>
> Presumably what you can do to get the distance in a multidimensional space
> involving N factors from PCA woould be to save factor scores for the
> elements.
> (You might have to use a general purpose stats package such as SPsS or
> Minitab for the PCA to do this - I'm not sure whether it's an option in the
> specialist grid packages). Then use Pythagoras's Theorem, in as many
> dimensions as there are factors, to calculate each distance. I haven't done
> such a calculation since high school, but it's really simple in principle
> and if I weren't in a tearing hurry I'd work it out here and now. Can any
> proper maths person chip in and confirm the answer?! Something like the
> square root of the sum of the squares of the differences between the scores
> on each factor ...
That's pretty much what Patrick Slater included in the Ingrid package
that he signed over to me. It is this unique routine for determining
probabilistic element distances that distinguishes WinGrid's PCA results
from the other packages which feed the PCA routine using only classical
correlations.
Also collected is the total variation for each element and construct
which is then used to signify positions within the Multi-Dimensional
Sort.
The full source code for the WinGrid program is available if any group,
such as an ethics committee, needs to be assured on this point or
research the basis that is used.
It's not what you get out of PCA but what you put in that counts. For
example in WinGrid 0.7.3 (due out soon) you can manipulate the graphics
that denote elements using the option of including the distinguishing
perception features of these graphics into your grid. Normalized
eigenvalues are one thing but the decision for me to go with an HSV
(Hue, Saturation, Value) transformation into a 166 color space instead
of the 255 for each of Red, Green, or Blue made all the difference in
being able to classify the images. Two days ago I was able to
GetBitmapBits working it was to the newsgroups that I turned to to dig
up the following thesis on how to use HSV.
Integrated Spatial and Feature Image
Systems: Retrieval, Analysis and Compression
http://disney.ctr.columbia.edu/jrsthesis/
Now I have to code the transformation. Cheerio.
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