A Novel Robust Fuzzy Rough Set Model for Feature Selection

Table 2

Comparison of classification performance of different FRS models on KNN in original and noisy data.

Datasets	Noise level (%)	FRS	β-PFRS	K-trimmed FRS	K-means FRS	K-median FRS	SFRS	RS-FRS
Glass	0	0.678 ± 0.134	0.650 ± 0.068	0.631 ± 0.061	0.650 ± 0.078	0.655 ± 0.099	0.678 ± 0.134	0.668 ± 0.031
	5	0.629 ± 0.061	0.649 ± 0.027	0.630 ± 0.037	0.647 ± 0.091	0.648 ± 0.043	0.655 ± 0.096	0.656 ± 0.029
	10	0.628 ± 0.098	0.647 ± 0.066	0.626 ± 0.110	0.645 ± 0.019	0.644 ± 0.068	0.648 ± 0.089	0.649 ± 0.015
Wine	0	0.931 ± 0.072	0.926 ± 0.054	0.926 ± 0.054	0.931 ± 0.072	0.931 ± 0.072	0.931 ± 0.072	0.931 ± 0.072
	5	0.892 ± 0.069	0.910 ± 0.045	0.925 ± 0.059	0.930 ± 0.059	0.924 ± 0.062	0.920 ± 0.073	0.928 ± 0.086
	10	0.876 ± 0.058	0.909 ± 0.038	0.924 ± 0.035	0.912 ± 0.072	0.908 ± 0.054	0.919 ± 0.071	0.926 ± 0.044
Heart	0	0.744 ± 0.069	0.759 ± 0.082	0.741 ± 0.105	0.730 ± 0.078	0.730 ± 0.078	0.744 ± 0.069	0.744 ± 0.069
	5	0.735 ± 0.071	0.739 ± 0.059	0.740 ± 0.110	0.728 ± 0.080	0.727 ± 0.013	0.741 ± 0.067	0.742 ± 0.038
	10	0.719 ± 0.082	0.733 ± 0.086	0.734 ± 0.044	0.726 ± 0.019	0.727 ± 0.078	0.736 ± 0.054	0.736 ± 0.025
Segment	0	0.946 ± 0.109	0.949 ± 0.109	0.953 ± 0.109	0.955 ± 0.109	0.953 ± 0.109	0.946 ± 0.033	0.946 ± 0.109
	5	0.944 ± 0.038	0.948 ± 0.036	0.949 ± 0.032	0.951 ± 0.092	0.952 ± 0.034	0.945 ± 0.055	0.945 ± 0.010
	10	0.941 ± 0.040	0.947 ± 0.032	0.946 ± 0.053	0.949 ± 0.039	0.947 ± 0.037	0.944 ± 0.071	0.944 ± 0.104
Hepatitis	0	0.765 ± 0.107	0.765 ± 0.107	0.765 ± 0.107	0.765 ± 0.107	0.765 ± 0.107	0.765 ± 0.107	0.765 ± 0.107
	5	0.763 ± 0.092	0.764 ± 0.108	0.763 ± 0.045	0.764 ± 0.099	0.760 ± 0.123	0.764 ± 0.092	0.764 ± 0.062
	10	0.750 ± 0.118	0.759 ± 0.075	0.760 ± 0.075	0.764 ± 0.081	0.753 ± 0.077	0.750 ± 0.028	0.762 ± 0.104
ICU	0	0.868 ± 0.162	0.879 ± 0.183	0.879 ± 0.183	0.868 ± 0.129	0.868 ± 0.129	0.868 ± 0.162	0.880 ± 0.042
	5	0.856 ± 0.176	0.859 ± 0.087	0.860 ± 0.158	0.857 ± 0.162	0.855 ± 0.146	0.861 ± 0.054	0.863 ± 0.107
	10	0.850 ± 0.023	0.855 ± 0.126	0.853 ± 0.101	0.856 ± 0.023	0.852 ± 0.176	0.856 ± 0.010	0.862 ± 0.093
German	0	0.716 ± 0.037	0.712 ± 0.061	0.713 ± 0.045	0.713 ± 0.032	0.713 ± 0.032	0.716 ± 0.037	0.716 ± 0.037
	5	0.708 ± 0.038	0.710 ± 0.046	0.710 ± 0.059	0.709 ± 0.037	0.712 ± 0.041	0.713 ± 0.063	0.714 ± 0.031
	10	0.706 ± 0.033	0.710 ± 0.035	0.708 ± 0.042	0.708 ± 0.091	0.709 ± 0.032	0.710 ± 0.025	0.713 ± 0.088
Soy	0	0.850 ± 0.141	0.825 ± 0.134	0.850 ± 0.141	0.850 ± 0.141	0.850 ± 0.141	0.850 ± 0.141	0.850 ± 0.141
	5	0.790 ± 0.062	0.819 ± 0.077	0.818 ± 0.025	0.818 ± 0.018	0.816 ± 0.050	0.820 ± 0.041	0.820 ± 0.112
	10	0.760 ± 0.046	0.818 ± 0.082	0.810 ± 0.082	0.806 ± 0.087	0.809 ± 0.246	0.816 ± 0.092	0.818 ± 0.070
Horse	0	0.864 ± 0.056	0.845 ± 0.051	0.834 ± 0.060	0.834 ± 0.060	0.840 ± 0.061	0.845 ± 0.051	0.864 ± 0.056
	5	0.830 ± 0.042	0.829 ± 0.061	0.823 ± 0.072	0.830 ± 0.055	0.825 ± 0.073	0.828 ± 0.052	0.828 ± 0.081
	10	0.815 ± 0.056	0.825 ± 0.048	0.818 ± 0.065	0.829 ± 0.061	0.824 ± 0.074	0.826 ± 0.014	0.827 ± 0.099
WDBC	0	0.937 ± 0.036	0.955 ± 0.019	0.956 ± 0.023	0.946 ± 0.034	0.952 ± 0.034	0.937 ± 0.028	0.937 ± 0.036
	5	0.928 ± 0.032	0.933 ± 0.041	0.951 ± 0.020	0.941 ± 0.037	0.952 ± 0.029	0.936 ± 0.071	0.936 ± 0.111
	10	0.920 ± 0.027	0.927 ± 0.021	0.949 ± 0.038	0.940 ± 0.034	0.951 ± 0.067	0.935 ± 0.083	0.935 ± 0.027
WPBC	0	0.757 ± 0.050	0.727 ± 0.083	0.721 ± 0.101	0.711 ± 0.095	0.721 ± 0.082	0.726 ± 0.101	0.757 ± 0.050
	5	0.721 ± 0.087	0.721 ± 0.066	0.712 ± 0.114	0.711 ± 0.098	0.711 ± 0.069	0.722 ± 0.081	0.751 ± 0.114
	10	0.720 ± 0.089	0.720 ± 0.053	0.710 ± 0.095	0.709 ± 0.108	0.706 ± 0.101	0.719 ± 0.077	0.747 ± 0.093
Sonar	0	0.731 ± 0.067	0.774 ± 0.060	0.779 ± 0.083	0.769 ± 0.098	0.769 ± 0.098	0.731 ± 0.067	0.780 ± 0.091
	5	0.730 ± 0.063	0.750 ± 0.055	0.763 ± 0.064	0.765 ± 0.106	0.764 ± 0.077	0.729 ± 0.013	0.772 ± 0.123
	10	0.728 ± 0.067	0.744 ± 0.089	0.726 ± 0.070	0.726 ± 0.075	0.730 ± 0.059	0.728 ± 0.088	0.761 ± 0.105
Average		0.798 ± 0.072	0.805 ± 0.069	0.804 ± 0.074	0.804 ± 0.074	0.804 ± 0.080	0.804 ± 0.068	0.812 ± 0.073