Classification of Compositional Data Using Mixture Models: a Case Study Using Granulometric Data 393
Fig.4 Regionalized classification based on hierarchical
clustering procedure applied
to raw granulometric data
the groups form geographic sequences corresponding to the source area to depocenter sequence represented by groups 1 to 6.
The overall error rate (see Table 2) of the linear discriminant rules associated
to this classification under the assumption of equal prior probabilities is equal
to 7.3% and can be considered reasonably low. Samples of group 5 are the best
characterized, whereas there is a significant confusion between samples of
groups 1 and 2. Although the confusion between samples belonging to adjacent
groups seems to be natural, it is surprising that almost 8% of samples from
group 3 were wrongly classified in group 7.
Table 2 Resubstitution results for linear discriminant analysis (hierarchical clustering)
Assigned group
True group
2
3
4
5
6
7
1
150
14
0
0
0
0
3
2
11
335
0
0
0
0
0
3
0
32
171
13
0
0
0
4
0
0
8
198
0
0
5
0
0
0
8
218
0
0
6
0
0
2
2
0
54
0
7
0
0
15
0
0
44
Total N
161
381
196
222
219
55
47
Nwrong
11
46
25
24
3
Error rate
6.8%
12.1%
12.8%
10.8%
0.5%
1.8%
6.4%
Overall error rate: 7.3%