Advances in Operations Research

Research Article

Mathematical Programming Approaches to Classification Problems

Table 8

The apparent classification rates of the different models (in percentage).
D 1 D 2 D 3 D 4
( 𝑛 1 = 2 1 ; 𝑛 2 = 2 5 ) ( 𝑛 1 = 2 2 ; 𝑛 2 = 4 0 ) ( 𝑛 1 = 5 0 ; 𝑛 2 = 5 0 ) ( 𝑛 1 = 4 4 4 ; 𝑛 2 = 2 3 9 )
NonnormalNonnormalNonnormalNonnormal
FDL89,1 ( 5 )74,2( 1 6 )91 ( 9 )96,3 ( 2 5 )
LG91,3 ( 4 )74,2 ( 1 6 )93 ( 7 )96,9 ( 2 1 )
FDQ76,08 ( 1 4 )72,58 ( 1 7 )85 ( 1 5 )90,8 ( 6 3 )
Second order MSD model93,47 ( 3 )75,8 ( 1 5 )85 ( 1 5 )90,8 ( 6 3 )
𝑆 = 2 𝑆 = 3 𝑆 = 2 𝑆 = 3 𝑆 = 2 𝑆 = 3 𝑆 = 2 𝑆 = 3
Piecewise MCA91,3 ( 4 )100 (0)72,5 ( 1 7 )98,39 ( 1 )99 ( 1 )100 (0)87,55 ( 8 5 )
Piecewise MSD97,8 ( 1 )97,8 ( 1 )87,1 ( 8 )96,8 ( 2 )99 ( 1 )100 (0)
Piecewise QSMCA100 (0)100 (0)100 (0)98,97 ( 7 )100 (0)
Piecewise QSMSD97,8 ( 1 )100 (0)100 (0)100 (0)100 (0)
𝐷 = 2 𝐷 = 3 𝐷 = 2 𝐷 = 3 𝐷 = 2 𝐷 = 3 𝐷 = 2 𝐷 = 3
SPSN’2100 (0)_100 (0)98,24 ( 1 2 )
QSPSN’2100 (0)100 (0)100 (0)98,82 ( 8 )
GSPSN’2100 (0)83,87 ( 1 0 )100 (0)99( 1 )100 (0)98,82 ( 8 )99,7 ( 2 )
QGSPSN’2100 (0)100 (0)97 ( 3 )100 (0)99,85 ( 1 )100 (0)
The values in parentheses are the numbers of misclassified observations.