of this
ensed
ilistic
mown
attern
(1)
ble to
Q)
(3)
(4)
ıtterns
The decision function becomes:
g(*) - -inlzi |-(s-m) zi. («-m) (6)
The implementation of the decision rule of the maximum
likelihood include the use of the Equation (6). It is calculated for
each class and the highest value of g;(x) is selected for the
classification.
2.2 Back-Propagation Classifier
Neural networks are computational systems, either hardware or
software, which mimic the computational abilities of biological
systems by using large numbers of simple interconnected
artificial neurons (Maren, Harston, Pap 1990). In this study the
backpropagation network architecture was used. This network,
illustrated generally in Figure 1, is designed to operate as a three
layer, feedforward network, using the supervised mode of
learning.
OUTPUT PATTERN
OUTPUT LAYER
) HIDDEN LAYER
P: y + md 7 INPUT LAYER
INPUT PATTERN
Figure 1. Three-layer feedforward network
The basic element of a neural network is the processing element.
Except for the input layer elements, the network input to each
element is the sum of the weighted outputs of the elements in the
prior layer:
nel; = X wo. (7)
where variable w ji Tepresents the connection strength for the
; is the
activation of element. The output sigmoidal activation function
given in the Equation (8), allows a network to solve problems
that a linear network as the perceptron cannot solve.
current element to an element in the prior layer, and o
Intemational Archives of Photogrammetry and Remote Sensing. Vol. XXXII, Part 7, Budapest, 1998
n = és : (8)
l+e J
As with all supervised classifiers, neural network have to be
trained. In the learning phase of training such a network, the
network weights are adjusted in an iterative, gradient descent
procedure called backpropagation, based on the generalized delta
rule (Rumelhart et al 1986). In the training phase a training
pattern is presented at the input layer. The outputs of the
network are then produced and compared to the desired output
vector. The goal of the procedure is to minimize:
2
Ez zr, — » (9)
which is the error between the desired f and actual o
pk pk
outputs of the network, where p indexes the training patterns
and k indexes the output elements of the network.
All the patterns are repeatedly presented to the network until the
network learns the patterns. The weights between two layers i
and ; are computed iteratively by using the generalized delta
rule:
Aw (m + 1) = 501) + aw ;;(n) (10)
where the left-hand side of the equation denotes the changes of
the weights at the (n*l)th iteration, 7 is a learning rate
parameter, Jj is the rate of change of error with respect to the
input to the element in layer j , and a is a momentum
parameter.
3. DATA
In this research, Landsat Thematic Mapper (TM) image of the
middle part of Croatia is used as input to both a maximum
likelihood classifier and a neural network classifier.. In Figure 2.
channel 5 of this scene is shown. The study area had 15 land-
cover classes, which are listed in Table 1.
Table 1. Classes used for classification.
# of # of
Class # Class Train Test
Pixels Pixels
1 New Forest 108 230
2 Forest 88 235
3 Wet siol 66 293
4 Arid soil 72 344
5 Maize-I 84 243
6 Maize-II 69 241
7 Dry vegetation 60 156
8 Stubble-field 84 227
9 Individ. parcels 78 255
10 Barley I 98 297
11 Barley II 89 275
12 Oil rape I 66 213
13 Oil rape II 69 210
14 Wet vegetation 69 260
13 Sunflower 96 164
Total 1196 3643
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