Full text: XVIIIth Congress (Part B2)

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using 
Karhunen-Lówe transformation was about 10% when 
dataset IA with number of samples in class 40 (N=5, 
d=8) was classified. In this case RES error varied 
between 7% - 10% (deviation 2.8% - 3.5%) with varying 
k 2 - 10 and LOO error varied between 13% - 10% 
(deviation 3.5% - 4.7%) with varying k 2 - 10. When 
number of samples in class was increased (N=10) 
classification error was about 10.5%, RES error varied 
between 7% - 10% (deviation 2.5% -3.3%) and LOO error 
varied between 13% - 11% (deviation 3.4% - 4.1%). When 
number of samples in class was again increased (N=100) 
classification error decreased to about 10%, RES error 
varied between 7% - 10% (deviation 0.5% - 0.8%) and 
LOO error varied between 12% - 10% (deviation 0.8% - 
1.0%). Transformed two features contained on an 
average 46.6% from original information when N=5 
44.8% when N=10 and 43.0% when N=100. 
? 
SOM case A with N=5, the average classification error 
varied between 13% - 14.5%, RES error varied between 
8% - 13% (deviation 4.5% - 6.5%) and LOO error varied 
between 16% - 13% (deviation 6.5% - 10%). When 
number of samples in class was increased (N=10), the 
average classification error varied between 11.5% - 
12.5%, RES error varied between 8% - 11% (deviation 
3% - 4.5%) and LOO error varied between 14% - 12% 
(deviation 4.5% - 6.8%). When number of samples was 
again increased (N=100), the average classification error 
was 10.5% in all cases, RES error varied between 8% - 
10% (deviation 1.0% - 1.5%) and LOO error varied 
between 13% - 11% (deviation 1.5% - 2.2%). 
SOM case B with N=5, the average classification error 
varied between 13.5% - 15.5%, RES error varied between 
7% - 14% (deviation 2.8% - 5.8%) and LOO error varied 
between 17% - 14% (deviation 3.8% - 5.6%). When 
number of samples in class was increased (N=10), the 
average classification error varied between 12% - 13.5%, 
RES error varied between 8% - 12% (deviation 1.8% - 
3.2%) and LOO error varied between 16% - 13% 
(deviation 2.4% - 4.2%). When number of samples was 
again increased (N=100), the average classification error 
varied between 11% - 12.5%, RES error varied between 
8% - 12% (deviation 0.6% - 1.2%) and LOO error varied 
between 13% - 12% (deviation 1.0% - 1.5%). 
7. CONCLUSIONS 
The classification errors using different feature 
extraction methods were quite same, differences were 
small. Main difference was when number of samples per 
class was small, then the classification errors with 
features computed using Karhunen-Lôwe transformation 
were smaller than the classification errors with features 
computed using SOM. Another difference was when 
dataset II was used, then the classification errors with 
features computed using Karhunen-Lówe transformation 
were also smaller. When the number of samples per 
class increased, the difference decreased. In these cases 
feature extraction methods based on SOM can be used, 
because computational time is shorter. 
379 
8. REFERENCES 
Devivjer, P., Kittler, J., 1982. Pattern Recognition - A 
Statistical Approach. Prentice-Hall. 
Fukunaga, K., 1990. Introduction to Statistical Pattern 
Recognition. Academic Press, pp. 399-424. 
Hecht-Nielsen, R., 1990. Neurocomputing. Addison- 
Wesley, pp. 63-65. 
Kangas, J., 1994. On the analysis of pattern sequences 
by self-organizing maps. Thesis for the degree of Doctor 
of Technology, Helsinki University of Technology, 
Laboratory of Computer and Information Science, Espoo, 
Finland. 
Kohonen, T., 1990. The self-organizing map. Proceedings 
of IEEE, 78(9), pp. 1464-1480. 
Lippmann, R.P., 1987. An introduction to computing 
with neural nets. IEEE Acoustics, Speech and Signal 
Processing Magazine, 4(2), pp. 4-22. 
Tou, J., Gonzales, R., 1974. Pattern Recognition 
Principles. Addison-Wesley, pp. 271-282. 
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B2. Vienna 1996 
 
	        
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