dE SN adu ES
2. FEATURE EXTRACTION BY KOHONEN MAP
The objective of the feature extraction phase is to identify the
spectral classes present in the image and to define the set of
correspondent samples to be used in the classification phase
afterwards.
There is no well-developed theory for feature extraction,
mostly features are application-oriented and often found by
heuristic methods and interactive data analysis.
An important basic principle is that the features must be
independent of class membership because, by definition, at the
feature extraction phase the membership to the classes is not
yet known. This implies that any learning methods used for
feature extraction should be unsupervised in the sense that the
target class for each object is unknown (Oja et al. 1994).
One of the approaches is the use of competitive learning
resulting in data clustering. An example is Kohonen's Self-
Organizing Map (SOM) (Kohonen 1988).
It’s well known the SOM property of dividing the input space
into convex regions, where a set of reference vectors associates
vector codes with the input space. The classification of an
image may then be based on the cluster codes found to the
image by the SOM.
In our approach we generated an auxiliary visual tool from the
SOM, denominated Kohonen Clusters Map (KCM), which
enables to identify the spectral classes present in the image
through the visualization of the clusters generated by SOM.
2.1. SOM Description
The SOM belongs to the class of unsupervised neural netwoks
based on competitive learning, in which only one output
neuron , or one per local group of neurons at a time gives the
active response to the current input signal. The level of activity
indicates the similarity between the input signal vector and its
respective weight vector. A standard way of expressing
similarity is through the Euclidian distance between these
vectors.
hexagonal
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Figure 2: Geometrical representations of neurons
for SOM.
Since the distance between the weight vector of a given neuron
and the input data vector is minimal to all neurons in the
network, this neuron together with a predefined set of
neighbour neurons will have their weights automatically
updated by the learning algorithm. The neighbourhood for each
neuron may be defined accordingly to the geometrical form,
over which the neurons are arranged. Figure 2 depicts two
examples of representation proposed by (Kohonen 1989): a
rectangular grid and an hexagonal grid.
A short description of the learning algorithm of SOM is given
bellow:
Step I: Select a training pattern X — (x4, X»,..., xw) and present
it as an input to the network.
Step 2: Compute distances di between the input vector, and
each j neuron's weight vector, acording to:
N
d;=S &0-w,07 (D)
j
where x;(t) is the j-th input in a given iteraction and
Wi ;(t) is the weight of neuron j from the input layer connected
to neuron i from the output layer.
*
Step 3: Select neuron i with the smallest distance among all
.* .
other neurons, and update the weight vector of 1 and its
neighbours using the following expression:
Wi (t1) & wi ;(0 + (t) * (x; (0 = wi, ; (0)
for i€ N.«,j- L2... N (2)
*
where N. is a set that contains 1 and its neighbours, and
oft) is the learning rate, usually smaller than 1. This
procedure repeats until the the weight update is no longer
significant.
By the end of the learning process each neuron or group of
neighbour neurons will represent a distinct pattern among the
set of patterns presented as input to the network.
2.2. Kohonen Clusters Map (KCM)
In this approach, 3x3 pixel windows taken from the original
image were used as training patterns for the SOM. These
patterns were randomly and uniformly obtained from all over
the image and presented as input vectors to the SOM. Since the
SOM has the property of arranging its weight vectors in
rectangular or hexagonal grids and considering that both input
data vectors and weight vectors have the same dimension, this
enables to generate an image of the weight grid of the SOM.
The resulting grid image, after the unsupervised learning by
the SOM, was denominated Kohonen Clusters Map (KCM).
Figure 5 shows an example of a rectangular KCM generated
from the test image (Fig. 8).
The KCM produces a visual auxiliary tool for the task of
identifying and selecting the spectral classes present in the
image and their correspondent training samples, which will be
used afterwards in the module of neural classification. The
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International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B2. Vienna 1996
KCM
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