Table 9 The average recall, precision and \(F_{1}\)-score of Bimodal 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 0.992 (0.00) 1.000 (0.00) 0.996 (0.00) 0.910 (0.16) 1.000 (0.00) 0.944 (0.10) 0.980 (0.06) 1.000 (0.00) 0.989 (0.03)
Max norm 0.999 (0.00) 1.000 (0.00) 0.999 (0.00) 0.980 (0.06) 0.974 (0.05) 0.975 (0.04) 0.960 (0.07) 0.972 (0.06) 0.965 (0.06)
One norm 1.000 (0.00) 1.000 (0.00) 1.000 (0.00) 0.970 (0.06) 0.963 (0.06) 0.965 (0.05) 0.960 (0.07) 0.961 (0.07) 0.960 (0.06)
mix norm 0.998 (0.00) 1.000 (0.00) 0.999 (0.00) 0.990 (0.03) 0.974 (0.05) 0.981 (0.03) 1.000 (0.00) 0.974 (0.05) 0.986 (0.03)
MoG 1.000 (0.00) 1.000 (0.00) 1.000 (0.00) 0.990 (0.03) 0.974 (0.05) 0.981 (0.03) 0.960 (0.09) 0.964 (0.06) 0.959 (0.06)
PDE 0.980 (0.04) 1.000 (0.00) 0.989 (0.02) 0.980 (0.04) 0.973 (0.06) 0.976 (0.04) 0.980 (0.04) 0.973 (0.06) 0.976 (0.04)
1-NN 1.000 (0.00) 1.000 (0.00) 1.000 (0.00) 0.910 (0.09) 0.923 (0.07) 0.913 (0.07) 0.930 (0.05) 0.924 (0.07) 0.926 (0.05)
k-NN 0.998 (0.01) 1.000 (0.00) 0.999 (0.00) 0.980 (0.06) 0.965 (0.06) 0.970 (0.04) 0.950 (0.10) 0.911 (0.07) 0.925 (0.06)
SVDD 0.960 (0.02) 1.000 (0.00) 0.980 (0.01) 0.890 (0.14) 0.979 (0.04) 0.926 (0.09) 0.920 (0.07) 0.978 (0.04) 0.947 (0.06)
5%
Two norm 0.989 (0.00) 0.990 (0.00) 0.990 (0.00) 0.990 (0.03) 0.919 (0.10) 0.951 (0.07) 0.990 (0.03) 0.911 (0.10) 0.946 (0.06)
Max norm 1.000 (0.00) 0.990 (0.00) 0.995 (0.00) 0.980 (0.06) 0.933 (0.09) 0.953 (0.06) 0.990 (0.03) 0.925 (0.08) 0.954 (0.05)
One norm 1.000 (0.00) 0.990 (0.00) 0.995 (0.00) 0.990 (0.03) 0.910 (0.10) 0.946 (0.06) 0.990 (0.03) 0.911 (0.10) 0.946 (0.06)
Mix norm 1.000 (0.00) 1.000 (0.00) 1.000 (0.00) 1.000 (0.00) 0.927 (0.09) 0.960 (0.05) 1.000 (0.00) 0.927 (0.09) 0.960 (0.05)
MoG 1.000 (0.00) 0.996 (0.01) 0.998 (0.00) 1.000 (0.00) 0.918 (0.09) 0.955 (0.05) 0.980 (0.06) 0.906 (0.09) 0.940 (0.07)
PDE 1.000 (0.00) 0.993 (0.01) 0.996 (0.00) 1.000 (0.00) 0.912 (0.10) 0.951 (0.05) 1.000 (0.00) 0.903 (0.09) 0.946 (0.05)
1-NN 1.000 (0.00) 0.944 (0.01) 0.971 (0.01) 0.910 (0.09) 0.684 (0.12) 0.776 (0.09) 0.930 (0.05) 0.693 (0.11) 0.790 (0.08)
k-NN 1.000 (0.00) 0.996 (0.01) 0.998 (0.00) 0.990 (0.03) 0.910 (0.10) 0.946 (0.07) 1.000 (0.00) 0.871 (0.12) 0.927 (0.07)
SVDD 0.971 (0.01) 0.963 (0.02) 0.967 (0.01) 0.950 (0.07) 0.883 (0.10) 0.912 (0.08) 0.950 (0.05) 0.875 (0.11) 0.908 (0.07)
10%
Two norm 0.973 (0.01) 0.994 (0.01) 0.983 (0.01) 0.970 (0.05) 0.926 (0.07) 0.947 (0.05) 0.930 (0.09) 0.941 (0.08) 0.934 (0.08)
Max norm 1.000 (0.00) 0.971 (0.01) 0.985 (0.00) 1.000 (0.00) 0.888 (0.10) 0.938 (0.05) 0.990 (0.03) 0.862 (0.09) 0.919 (0.05)
One norm 0.982 (0.01) 0.998 (0.00) 0.989 (0.01) 0.960 (0.08) 0.934 (0.07) 0.946 (0.07) 0.920 (0.08) 0.931 (0.08) 0.925 (0.07)
Mix norm 0.999 (0.00) 0.902 (0.01) 0.948 (0.00) 1.000 (0.00) 0.923 (0.07) 0.958 (0.04) 0.960 (0.08) 0.913 (0.08) 0.932 (0.06)
MoG 1.000 (0.00) 0.993 (0.01) 0.996 (0.00) 1.000 (0.00) 0.907 (0.07) 0.950 (0.04) 0.990 (0.03) 0.897 (0.07) 0.940 (0.05)
PDE 1.000 (0.00) 0.990 (0.00) 0.995 (0.00) 1.000 (0.00) 0.907 (0.07) 0.950 (0.04) 1.000 (0.00) 0.907 (0.07) 0.950 (0.04)
1-NN 1.000 (0.00) 0.901 (0.00) 0.948 (0.00) 0.900 (0.09) 0.606 (0.09) 0.720 (0.07) 0.910 (0.07) 0.601 (0.09) 0.719 (0.07)
k-NN 0.926 (0.03) 0.992 (0.01) 0.958 (0.02) 0.980 (0.04) 0.908 (0.04) 0.942 (0.04) 0.970 (0.05) 0.894 (0.06) 0.929 (0.04)
SVDD 0.946 (0.01) 0.951 (0.01) 0.949 (0.01) 0.910 (0.09) 0.829 (0.11) 0.864 (0.09) 0.850 (0.12) 0.810 (0.10) 0.828 (0.10)
15%
Two norm 0.993 (0.01) 0.966 (0.02) 0.979 (0.01) 0.960 (0.07) 0.942 (0.09) 0.948 (0.06) 0.960 (0.05) 0.925 (0.09) 0.939 (0.06)
Max norm 1.000 (0.00) 0.935 (0.01) 0.966 (0.01) 1.000 (0.00) 0.888 (0.09) 0.938 (0.05) 1.000 (0.00) 0.863 (0.12) 0.923 (0.07)
One norm 0.980 (0.01) 0.962 (0.01) 0.971 (0.01) 0.970 (0.05) 0.948 (0.08) 0.957 (0.05) 0.950 (0.07) 0.927 (0.11) 0.934 (0.07)
Mix norm 0.995 (0.01) 0.965 (0.01) 0.980 (0.01) 0.970 (0.05) 0.948 (0.08) 0.957 (0.05) 0.940 (0.08) 0.942 (0.09) 0.936 (0.06)
MoG 1.000 (0.00) 0.959 (0.01) 0.979 (0.00) 1.000 (0.00) 0.918 (0.09) 0.955 (0.05) 1.000 (0.00) 0.911 (0.09) 0.951 (0.05)
PDE 1.000 (0.00) 0.954 (0.01) 0.976 (0.00) 1.000 (0.00) 0.918 (0.09) 0.955 (0.05) 1.000 (0.00) 0.928 (0.09) 0.960 (0.05)
1-NN 1.000 (0.00) 0.848 (0.01) 0.917 (0.00) 0.900 (0.08) 0.562 (0.06) 0.691 (0.06) 0.880 (0.09) 0.554 (0.05) 0.679 (0.06)
k-NN 0.995 (0.01) 0.950 (0.01) 0.972 (0.00) 1.000 (0.00) 0.911 (0.09) 0.951 (0.05) 0.980 (0.06) 0.839 (0.08) 0.901 (0.06)
SVDD 0.932 (0.01) 0.980 (0.01) 0.956 (0.01) 0.870 (0.13) 0.961 (0.09) 0.908 (0.09) 0.880 (0.12) 0.966 (0.08) 0.914 (0.07)
20%
Two norm 0.987 (0.01) 0.943 (0.01) 0.964 (0.01) 0.990 (0.03) 0.932 (0.07) 0.958 (0.04) 0.980 (0.06) 0.932 (0.07) 0.952 (0.04)
Max norm 1.000 (0.00) 0.917 (0.02) 0.956 (0.01) 0.990 (0.03) 0.888 (0.10) 0.933 (0.05) 0.980 (0.04) 0.871 (0.10) 0.919 (0.06)
One norm 1.000 (0.00) 0.941 (0.01) 0.970 (0.01) 0.980 (0.06) 0.921 (0.07) 0.947 (0.05) 0.980 (0.06) 0.921 (0.07) 0.947 (0.05)
Mix norm 1.000 (0.00) 0.944 (0.01) 0.971 (0.01) 1.000 (0.00) 0.909 (0.08) 0.950 (0.05) 1.000 (0.00) 0.909 (0.08) 0.950 (0.05)
MoG 1.000 (0.00) 0.952 (0.01) 0.976 (0.01) 1.000 (0.00) 0.923 (0.07) 0.958 (0.04) 1.000 (0.00) 0.923 (0.07) 0.958 (0.04)
PDE 1.000 (0.00) 0.951 (0.01) 0.975 (0.00) 1.000 (0.00) 0.923 (0.07) 0.958 (0.04) 1.000 (0.00) 0.923 (0.07) 0.958 (0.04)
1-NN 1.000 (0.00) 0.800 (0.01) 0.889 (0.00) 0.960 (0.07) 0.555 (0.04) 0.702 (0.04) 0.940 (0.05) 0.528 (0.05) 0.675 (0.05)
k-NN 0.972 (0.02) 0.947 (0.01) 0.959 (0.01) 0.990 (0.03) 0.889 (0.07) 0.935 (0.05) 1.000 (0.00) 0.898 (0.07) 0.945 (0.04)
SVDD 0.942 (0.01) 0.860 (0.02) 0.899 (0.02) 0.880 (0.14) 0.881 (0.12) 0.869 (0.10) 0.850 (0.12) 0.832 (0.14) 0.826 (0.07)
  1. The bolded value is the best within the group