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I am calculating PCA using a numpy/python approach. The principal components are in the form of GIS grids (rasters), created in a manner very similar to the GRASS GIS approach described here: http://grass.fbk.eu/gdp/html_grass62/r.covar.html

Every cell in an output component grid contains a PC score. Within each component grid there is a range of negative to positive PC scores. Is it okay to convert the scores to absolute value? Is the direction of the value important, or just the relative within-component (i.e., within-grid) magnitude?

Thanks.

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How do you intend to interpret the results? For some interpretations only the magnitude matters (but for most interpretations the sign is crucial). – whuber♦ Sep 19 '12 at 14:32
The per-pixel PC scores will be used to compare a pixel's relative within-grid importance in contributing to the explained variance (no across-grid comparisons can be made due to the orthogonal nature of the components). Aside from that, I'm not sure what other interpretations could be made? – vulture Sep 19 '12 at 19:56
Absolute sign is meaningless, but relative sign contains the same kind of information as the distinction between a negative correlation and a positive correlation. This may become clearer if you consider doing PCA on two variables rather than millions :-). – whuber♦ Sep 19 '12 at 20:00
I ran it on a set of clipped grids containing just a few pixels, but that didn't help answer my question. Let me ask this a different way: If one pixel has a score of 700 and another has a score of -700, have they both contributed the same amount to the explained variance, or has the positive pixel contributed twice as much? – vulture Sep 20 '12 at 1:56

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