# A Feature Selection Algorithm Performance Metric for Comparative Analysis
## 7 Results
They are all ranked on the same level and therefore do not provide any information regarding the  
\begin{table}
\begin{tabular}{l c c c c c c c} \hline  & **RAND** & **AMSO** & **GAFS** & **SBFS** & **SFFS** & **PCFS** & **IGFS** \\ \hline D1 & 0.2307 (0.28–0.17) & 0.3942 (0.40–0.38) & 0.4607 (0.47–0.45) & 0.3985 & 0.4620 & 0.3235 & 0.3642 \\ D2 & 0.1488 (0.19–0.13) & 0.2684 (0.27–0.27) & 0.2684 (0.27–0.27) & 0.2684 & 0.2684 & 0.2684 & 0.2684 \\ D3 & 0.1959 (0.21–0.18) & 0.3043 (0.31–0.30) & 0.2984 (0.31–0.29) & 0.1975 & 0.3253 & 0.2936 & 0.2996 \\ D4 & 0.1362 (0.16–0.13) & 0.4324 (0.43–0.38) & 0.4688 (0.51–0.44) & 0.3685 & 0.1875 & 0.2299 & 0.2506 \\ D5 & 0.1130 (0.13–0.10) & 0.1995 (0.20–0.19) & 0.2207 (0.23–0.21) & 0.2225 & 0.2207 & 0.1497 & 0.1902 \\ D6 & 0.1105 (0.13–0.08) & 0.2238 (0.23–0.22) & 0.2284 (0.23–0.23) & 0.2251 & 0.2284 & 0.1978 & 0.1978 \\ D7 & 0.1886(0.21–0.16) & 0.2687 (0.27–0.27) & 0.2703 (0.27–0.27) & 0.2748 & 0.2703 & 0.2500 & 0.2360 \\ D8 & 0.1987 (0.21–0.16) & 0.2500 (0.25–0.25) & 0.2500 (0.25–0.25) & 0.2500 & 0.2500 & 0.2500 & 0.2500 \\ D9 & 0.1899 (0.20–0.18) & 0.2500 (0.25–0.25) & 0.2500 (0.25–0.25) & 0.2500 & 0.2500 & 0.2500 & 0.2500 \\ D10 & 0.1321 (0.17–0.11) & 0.3320 (0.34–0.33) & 0.3536 (0.36–0.34) & 0.3001 & 0.3378 & 0.3217 & 0.2785 \\ D11 & 0.2053 (0.22–0.17) & 0.2500 (0.25–0.25) & 0.2500 (0.25–0.25) & 0.2500 & 0.2500 & 0.2500 & 0.2500 \\ D12 & 0.1563 (0.19–0.11) & 0.2484 (0.26–0.24) & 0.2807 (0.28–0.26) & 0.2817 & 0.2057 & 0.2217 & 0.2025 \\ D13 & 0.1551 (0.18–0.14) & 0.2841 (0.29–0.28) & 0.3111 (0.32–0.31) & 0.3038 & 0.3089 & 0.2901 & 0.3142 \\ D14 & 0.1923 (0.21–0.12) & 0.4629 (0.46–0.42) & 0.4368 (0.44–0.42) & 0.4238 & 0.4335 & 0.3523 & 0.3226 \\ D15 & 0.1806 (0.20–0.16) & 0.2379 (0.24–0.24) & 0.2379 (0.24–0.24) & 0.2379 & 0.2357 & 0.2169 & 0.2169 \\ D16 & 0.1899 (0.20–0.18) & 0.2500 (0.25–0.25) & 0.2500 (0.25–0.25) & 0.2500 & 0.2500 & 0.2500 & 0.2500 \\ D17 & 0.1885 (0.20–0.18) & 0.4027 (0.40–0.39) & 0.3663 (0.39–0.33) & 0.2781 & 0.4124 & 0.2825 & 0.2619 \\ D18 & 0.1716 (0.25–0.03) & 0.3399 (0.34–0.34) & 0.3399 (0.34–0.34) & 0.3073 & 0.3399 & 0.3399 & 0.3399 \\ D19 & 0.0947 (0.13–0.06) & 0.2301 (0.24–0.22) & 0.2453 (0.25–0.23) & 0.2093 & 0.2712 & 0.1603 & 0.1603 \\ D20 & 0.1675 (0.19–0.15) & 0.3000 (0.30–0.29) & 0.3512 (0.37–0.34) & 0.3210 & 0.3909 & 0.3223 & 0.2860 \\ D21 & 0.1176 (0.18–0.08) & 0.3522 (0.35–0.34 choice of the feature selection algorithm. Datasets where all algorithms resulted in the same ranks are pruned from further analysis. Figure 3 summarises the distribution of the ranks for each algorithm in Table 9 and Figure 3 shows that all the algorithms did perform the best on at least one problem. The SFFS algorithm, according to Figure 3, was the only algorithm that performed the worst for at least one dataset. It is clear that there is no one algorithm that is the best for all scenarios. Algorithm GAFS has a denser distribution in the lower ranks in comparison to the other algorithms. GAFS performs effectively more often than other algorithms but is not infallible with regard to the best performance. Figure 3 provides valuable information regarding the distribution of algorithm ranks but does not consider algorithms that share a rank. The box plots in Figure 3 do not show the worst performing algorithm as rank 6 for scenarios where two or more distinct algorithms performed equally. As an example, should any two algorithms have been ranked on the same level then the worst rank for the specific dataset would be rank 5. Table 10 shows the number of times each algorithm was ranked as the lowest (best) and highest (worst) with respect to other candidate algorithms. These results are based on the penalty scaling constant of \(k_{p}=0.25\), and the classification scaling constant of \(k_{c}=1.0\). These scaling constants were determined in Section 5 as a result of sanity tests with regard to which feature selection objectives this study has considered as important. Table 10 clearly shows that all algorithms did perform the worst and the best for at least one dataset.