Principal Components for Imagery

Basics of principal components.

Examples with two bands.

Because most satellite images have bands which are highly correlated as shown in a correlation matrix, there is actually a lot of redundancy in the different bands. It might be possible to create fewer new bands that contain all the information in the scene, and requires less storage space. These new bands, especially the first,  might provide an improved analysis tool.

Selected on Imagery analysis menu, after you have opened the satellite as multiple grids.

  PC 1 PC 2 PC 3 PC 4 PC 5 PC 6 PC 7 Notes--This was a Landsat 4/5 scene.
                 
Eigenvalues 822.44 44.8 20.35 5.89 3.12 2.76 0.91  
                 
Percent Variance Explained 91.36 4.98 2.26 0.65 0.35 0.31 0.1

These sum to 100%.  By the time you get to the last PC, it might be all noise.

                 
Loadings                
Band 1 0.0701 0.4729 0.6014 -0.104 0.565 0.0688 -0.274

The sum of squares of loadings for each band equals 1

Band 2 0.0797 0.211 0.3297 0.0016 -0.087 -0.074 0.9097

Band 2 is "alone" on PC7; the other loadings are very small.

Band 3 0.171 0.2042 0.3356 0.2599 -0.569 -0.585 -0.286  
Band 4 0.5381 -0.680 0.449 -0.084 -0.034 0.1923 -0.040 Second highest loading on PC1
Band 5 0.7522 0.2245 -0.454 -0.204 0.2223 -0.291 0.0447 Highest loading on PC1
Band 6 0.1539 -0.045 -0.083 0.9324 0.2973 0.0773 0.0599

Band 6 is "alone" on PC4, because the TIR is so different from the other bands, and has extremely low loadings on all the others.

Band 7 0.2839 0.419 -0.045 0.0615 -0.459 0.7208 -0.091  
 
TM band 3.
PC1 image, from a 6 band TM analysis.  Note the sharp details on land, and the clear distinction between land and water.  This is similar to the results in the table above, but did not include Band 6.

This image is much better than the Band 3 image above, and actually similar to bands 4 or 5 (which also have the highest loadings on PC1).

This PC explains 83% of the variance in the image's 6 bands.

PC6 image, from a 6 band TM analysis. Note that this image appears mostly noise, with only a faint hint of the location of shoreline. 

This PC explains 0.1% of the variance in the image's 6 bands.


Last revision 12/29/2017