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] by Survey 
IAPRS & SIS, Vol.34, Part 7, "Resource and Environmental Monitoring", Hyderabad, India,2002 
  
of India. By on-screen-visual interpretation on the standard 
false color composite (F.C.C) of the subscene, confirmed by 
ground visit and GPS coordinates (Geo Explorer 3), 
homogeneous regions with more than 30 pixels of the three 
classes are identified. All the four bands of LISS III viz. 520 — 
590 nm, 620 — 680 nm, 770 — 860 nm and 1550 — 1700 nm are 
used. Mean (1) and standard deviation (0) of each of the four 
bands for each class have been extracted through signature 
editor of ERDAS Imagine 8.3.1 software as shown in Table 1. 
3.2 Synthetic data 
For the purpose of generating synthetic data, the concept of 
linear mixture modeling is employed. Using the mean and 
standard deviation values of Table 1, a set of 30 pixel vectors, 
10 for each class are randomly generated such that any pixel 
value in any band of a particular class lies within the range of 
‘one standard deviation’. From these synthetic data, a simulated 
class matrix [S] could be randomly generated with three rows 
corresponding to the three classes and four columns 
corresponding to the four bands. Thus, 
[S]3x4 = [Wij + Og] — ------------- (7) 
Adequate care has been taken to remove the overlap of the 
range of pixel values at the extremities for each band between 
the three classes. Two separate sets of membership matrices are 
designed for training and testing respectively. Any elemental 
membership vector [m] = [m; m; my] has the property that m ; 
+m; +m 1, 0S mil; O0 < m; < 1; and O0 < mp < 1 where m; 
represents degree of membership of the pixel in class i in a 0 to 
1 scale and correspondingly m; and my represents the degree of 
membership of the same pixel in class j and class k 
respectively. Multiplying the membership matrices with the 
corresponding simulated class matrices produces the synthetic 
training and test data respectively. All the pixel values are then 
normalized by dividing with the maximum of all maximum [u; 
+ Oj] values. After the synthetic input vectors are obtained, the 
membership matrix to be used as desired output during training 
is modified to incorporate untrained classes as a single unit 
such that an elemental output vector [m;4] — [m; mj m, mj] 
where mj = 1 — (m ; + m; + my). Thus m; reflects the 
proportionate residual presence of untrained classes. Finally, 
synthetic patterns numbering 75 for training the neural network 
and 450 for testing model performance are thus obtained. 
4.0 METHOD 
The methodology adopted relies on two basic characteristics of 
back-propagation neural network: first, its ability to act as a 
universal function approximator of complex relationship 
(Haykin, 1994) and second, its well-known interpolation 
capability. The network has been trained with a set of synthetic 
pixel vectors that lie ‘within one standard deviation limit of the 
mean’ of the three defined classes as input. Accordingly, the 
relative degree of membership of these pixels to the three 
classes and ‘other unknown categories as a single class’ are 
considered as the desired output. Thus, the number of nodes in 
the input layer is four corresponding to the four input bands and 
the same in the output layer are four, three for the defined 
classes and one to take care of all the undefined land cover 
features. Incorporation of this additional output node for 
undefined classes is the major modification against the 
conventional rule of considering number of output nodes equal 
to the number of defined classes. With this provision, existence 
of unknown categories from 0 to 100% within any pixel could 
be incorporated in the learning scheme along with the fractional 
abundance of the three defined classes. For the optimization of 
the weights by gradient descent method, a scheme of adaptive 
learning rate with a fixed momentum coefficient of 0.95 is 
adopted. Based on earlier experience, hyperbolic tangent 
functions in hidden layer and linear function in output layer are 
used as transfer function (Kalita and Devi, 2002). Further, the 
requisite number of nodes in the hidden layer is determined by 
trial and error. All the 75 training patterns are presented to the 
network for epoch learning in an iterative way (Haykin, 1994). 
For assessment of the performance of the model, primarily, 
outputs of synthetic test data with 450 pixel vectors are used. 
Error analysis is carried out in terms of per-pixel root mean 
squared error (RMSE), class independent membership value 
wise algebraic error and class specific correlation coefficients 
between the known and predicted outputs. Further, to 
appreciate the behavior of the model with respect to real data, 
outputs for six sets of real test data corresponding to six classes 
in the scene are also derived and analyzed. These six classes 
include three defined (marshy water, aquatic vegetation and 
residential area) and three undefined (barren land, road and 
forest) classes. The test pixel vectors are extracted from the 
same LISS III scene after ground truth verification. 
5.0 ANALYSES AND RESULTS 
5.1 Trial session in training the network 
The trial session is started with an architecture of 4-2-3, which 
signifies 4 input-2 hidden -3 output nodes in a two layer 
network. Sum squared error (SSE) of training obtained for this 
topology after 80,000 epochs is found as 0.68 against a prefixed 
error goal of 0.01. Since this network structure is not 
satisfactory, in the next trial, one node is added to the hidden 
layer and the training process is repeated. Proceeding in this 
manner, a SSE of 0.0162 at 60 000 epochs for an architecture of 
4-20-3 is obtained. Since with further addition of nodes in the 
hidden layer did not show any significant lowering of SSE, this 
accuracy is considered as satisfactory for the purpose of this 
study. It is noteworthy here that the scheme of adaptive 
learning rate with a fixed momentum coefficient proved to be 
advantageous since choosing appropriate values of these 
parameters during training is a difficult task. 
5.2 Per-pixel Root mean squared error analysis 
Root mean squared error (RMSE) for all the 450 synthetic test 
pixels vectors with four output elements in each have been 
computed with respect to the known degree of membership of 
each pixel to the four categories (three defined classes and one 
embracing all undefined classes). The distribution of 
cumulative percentage of number of pixels with respect to 
uniformly graded RMSE limits in ascending order is presented 
in Figure 2. The minimum RMSE achieved is 0.001; however 
the maximum RMSE for a pixel vector is obtained as 0.091.