Hi -

I understand that principle components are calculated such that the first explains the greatest amount of variation in a dataset, the second PC explains the greatest amount of remaining variation, and so on. I understand PCs are uncorrelated variables that retain information in the original dataset using reduced dimensions.

What I'm unclear on is what PCs mean in terms of the multiband raster output from the Principal Components tool. I can look at my Eigenvalues for each PC and determine how many to use to maintain the variation in my dataset, but I don't know how to interpret the PCs in raster form.

For example, here is PC1, with values ranging from 4.6 (red) to 0 (blue). What do these values mean? My best guess is that these values are 'distances' or errors from the PC1 axis.

Hi Heather

The PCA summarises all of your data into the new axes that best explain the

variation found in your data set, with most of the variation being

explained in the first few axes (you probably already know all that).

But to figure out what the various axes actually represent, relating back

to your input raters, then I find it very useful to run the Band Collection

Statistics tool (Spatial Analyst Tools/Multivariate/Band Collection

Statistics).

For your input raster bands, add both your PCA exes and the various raster

bands that were used to create the PCA axes, and make sure to tick the

"Compute covariance and correlation matrices" tick-box. This will then

create a statistics text file where it calculates the correlation between

each of the PCA axes and the various raster files used as input (both

positive and negative correlations). So, for example, it will show that

altitude may have a correlation value of 0.99, mintempcoldmonth 0.90,

maxtempwarmmonth 0.91, etc.(this is from a real example) with PCA axis 2.

The input variables used in this example are inherently correlated as

temperature decreases with altitude and the PCA has nicely distilled all of

this this variation into a single axis.

So then you know what the pixels represent when interpreting your analysis.

Lastly, PCA needs to standardize the input variables so that it can compare

apples with apples, and so analyse altitude, rainfall, temperature,

vegetation indices, clay percentage, etc.(all which are corded on different

scales) into one PCA analysis.

I hope this helps.

Regards

Mervyn