10de, if one
le category
de becomes
les than 1%
‚a terminal
titioned by
| nodes are
))
(b), and (d)
inal nodes
nct part in
stic of each
1e decision
egories are
categories
les are se-
bles are se-
letermined
in deter-
beginning.
groups of
ively, error
ined nodes
V2:p/100 |
ide by one
is created.
e created,
etermined
this node
ined node.
STEP3: Node division through STEP1 and STEP2
is repeated while there are nonterminal nodes.
Error tolerance parameter p(%) ensures reliability
about determined nodes with training data. When
p is smaller, classification about determined node is
better and size of determined node is smaller.
5. EXPERIMENT
Tests for the design of trees and classification of sam-
ples by this methods were executed. In the exper-
iment, error tolerance parameter p was selected as
3%, 5%, and 7% making a compromise between clas-
sification accuracy and total proportion of determined
data. Simulated artificial random data and real Land-
sat completely-enumerated data were used for the ex-
periment. The relations between nature of categories
and tree configuration were checked. Performance of
triplet tree classifier was compared with usual binary
decision tree and Bayesian classifiers.
5.1 Simulated artificial data
A set of five categories, two-feature data was gener-
ated by program. Each category had 100 training
samples and 1000 test samples. The mean vectors of
the five categories are as follows and illustrated in Fig
a}:
(etr
Fig.5 The mean vectors in simulated data
Example of designed triplet trees is shown in Fig.6.
A variable was selected in tern at tree node hierarchy
based on the design procedure.
Table 1,2,3 show classification results by triplet
tree and Table 4 and 5 usual show classification
results by binary decision tree (BDT) and two
Bayesian method: linear discriminate function(LDF),
and quadratic discriminate function(QDF). Results of
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996
triplet trees is only for samples in determined nodes,
but result of other methods is for all samples. Triplet
trees improve performance of BDT. Classification ac-
curacy and classification reliability are found to be
equivalent to one step Bayesian methods, by exclud-
ing indistinct part of data to undetermined nodes.
Fig.6 Triplet tree for p = 5%
Table 1. Number of samples in determined node
for simulation data
tolerance parameter p 3% 5% 7%
Number of samples 3106 3569 4014
ratio (%) 62.1 71.4 80.3
Table 2. Classification accuracy for determined nodes
p | CAT1 CAT2 CAT3 CATA4 CATS| Total
3% | 87.1 26.5 882 940 31.9 82.3
5% | 89.4 82.1 85.4 82.9 42.6 79.3
T% | 83.7 30.5 85.1 77.9 39.6 80.3
Table 3. Classification reliability
(= 100 — commission_error) for determined nodes
p | CAT1 CAT2 CAT3 CAT4 CAT5
3% | 83.6 89.5 84.5 82.1 51.6
5% | 76.5 86.7 81.9 87.5 52.6
7% | 75.0 79.2 78.5 86.1 48.8
Table 4. Classification accuracy by BDT, LDF and QDF
Classifier | CAT1 CAT2 CAT3 CAT4 CATS5| Total
BDT 40.1 69.0 19.9 64.3 28.2 | 44.3
LDF 782 794 323377909 51.5 | 74.1
QDF 78.1 78.0 32.1 79.2 53.1 74.3
Table 5. Classification reliability by BDT, LDF and
QDF
Classifier | CAT1 CAT2 CAT3 CAT4 CATS
BDT 69.1 77.6 13.9834 20:5
LDF 76.0 80.2 18.8 77.8 55.9
QDF 76.4 80.7 79.2 78.1 56.0
5.2 Real Landsat completely-enumerated
data
A completely enumerated image(Tanaka,1992) was
used in this experiment. Detailed digital land-use
data were aggregated to 50m x 50m cell size of seven
land cover classes, and the synthesis image was built
by matching these classes for geocoded four bands
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