Table 13 The average recall, precision and \(F_{1}\) \({{\varvec{F}}}_{1}\)-score of Iris-virginica data depending on the noise level (standard deviation in parentheses)

From: Norm ball classifier for one-class classification

Classifier Training Validation Test
Recall Precision \({F}_{1}\)-score Recall Precision \({F}_{1}\)-score Recall Precision \({F}_{1}\)-score
0%
Two norm 0.918 (0.03) 1.000 (0.00) 0.957 (0.02) 0.900 (0.09) 0.884 (0.11) 0.882 (0.04) 0.840 (0.15) 0.808 (0.16) 0.799 (0.06)
Max norm 0.953 (0.02) 1.000 (0.00) 0.976 (0.01) 0.900 (0.09) 0.922 (0.07) 0.907 (0.06) 0.860 (0.15) 0.871 (0.12) 0.846 (0.06)
One norm 0.973 (0.03) 1.000 (0.00) 0.986 (0.01) 0.900 (0.13) 0.875 (0.20) 0.861 (0.12) 0.838 (0.08) 0.866 (0.13) 0.840 (0.04)
Mix norm 1.000 (0.00) 1.000 (0.00) 1.000 (0.00) 1.000 (0.00) 0.738 (0.26) 0.822 (0.19) 0.980 (0.04) 0.739 (0.32) 0.795 (0.23)
MoG 0.973 (0.03) 1.000 (0.00) 0.986 (0.01) 0.938 (0.05) 0.874 (0.16) 0.899 (0.10) 0.940 (0.05) 0.849 (0.19) 0.879 (0.11)
PDE 0.960 (0.08) 1.000 (0.00) 0.978 (0.04) 0.960 (0.08) 0.864 (0.13) 0.900 (0.06) 0.940 (0.08) 0.869 (0.14) 0.892 (0.07)
1-NN 1.000 (0.00) 1.000 (0.00) 1.000 (0.00) 0.900 (0.15) 0.706 (0.24) 0.750 (0.13) 0.800 (0.18) 0.777 (0.20) 0.760 (0.13)
k-NN 0.871 (0.04) 1.000 (0.00) 0.931 (0.02) 0.860 (0.08) 0.812 (0.16) 0.822 (0.07) 0.820 (0.10) 0.752 (0.21) 0.761 (0.10)
SVDD 0.912 (0.02) 1.000 (0.00) 0.954 (0.01) 0.860 (0.10) 0.960 (0.05) 0.901 (0.05) 0.840 (0.14) 0.927 (0.09) 0.869 (0.07)
5%
Two norm 0.925 (0.03) 1.000 (0.00) 0.961 (0.01) 0.860 (0.08) 0.840 (0.20) 0.827 (0.08) 0.820 (0.17) 0.761 (0.23) 0.741 (0.13)
Max norm 0.960 (0.01) 1.000 (0.00) 0.979 (0.01) 0.940 (0.05) 0.793 (0.18) 0.848 (0.11) 0.980 (0.04) 0.786 (0.16) 0.861 (0.10)
One norm 0.972 (0.03) 0.969 (0.04) 0.969 (0.02) 0.840 (0.10) 0.880 (0.12) 0.846 (0.03) 0.860 (0.14) 0.739 (0.20) 0.758 (0.08)
Mix norm 0.966 (0.02) 0.974 (0.03) 0.969 (0.02) 0.920 (0.08) 0.836 (0.17) 0.859 (0.07) 0.900 (0.06) 0.746 (0.19) 0.798 (0.11)
MoG 1.000 (0.00) 1.000 (0.00) 1.000 (0.00) 0.940 (0.05) 0.876 (0.17) 0.894 (0.10) 0.900 (0.09) 0.814 (0.19) 0.841 (0.12)
PDE 0.780 (0.12) 1.000 (0.00) 0.872 (0.07) 0.780 (0.12) 0.939 (0.08) 0.843 (0.05) 0.780 (0.13) 0.870 (0.12) 0.807 (0.06)
1-NN 1.000 (0.00) 0.943 (0.02) 0.971 (0.01) 0.776 (0.15) 0.454 (0.20) 0.555 (0.18) 0.676 (0.14) 0.485 (0.21) 0.544 (0.17)
k-NN 0.918 (0.03) 1.000 (0.00) 0.957 (0.01) 0.900 (0.06) 0.807 (0.20) 0.836 (0.12) 0.860 (0.14) 0.802 (0.17) 0.806 (0.08)
SVDD 0.755 (0.03) 1.000 (0.00) 0.860 (0.02) 0.760 (0.16) 0.950 (0.10) 0.826 (0.07) 0.740 (0.19) 0.902 (0.13) 0.785 (0.08)
10%
Two norm 0.885 (0.03) 1.000 (0.00) 0.938 (0.02) 0.900 (0.09) 0.878 (0.15) 0.876 (0.08) 0.840 (0.15) 0.794 (0.16) 0.791 (0.07)
Max norm 0.973 (0.01) 1.000 (0.00) 0.986 (0.01) 0.940 (0.05) 0.776 (0.17) 0.839 (0.11) 0.980 (0.04) 0.770 (0.18) 0.849 (0.11)
One norm 0.979 (0.03) 0.894 (0.02) 0.935 (0.02) 0.733 (0.19) 0.511 (0.14) 0.583 (0.13) 0.769 (0.21) 0.444 (0.17) 0.553 (0.17)
Mix norm 0.973 (0.01) 1.000 (0.00) 0.986 (0.01) 0.940 (0.05) 0.776 (0.17) 0.839 (0.11) 0.980 (0.04) 0.770 (0.18) 0.849 (0.11)
MoG 0.993 (0.01) 1.000 (0.00) 0.996 (0.01) 0.878 (0.07) 0.903 (0.10) 0.886 (0.07) 0.860 (0.10) 0.870 (0.12) 0.859 (0.08)
PDE 0.740 (0.15) 1.000 (0.00) 0.842 (0.09) 0.740 (0.15) 0.935 (0.08) 0.814 (0.08) 0.760 (0.14) 0.879 (0.11) 0.803 (0.08)
1-NN 1.000 (0.00) 0.891 (0.01) 0.942 (0.01) 0.776 (0.15) 0.492 (0.15) 0.589 (0.13) 0.676 (0.14) 0.448 (0.17) 0.522 (0.14)
k-NN 0.918 (0.03) 1.000 (0.00) 0.957 (0.01) 0.900 (0.06) 0.779 (0.19) 0.821 (0.12) 0.860 (0.14) 0.774 (0.10) 0.800 (0.06)
SVDD 0.769 (0.03) 1.000 (0.00) 0.869 (0.02) 0.780 (0.15) 0.831 (0.14) 0.783 (0.06) 0.760 (0.19) 0.756 (0.20) 0.711 (0.03)
15%
Two norm 0.823 (0.03) 0.961 (0.04) 0.887 (0.03) 0.800 (0.11) 0.787 (0.14) 0.784 (0.09) 0.740 (0.22) 0.731 (0.09) 0.723 (0.14)
Max norm 0.973 (0.01) 0.960 (0.02) 0.966 (0.01) 0.960 (0.05) 0.805 (0.16) 0.864 (0.09) 0.980 (0.04) 0.751 (0.17) 0.838 (0.10)
One norm 0.972 (0.03) 0.856 (0.01) 0.910 (0.02) 0.833 (0.09) 0.431 (0.11) 0.561 (0.11) 0.856 (0.15) 0.428 (0.10) 0.568 (0.11)
Mix norm 0.973 (0.01) 0.960 (0.02) 0.966 (0.01) 0.960 (0.05) 0.805 (0.16) 0.864 (0.09) 0.980 (0.04) 0.751 (0.17) 0.838 (0.10)
MoG 0.952 (0.02) 0.972 (0.01) 0.962 (0.01) 0.858 (0.08) 0.901 (0.10) 0.875 (0.07) 0.838 (0.10) 0.851 (0.14) 0.839 (0.10)
PDE 0.720 (0.17) 0.976 (0.02) 0.816 (0.11) 0.720 (0.17) 0.876 (0.12) 0.772 (0.09) 0.740 (0.15) 0.843 (0.10) 0.771 (0.05)
1-NN 1.000 (0.00) 0.845 (0.01) 0.916 (0.01) 0.980 (0.04) 0.336 (0.02) 0.501 (0.03) 0.960 (0.05) 0.332 (0.03) 0.493 (0.04)
k-NN 0.804 (0.08) 0.958 (0.03) 0.873 (0.06) 0.860 (0.10) 0.789 (0.13) 0.810 (0.06) 0.780 (0.12) 0.757 (0.16) 0.751 (0.07)
SVDD 0.734 (0.04) 1.000 (0.00) 0.846 (0.03) 0.656 (0.10) 0.950 (0.06) 0.768 (0.06) 0.613 (0.11) 0.938 (0.08) 0.736 (0.09)
20%
Two norm 0.851 (0.03) 0.947 (0.02) 0.896 (0.02) 0.880 (0.08) 0.757 (0.21) 0.786 (0.10) 0.800 (0.13) 0.694 (0.26) 0.701 (0.12)
Max norm 0.932 (0.03) 0.958 (0.03) 0.945 (0.03) 0.900 (0.06) 0.817 (0.15) 0.844 (0.06) 0.900 (0.09) 0.767 (0.20) 0.801 (0.09)
One norm 1.000 (0.00) 0.795 (0.02) 0.886 (0.01) 0.900 (0.20) 0.389 (0.04) 0.529 (0.03) 0.860 (0.15) 0.354 (0.04) 0.499 (0.06)
Mix norm 0.932 (0.03) 0.958 (0.03) 0.945 (0.03) 0.900 (0.06) 0.817 (0.15) 0.844 (0.06) 0.900 (0.09) 0.767 (0.20) 0.801 (0.09)
MoG 1.000 (0.00) 0.961 (0.02) 0.980 (0.01) 0.880 (0.10) 0.920 (0.16) 0.883 (0.08) 0.840 (0.14) 0.848 (0.19) 0.835 (0.14)
PDE 0.720 (0.19) 0.961 (0.02) 0.809 (0.13) 0.720 (0.19) 0.938 (0.12) 0.786 (0.10) 0.700 (0.18) 0.871 (0.16) 0.752 (0.10)
1-NN 1.000 (0.00) 0.791 (0.01) 0.883 (0.01) 0.880 (0.19) 0.375 (0.12) 0.520 (0.14) 0.780 (0.17) 0.352 (0.10) 0.477 (0.11)
k-NN 0.824 (0.04) 0.976 (0.02) 0.892 (0.02) 0.860 (0.10) 0.740 (0.19) 0.770 (0.08) 0.798 (0.06) 0.761 (0.22) 0.754 (0.11)
SVDD 0.687 (0.03) 0.953 (0.00) 0.798 (0.02) 0.656 (0.10) 0.865 (0.12) 0.734 (0.06) 0.613 (0.11) 0.840 (0.20) 0.691 (0.10)
  1. The bolded value is the best within the group
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