has 
tral 
ion 
tral 
be 
est 
me 
za 
few 
ing 
of 
the 
ilar 
cels 
ion 
ean 
ces 
ters 
| of 
uch 
be 
and 
ium 
and 
the 
Cis 
E). 
SB) 
SES 
the 
that 
) its 
ses. 
ium 
the 
thin 
um 
1ser 
ICES 
eter 
ixel 
1 of 
Petrie, Gregg 
the results, the hyperspectral bands corresponding to the Landsat 7 band centers were selected, using 172 pixels 
randomly selected across the hyperspectral image. 
Joining tree clustering of the Landsat subset of the Whitewater region resulted in 43 classes at 1096 and 22 classes at 
15% of the maximum linkage distance. Analysis of 22 classes yielded over 40% of the classes with less than five 
observations; thus, 22 was the maximum number of classes evaluated with k-means clustering. The maximum 
F-statistic was achieved at 3 classes; however 12 classes met all the criteria (Figure 3). From the diagnostic plot, it is 
apparent that analysis of a number of classes greater than 12 resulted in a weighted F-statistic that was over 20% 
smaller than that achieved with three classes. Also, we can see that an analysis of a number of classes greater than 19 
yielded too many classes with less than five observations. Thus, 12 classes were chosen as the optimum number of 
classes for identification. The same analysis was applied to the hyperspectral imagery, resulting in 17 classes being 
chosen as the optimum number of class sizes for identification. The higher spatial resolution did yield a greater 
optimum number of classes. This result is likely due to the smaller pixel size of hyperspectral data, which includes 
greater variability in spectral response (less smoothing) than found in the larger pixel size imagery. 
  
Landsat Whitewater Data 
  
0 5 10 15 20 25 
Number of Classes 
  
—e— Percent Difference from Maximum F 
—&— Percent out of 22 Classes with « 5 Obs 
Maximum Distance 
75th Percentile of Distance for 2 Classes 
  
  
  
  
  
  
Figure 3. Diagnostic plot to determine the optimum number of classes using the seven bands from 200 pixels randomly 
sampled from the Landsat footprint of the Whitewater Region. For this example, a k value of 12 (12 classes) met all of 
the criteria. 
The protocol developed to determine the number of classes for identification is not limited to image data, and thus can 
provide the basis for the optimal physical stratification of the landscape with Geographic Information System layers. 
This is an important aspect of our strategy for effectively exploiting Landsat and other imagery. Further, the protocol 
also aids the collection of field data by supporting the optimal classification of a landscape into homogenous blocks for 
stratified random sampling. This protocol may have applications for supervised classification as well, by guiding the 
user to select the optimum number of training sets. 
  
International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B7. Amsterdam 2000. 1147