 6, 2013, at 10:47 AM, <grass-user-request at lists.osgeo.org>
 wrote:

> From: Nikos Alexandris <nik at nikosalexandris.net>
> Subject: Re: [GRASS-user] Creating PCA Plot
> Date: February 6, 2013 2:03:06 AM MST
> To: Rashad M <mohammedrashadkm at gmail.com>
> Cc: <grass-user at lists.osgeo.org>
> 
> 
> Rashad M wrote:
> 
>> Hi,
> 
> Hi Rashad :-)
> 
>> How to create a PCA plot for two channels of a landsat image.?
> 
> In grass use d.correlate, in R too many options!
> 
>> i.pca outputs a eigen values, vectors and percentage importance
> 
> Quoting myself :-p:
> 
> --%<---
> The eigenvalues define proportionally the length of the axes of variation
> and the eigen or characteristic vectors define the direction of the
> variation (Ahearn and Wee, 1991). Since both the eigenvectors and the PCs
> only define directions, they can be arbitrarily multiplied by −1
> (Cadima and Jolliffe, 2009).
> --->%--
> 
> Effectively, percentages indicate the amount of variance that has been
> redistributed in a Principal Component -- remember, PCs are sorted from
> the one that holds the largest variance to the one that holds the smallest
> variance.
> 
>> Could anybody explain how to plot it?
> 
> You mean just a bi-variate scatter-plot?
> 
> PCA is a linear transformation for multivariate data sets. The new,
> transformed variables (or dimensions or channels or you name them) can
> then be plotted the same way as any other raster map. E.g., d.histogram
> for single stuff, d.correlate (for a scatter-plot) and probably more.
> 
> 
>> Does i.pca transforms/changes pixel values?
> 
> Yes.
> 
> Normally, one would select Landsat bands of interest, i.e. bands that are
> profiling "wanted" landscape features. A PCA would then transform a set of
> bands into something new: sorted variables in which the original variance
> of the data is redistributed in a way that the first Principal Components
> contain most of it, while the higher order transformed variables contain
> the smallest amounts of the original variance.  Note, changes tend to
> appear in some of the higher order PCs.  Noise, is most of the time
> accumulated in the last PC. And, of course, there are many and diverse
> uses of PCs (like compression, fusion, etc.).
> 
> (So,) If you have your PCs of interest, then you can scatter-plot them in
> grass with <d.correlate> for example.  In R, however, you can load, in
> theory, infinite number of dimensions (in your wording == channels) and
> plot really nice and fancy stuff.
> 
> I have tried to clearly present the PCA concept in my work.  Will send you
> a link and stuff of mine -- they might be useful for you to make them even
> better (!).
> 
> Additionally, recently I have seen some very nice tri-variate PC plots in
> some presentation... (dunno remember now, it was certainly someone inside
> the GRASS GIS community!).
> 
> Ah, don't forget to have a look in GRASS-Wiki (and maybe help iron the
> page!): <http://grasswiki.osgeo.org/wiki/Principal_Components_Analysis>.
> 
> Best, N

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