Information Technology Reference
In-Depth Information
Table 18.8
Classification results in discriminant analysis; 55.1% of original grouped cases
correctly classified
Syst3 Predicted Group Membership Total
1.
2.
3.
1.
6
14
3
23
Count
2.
5
27
9
41
Original
3.
0
13
21
34
1.
26.1 60.9
13.0
1.0
%
2
12.2 65.9
22.0
1.0
3.
0
38.2
61.8
1.0
Table 18.9
Fuzzy rules for discriminant analysis model
Rule If
Age
is and
Bmi
is then
Syst3
is
Rule If
Age
is and
Bmi
is then
Syst3
is
1
54.4
20.8
1.3
11
59.1
26.9
2.1
2
56.2
25.6
1.3
12
63.0
25.1
2.4
3
42.9
31.7
1.5
13
65.9
26.7
2.4
4
50.1
20.5
1.5
14
70.8
21.9
2.6
5
60.5
20.8
1.5
15
49.4
31.9
2.9
6
67.1
21.3
1.6
16
56.9
28.9
2.9
7
56.9
20.9
1.8
17
58.1
25.3
2.9
8
67.0
28.1
2.0
18
61.9
28.3
2.9
9
53.8
26.9
2.1
19
61.8
31.8
3.0
10
56.9
29.3
2.1
20
63.4
35.8
3.0
we may also apply the initial outputs directly in which case their values represent
both full and partial memberships to the systolic blood pressure groups.
Discriminant analysis a good example of such modeling in which the traditional
approach is quite complicated and thus, despite its important role in medicine, it is
not widely used in the research work.
Finally, we sketch some ideas how to apply the foregoing methods to other areas
of statistics.
18.5
Prospects for Enhanced Models
One enhanced version of the traditional regression model is the switching regression
model (e.g. [7] ) which is appropriate to data sets containing clusters (Fig. 18.15).
Then we may specify several fittings, one for each cluster. The specifications of
these fittings correspond to the idea already used in the analysis of variance, viz. the
point-wise distances to the fittings within the clusters should be minimized, whereas
the distances between the fittings should be maximized. In the latter case we thus
calculate the distances between the functions. As above, linear or nonlinear mathe-
matical functions can be used in the traditional case, whereas the fuzzy models can
