Correlation Matrix
Imagery analysis menu,
Multi-grids raster analysis. You must
first have converted the satellite image into a series of grids for numerical
computations.
A correlation matrix takes each pair of satellite bands (or other related grids) and computes the correlation
coefficient between
the reflectances in the two bands for each pixel in the image. Because the matrix is
symmetrical (the correlation between Bands 1 and 2 does not depend on the order
of considering the two bands), often only the upper half is presented. The
correlations along the principal diagonal are 1.0, since anything allows perfect
prediction of itself.
Correlation Matrix
| Band |
Band 1 |
Band 2 |
Band 3 |
Band 4 |
Band 5 |
Band 6 |
Band 7 |
Band 9 |
Band 10 |
Band 11 |
| Band 1 |
1.0000 |
0.9804 |
0.7420 |
0.6295 |
-0.0220 |
0.1765 |
0.3439 |
0.5334 |
-0.2145 |
-0.2889 |
| Band 2 |
0.9804 |
1.0000 |
0.8318 |
0.7498 |
0.0425 |
0.2912 |
0.4626 |
0.4757 |
-0.0816 |
-0.1565 |
| Band 3 |
0.7420 |
0.8318 |
1.0000 |
0.9440 |
0.4954 |
0.6991 |
0.7934 |
0.3144 |
0.4001 |
0.3149 |
| Band 4 |
0.6295 |
0.7498 |
0.9440 |
1.0000 |
0.4255 |
0.7220 |
0.8325 |
0.2141 |
0.4690 |
0.3973 |
| Band 5 |
-0.0220 |
0.0425 |
0.4954 |
0.4255 |
1.0000 |
0.8132 |
0.6598 |
0.0533 |
0.6981 |
0.6347 |
| Band 6 |
0.1765 |
0.2912 |
0.6991 |
0.7220 |
0.8132 |
1.0000 |
0.9565 |
0.0279 |
0.7919 |
0.7300 |
| Band 7 |
0.3439 |
0.4626 |
0.7934 |
0.8325 |
0.6598 |
0.9565 |
1.0000 |
0.0689 |
0.7228 |
0.6606 |
| Band 9 |
0.5334 |
0.4757 |
0.3144 |
0.2141 |
0.0533 |
0.0279 |
0.0689 |
1.0000 |
-0.3577 |
-0.4422 |
| Band 10 |
-0.2145 |
-0.0816 |
0.4001 |
0.4690 |
0.6981 |
0.7919 |
0.7228 |
-0.3577 |
1.0000 |
0.9875 |
| Band 11 |
-0.2889 |
-0.1565 |
0.3149 |
0.3973 |
0.6347 |
0.7300 |
0.6606 |
-0.4422 |
0.9875 |
1.0000 |
In this example from a Landsat 8 scene, the best correlation of 0.98 is between
bands 1 and 2 (both of which lie in the visible), and bands 10 and 11 in the
thermal IR. Several bands have negative correlations (especially 9
and the two TIR bands), and some have essentially no correlation (bands 1 and
5). The nature of this matrix depends entirely on what is in the scene;
there might be be no negative correlations.
If two bands were perfectly correlated they would be redundant; the recorded
reflectance in one channel could be used to predict exactly the value in the
other. Principal
Components analysis can suggest a new set of bands that reduces
data volume with little loss of information. When bands are highly correlated,
the outliers are unusual and might have the most interest to determine what is
different about them.
Correlation Matrix For A Different Scene (Rif of Morocco). Note there are
no negative correlations
| |
L8 Band 1 |
L8 Band 2 |
L8 Band 3 |
L8 Band 4 |
L8 Band 5 |
L8 Band 6 |
L8 Band 7 |
L8 Band 9 |
L8 Band 10 |
L8 Band 11 |
| L8 Band 1 |
1.0000 |
0.9799 |
0.8637 |
0.7910 |
0.6444 |
0.6496 |
0.6830 |
0.2110 |
0.4909 |
0.4638 |
| L8 Band 2 |
0.9799 |
1.0000 |
0.9427 |
0.8835 |
0.7638 |
0.7650 |
0.7925 |
0.3041 |
0.6167 |
0.5966 |
| L8 Band 3 |
0.8637 |
0.9427 |
1.0000 |
0.9792 |
0.9143 |
0.9141 |
0.9282 |
0.4366 |
0.7901 |
0.7786 |
| L8 Band 4 |
0.7910 |
0.8835 |
0.9792 |
1.0000 |
0.9429 |
0.9632 |
0.9744 |
0.4677 |
0.8420 |
0.8289 |
| L8 Band 5 |
0.6444 |
0.7638 |
0.9143 |
0.9429 |
1.0000 |
0.9651 |
0.9519 |
0.5164 |
0.8577 |
0.8458 |
| L8 Band 6 |
0.6496 |
0.7650 |
0.9141 |
0.9632 |
0.9651 |
1.0000 |
0.9956 |
0.5146 |
0.8894 |
0.8752 |
| L8 Band 7 |
0.6830 |
0.7925 |
0.9282 |
0.9744 |
0.9519 |
0.9956 |
1.0000 |
0.5025 |
0.8844 |
0.8713 |
| L8 Band 9 |
0.2110 |
0.3041 |
0.4366 |
0.4677 |
0.5164 |
0.5146 |
0.5025 |
1.0000 |
0.5187 |
0.5235 |
| L8 Band 10 |
0.4909 |
0.6167 |
0.7901 |
0.8420 |
0.8577 |
0.8894 |
0.8844 |
0.5187 |
1.0000 |
0.9957 |
| L8 Band 11 |
0.4638 |
0.5966 |
0.7786 |
0.8289 |
0.8458 |
0.8752 |
0.8713 |
0.5235 |
0.9957 |
1.0000 |
The scattergrams below show only two bands, a concession to human abilities,
while the Landsat scene has 10, several of which (coastal, cirrus, and thermal)
might be less useful. For Hyperspectral
imagery, there could be hundreds of bands, and the challenge is
even greater because the correlation matrix overwhelms the user with its size.
 |
Scatterplot of two bands from a scene in the Rif of Morocco with low
correlation.
There is a best fit line, but the predictions from it are not very
good.
|
 |
Scatterplot of two TIR bands from a scene in the Rif of Morocco with
very high correlation
The graph shows colors with concentrations of points, and most are in
the center of the cloud of points.
|
 |
Scatterplot of two bands from a scene in theAtlas of Morocco with
negative correlation
|
 |
Scatterplot of two bands from a scene including Rabat, Morocco.
The trend is not linear, and reflects the fact that the scene covers two
very distinct regions: Atlantic Ocean with clouds, and the coastal
plain.
|
Last revision 12/29/2017