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.|
|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.
The sum of squares of loadings for each band equals 1
Band 2 is "alone" on PC7; the other loadings are very small.
|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 is "alone" on PC4, because the TIR is so different from the other bands, and has extremely low loadings on all the others.
|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