UAR A.
ES 2. A TRIPLET TREE DIVISION-WAIT
MECHANISM
The proposed methods is an extension of binary deci-
sion tree classifiers. The proposed triple tree classifier
has two ‘determined nodes’ based on binary splitting
apan of categories and one optional ‘undetermined node” QC undetermined node
for uncertain subgroups.
Fig.1 Triplet tree structure.
Samples definitely classified by group distance cri-
teria are classified to determined nodes. Determined
nodes are labeled as definite categories and processed
in a similar manner repeatedly. The ambiguous sam-
ples are classified to undetermined node, and unde-
termined node is labeled as the same categories as
parent node. That is, undetermined node redun- f
dantly inherit categories from parent node. Samples, BONN
e proposed on the other hand, are divided into two determined ; |
| i nodes and one undetermined node with no redun- | i 7
N
\
ecognition
Zi
on tree has
d node’ for
n extension
e classifiers
by appling The mechanisms introduced in this proposed
his classifi- method are as follows. Fig.2 Segmentation to two determined nodes and one
undetermined node:
\
dancy. Classification of undetermined node is tried to Determined node : V
based on newly calculated group distances in the suc- E dd
ceeding step.
ssified data
: : . sample histogram and two boundaries.
e Samples definitely classified by group distance p €
criteria are assigned to determined nodes. De- ©
gid bound- termined nodes are labeled as definite categories.
1 boundary
ar from the
de division e The uncertain samples are assigned to undeter-
mined node and undetermined node is labeled as
the same categories as the parent node.
ons overlap
uitable and
e Boundaries of data segmentation to three chil-
dren nodes are determined based on error toler- Fig.3 Segmentation of feature space by a triplet tree.
ance criterion of training samples. Namely, by
two boundary lines approaching from the two
terminals of a variable to the middle point, each
an be de- determined nodes contain at most p percent of
mis-classification, where p is control parameter.
king these
ocessing of
lanisms are
3. ADVANTAGES OF THE PROPOSAL
dited By this triplet tree approach, problems (P1),(P2) and
Sone oni ; (P3) with usual tree methods stated at the Section 1
s are post- For more detail, Fig. 1 shows a triplet tree and ; :
; : : can be solved. Solutions by this approach are follow-
Fig. 2 illustrates a segmentation of samples to three ins (STL(S2) and (S3) respective]
child nodes. Fig. 3 illustrates a effective segmenta- B ) pectivety.
d termi ; ; i i
qued tion of feature space by two steps in a triplet tree, In (S1) Plural terminal nodes could be appeared for each
Tra case of two categories A, B. Based on binary split- category in proposed tree classifier. Partial deci-
ting of c ategories and two boundaries m the feature sion of classification is made at every division
space, a data histogram of parent node is calculated. of- node, and it restricts the influence of mis-
roposed to
SSI RCE {DR Samples belong outside two boundaries are allotted classification at higher nodes.
respectively to determined nodes. Samples belong be-
tween boundaries are allotted to undetermined node. (S2) Triplet tree is treated as en extension of binary
The blackly shown parts in the Fig. 1 are equivalent tree. It is more adaptive than binary tree and has
to the mis-classified samples in this segmentation, as advantages in classification accuracy in terms of
a tolerated limit of error. making the middle node hold uncertain groups
989
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996
