presentation - Department of Cognitive and Neural Systems - Boston ...

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Abstract


This poster presents results of three studies dealing with application
of ARTMAP neural networks for classification of remotely sensed
multispectral images.

1. Comparison of performance of ARTMAP classifiers with different
types of cluster representation. In this study, the best results were
obtained using Extended Gaussian ARTMAP.

2. A method for computation of classification accuracy index for
Gaussian ARTMAP neural network. This method can be used to
generate maps containing only pixels with prescribed minimum
accuracy of classification.

Methods for analysis and enhancement of neural
network classification of remotely sensed images


Norbert Kopčo, Peter Sinčák, and Rudolf Jakša

Department of Cognitive and Neural Szstems, Boston University

Computational Intelligence Group, Technical University of Ko
šice
, Slovakia

3. Preliminary results obtained on a hierarchical ARTMAP architecture
based on set of dichotomical classifiers. This neural network is
suitable for parallel processing of large data sets.



Refrences

Sin
čá
k, P., Veregin, H., and Kopčo, N.: Computational intelligence for classification of
remotely sensed images. Neural Network World, v. 5, 1998, pp. 577
-
593.

Sin
čák, P., Kopčo, N., and
Veregin H. (unpublished)
Conflation Techniques to Improve
Image Classification Accuracy.

Submitted to Photogrametric Engineering and Remote
Sensing.

Carpenter, G. and Grossberg, S. (1992)
Fuzzy ARTMAP: A Neural Network Architecture
for Incremental Supervised Learning of Analog Multidimensional Maps.
IEEE Trans. on
Neural Networks, 3: 197
-
214.

Williamson, J.R. (1996)
Gaussian ARTMAP: A Neural Network for Fast Incremental
Learning of Noisy Multidimensional Maps
, Neural Networks, pp. 881
-
897.

Cunningham, R. K. (1998)
Learning and recognizing patterns of visual motion, color,
and form.

Unpublished Ph.D. thesis. Boston University.


1. Evaluation of dependence on cluster
representation in ARTMAP classifiers



There is a large number of classification algorithms available without
detailed knowledge of their properties/performance.


Neural networks are considered to be assumption
-
less classifiers (for
a successful classification they do not require explicit assumptions
about the data distribution).


But

these systems have implicit assumptions built into them. These
assumptions are related to the data representation and algorithmic
properties of the system.


In the present study, the

dependence of the ARTMAP classifiers
performance on the internal cluster representation
is
analyzed for image data from remote sensing.

Data
-
set


Seven
-
dimensional Landsat TM image of the city of Ko
šice

(Figure 1)


Size of image: 368,125 pixels, out of which 6,331 classified by an
expert into seven categories (A
-

urban area, B
-

barren fields, C
-

bushes, D
-

agricultural fields, E
-

Meadows, F
-

Woods, and G
-

water)

Method of analysis


The performance is compared in terms of weighted PCC (Percent of
Correctly Classified) and the contingency tables.

Compared systems


Fuzzy ARTMAP
-

FA (Carpenter et al., 1992)

Gaussian ARTMAP
-

GA (Williamson, 1996)

Extended Gaussian ARTMAP
-

EGA (Cunningham, 1997)

Figure 1: Original image

ARTMAP classifier topology

Input

Output

MapField

(Labeling)

Recognition

(Clustering)

Comparison

Cluster representation:


Fuzzy ARTMAP: Hyper
-
rectangles


Gaussian ARTMAP: Gaussian

distributions without covariance


Extended Gaussian ARTMAP:

Gaussian distribution with covariance

F0

F1

F2

MF

OL

FA

EGA

GA

Results

Weighted PCC for five permutations of the training set and voting


Gaussian distribution more suitable as representation of
the clusters in image classification tasks (see Fig. 2)


Best performance achieved by Extended Gaussian ARTMAP
(although differences not very significant)

Contingency table for Extended Gaussian ARTMAP

Predicted class


Figure 2: Image classified by Extended Gaussian ARTMAP


Sensitivity to the ordering of the training set smaller for GA and
EGA than for the FA


During learning, FA always reached 100% accuracy. GA/EGA
accuracy was around 97.7%, which means stronger generalization.


2. Confidence Index


In remote sensing, a large amount of data is produced, which needs
to be quickly and reliably classified.


Often, explicit assessment of the reliability is needed.

Goals:


Develop a method for simple and fast assessment of the accuracy of
classification.


For the accuracy assessment, exploit computations done during the
classification process.


Develop the assessment method for the Gaussian ARTMAP
algorithm, which achieved the best performance in the previous
study.


Method


GA uses Bayes discrimination function:

(1)


The pattern is classified into the category with the largest
probability measure:

(2)


If
voting

is used, the probability measures are evaluated over all the
networks:

(3)


The
confidence index

is then defined as:

(4)

Figure 3: Confidence map for Gaussian ARTMAP classification
(expressed in %)

Confidence threshold


A confidence threshold can be defined, which, in combination with
the confidence index, can be used to generate maps with arbitrary
accuracy.


Two counteracting aspects of classification are influenced by the
choice of threshold: 1) accuracy of classification, and

2) number of unclassified patterns (see graph below)

Figure 4: Thresholded classification map for Gaussian ARTMAP
(accuracy 99%,
q
=〮㤲9
)

Results and discussion


The presented method offers a simple and fast way for assessment
of quality of the Gaussian ARTMAP neural network classification.



The method can be used also with other neural networks employing
the voting strategy.



The method offers a tool for production of maps with arbitrary
classification accuracy.



Because of the way in which this method exploits the computations
done during the classification, it is possible that the confidence
assigned to some of the classified points is incorrect.


Often, the complexity of the data is too high, or the size of the
data set is too large (in terms of memory or time requirements),
for standard versions of classifiers.


To overcome this problem, hierarchical/modular classification
systems are usually applied.


Here, a hierarchical structure based on ARTMAP networks is
proposed, and its properties are analyzed.


The system is called
Parallel ARTMAP,
because it consists of
ART sub
-
nets, each trained independently on a single category
(i.e., each sub
-
net learns to detect data from one category).


In the following simulations, fuzzy ART/ARTMAP system is used in
the sub
-
net modules of the network.

3. Hierarchical classifier


Parallel processing system


Every sub
-
net in the

clustering layer is

trained on data belonging

to a single class, i.e., it

learns to detect data from

that class.


Conflict resolution

module serves to resolve

conflicts if two or more

clustering nets identify

a pattern as “theirs”.


Two design choices:

1) rule for determination of optimal


for each clustering subnet,

2) conflict
-
resolving rule.

ART

Parallel ARTMAP system

Clustering subsystem

(class detectors)

Conflict

resolution

Class 1

data

Class 2

data

Class 3

data

Class n

data

ART

ART

ART

Optimal


deter浩nationrule

Each sub
-
net is trained

on patterns from

a single class using

cross
-
validation:

-

9/10
-

estimation set,

-

1/10
-

validation set.

Training is repeated for

different values of

.

Rule:

Choose


which corresponds to the the point just before the first dip

in the “true positive” graph.


This rule assures that each detector will correctly identify almost all

of the patterns belonging to it, while minimizing the false alarm rate.


0.7

0.8

0.9

1

0

0.2

0.4

0.6

0.8

1

Graph of performance of clustering sub
-
net for class #7

Parameter



Percent of correctly classified

Other classes

True “

” rate

My class (#7)

True “+” rate

Optimal

0.7

0.8

0.9

1

0

0.2

0.4

0.6

0.8

1

Class 1



PCC

0.7

0.8

0.9

1

0

0.2

0.4

0.6

0.8

1

Class 2



PCC

0.7

0.8

0.9

1

0

0.2

0.4

0.6

0.8

1

Class 3




PCC

0.7

0.8

0.9

1

0

0.2

0.4

0.6

0.8

1

Class 4



PCC

0.7

0.8

0.9

1

0

0.2

0.4

0.6

0.8

1

Class 5



PCC

0.7

0.8

0.9

1

0

0.2

0.4

0.6

0.8

1

Class 6



PCC

0.7

0.8

0.9

1

0

0.2

0.4

0.6

0.8

1

Class 7



PCC

Optimal


forallsub
-
nets

Other classes

True negative rate

My class

True positive rate

Optimal



For the previously defined

-
determination rule, all the sub
-
nets will
have almost 100% true positive rate.


But their false alarm rate (false negative rate) will be non
-
zero. So the
nets are biased towards identifying patterns as “theirs”. Moreover, the
false alarm rate will be different for each sub
-
net.


So the conflict resolving rule can be based on the true negative rate.

Conflict
-
resolving

rule

Rule:

If there is a conflict between two or more sub
-
nets, assign the pattern

to the class with the largest true negative rate.


This rule was chosen, because the parameters needed for conflict
resolution (true “
-
” rates) are easily computed during the

-
determination
process.

Results and discussion

Overall classification accuracy is 78.89%.

The decreased performance is caused mainly by the misclassification
of the patterns from classes C and F.

Despite worse performance, the system can be usefully applied to
large data sets. Also the speed of the system can be advantageous.
Choice of alternative rules for

-
determination and conflict resolution
can improve the performance.

Predicted class


Contingency table for Parallel ARTMAP