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Table 6

Range of selected validation indices in various clustering scenarios

Clustering scenarioIndexVEXBVkVFSOFTechnique I
Technique II
Technique III
VPCVPECI_meanEuc_meanN_UmaxR2
1. Four-component (TPI-Distance-CN-P25) min (1.1 < m < 2.2) 0.495 3,088 −21,395 1,295 0.205 0.083 0.058 1.762 5 0.264 
max (1.1 < m < 2.2) 1.785 11,110 −7,544 14,515 0.951 1.723 0.834 1.936 5,850 0.748 
for c = 6 and m = 1.6 0.628 3,914 −10,378 6,586 0.574 0.874 0.460 1.886 2,061 0.598 
2. Four-component (TPI-Distance-CN-P50) min (1.1 < m < 2.6) 0.498 3,099 −19,217 1,296 0.188 0.075 0.056 1.741 1 0.160 
max (1.1 < m < 2.6) 2.339 14,544 −1,096 12,191 0.957 2.044 0.907 1.936 5,866 0.751 
for c = 6 and m = 1.6 0.618 3,851 −10,109 6,619 0.563 0.892 0.477 1.882 1,976 0.593 
3. Four-component (TPI-Distance-CN- P100) min (1.1 < m < 2.3) 0.503 3,127 −21,166 1,036 0.284 0.099 0.062 1.762 2 0.264 
max (1.1 < m < 2.3) 2.569 16,170 −7,926 12,184 0.943 1.757 0.871 1.944 5,861 0.760 
for c = 6 and m = 1.6 0.691 4,306 −10,395 6,649 0.563 0.888 0.487 1.902 1,915 0.596 
4. Three-component (TPI-CN-P50) min (1.1 < m < 2.7) 0.171 1,166 −17,259 280 0.257 0.055 0.027 1.516 8 0.408 
max (1.1 < m < 2.7) 0.659 4,154 −2,752 7,411 0.968 1.895 0.812 1.670 6,456 0.839 
for c = 6 and m = 1.6 0.386 2,416 −10,509 3,896 0.690 0.642 0.326 1.636 3,261 0.739 
Previous studies min 0.13 −602.51 81.87 160 0.99 0.05 0 – – – 
max 14.49 852.36 3,549.6 1,280 0.21 2.11 1 – – – 
Clustering scenarioIndexVEXBVkVFSOFTechnique I
Technique II
Technique III
VPCVPECI_meanEuc_meanN_UmaxR2
1. Four-component (TPI-Distance-CN-P25) min (1.1 < m < 2.2) 0.495 3,088 −21,395 1,295 0.205 0.083 0.058 1.762 5 0.264 
max (1.1 < m < 2.2) 1.785 11,110 −7,544 14,515 0.951 1.723 0.834 1.936 5,850 0.748 
for c = 6 and m = 1.6 0.628 3,914 −10,378 6,586 0.574 0.874 0.460 1.886 2,061 0.598 
2. Four-component (TPI-Distance-CN-P50) min (1.1 < m < 2.6) 0.498 3,099 −19,217 1,296 0.188 0.075 0.056 1.741 1 0.160 
max (1.1 < m < 2.6) 2.339 14,544 −1,096 12,191 0.957 2.044 0.907 1.936 5,866 0.751 
for c = 6 and m = 1.6 0.618 3,851 −10,109 6,619 0.563 0.892 0.477 1.882 1,976 0.593 
3. Four-component (TPI-Distance-CN- P100) min (1.1 < m < 2.3) 0.503 3,127 −21,166 1,036 0.284 0.099 0.062 1.762 2 0.264 
max (1.1 < m < 2.3) 2.569 16,170 −7,926 12,184 0.943 1.757 0.871 1.944 5,861 0.760 
for c = 6 and m = 1.6 0.691 4,306 −10,395 6,649 0.563 0.888 0.487 1.902 1,915 0.596 
4. Three-component (TPI-CN-P50) min (1.1 < m < 2.7) 0.171 1,166 −17,259 280 0.257 0.055 0.027 1.516 8 0.408 
max (1.1 < m < 2.7) 0.659 4,154 −2,752 7,411 0.968 1.895 0.812 1.670 6,456 0.839 
for c = 6 and m = 1.6 0.386 2,416 −10,509 3,896 0.690 0.642 0.326 1.636 3,261 0.739 
Previous studies min 0.13 −602.51 81.87 160 0.99 0.05 0 – – – 
max 14.49 852.36 3,549.6 1,280 0.21 2.11 1 – – – 
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