# On the Optimal Size of Candidate Feature Set in Random forest
## Motivation
### Further Motivational Experiment  
In this section, we expand the experiment in Section 2.2 further to observe any specific pattern on the optimal size of candidate feature set. The experiment was conducted on 58 real or artificial datasets that are suitable for classification problem, which mostly came from UCI Data Repository [17] and R package named \(mlbench\)[18]. The datasets are summarized in Table 2. The design of the experiment is the same as in Section 2.2. The result of the experiment is summarized in Figure 2. The horizontal axis refers to 58 datasets and the vertical axis refers the difference between the optimal \(m\) and the default \(m\). Here, the optimal \(m\) means the size of feature set which showed the highest test accuracy. The datasets are arranged in the order of the difference between the optimal \(m\) and the default \(m\). \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Datasets** & **Observations** & **Classes** & **Variables** & **Sources** \\ \hline ail & 13,750 & 2 & 12 & [15] \\ cmc & 1473 & 3 & 9 & UCI (Contraceptive method choice) \\ int & 1000 & 2 & 9 & [16] \\ rng & 1000 & 2 & 10 & R library \(mlbench\) (Ringnorm) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The description of 4 datasets. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Datasets** & **Observations** & **Classes** & **Variables** & **Sources** \\ \hline aba & 4177 & 2 & 8 & UCI (Abalone) \\ ail & 13,750 & 2 & 12 & [15] \\ aus & 690 & 2 & 14 & UCI (Australian credit approval) \\ bal & 625 & 3 & 4 & UCI (Balance scale) \\ ban & 1372 & 2 & 4 & UCI (Bank note authentication) \\ bcw & 683 & 2 & 9 & [1] \\ bld & 345 & 2 & 6 & UCI (BUPA liver disorders) \\ blo & 748 & 2 & 4 & UCI (Blood transfusion center) \\ bod & 507 & 2 & 24 & [19] \\ bos & 506 & 3 & 13 & UCI (Boston housing) \\ bre & 699 & 2 & 9 & UCI (Wisconsin Breast Cancer) \\ cir & 1000 & 2 & 10 & R library _mlbench_ (Circle in a square) \\ cmc & 1473 & 3 & 9 & UCI (Contraceptive method choice) \\ col & 366 & 3 & 23 & UCI (Horse Colic) \\ cre & 690 & 2 & 15 & UCI (Credit approval) \\ cyl & 540 & 2 & 30 & UCI (Cylinder bands) \\ der & 358 & 6 & 34 & UCI (Dermatology) \\ dia & 768 & 2 & 8 & [15] \\ dna & 3186 & 3 & 60 & UCI (StatLog DNA) \\ ech & 131 & 2 & 6 & UCI (Echocardiogram) \\ eco & 336 & 4 & 7 & [15] \\ fis & 159 & 7 & 6 & [20] \\ ger & 1000 & 2 & 20 & UCI (German credit) \\ gla & 214 & 6 & 9 & UCI (Glass) \\ hea & 270 & 2 & 13 & UCI (StatLog heart disease) \\ hep & 155 & 2 & 19 & UCI (Hepatitis) \\ hil & 606 & 2 & 100 & UCI (Hill-valley) \\ imp & 205 & 6 & 23 & UCI (Auto imports) \\ int & 1000 & 2 & 9 & [16] \\ ion & 351 & 2 & 33 & UCI (Ionosphere) \\ iri & 150 & 3 & 4 & UCI (Iris) \\ lak & 259 & 6 & 14 & [15] \\ led & 6000 & 10 & 7 & UCI (LED display) \\ lib & 360 & 15 & 90 & UCI (Libras movement) \\ mam & 961 & 2 & 5 & UCI (Mammographic mass) \\ mar & 8777 & 10 & 4 & [15] \\ pid & 532 & 2 & 7 & UCI (PIMA Indian diabetes) \\ pks & 195 & 2 & 22 & UCI (Parkinsons) \\ pov & 97 & 6 & 6 & [21] \\ mg & 1000 & 2 & 10 & R library _mlbench_ (Ringnorm) \\ sat & 6435 & 6 & 36 & UCI (StatLog satellite image) \\ sea & 3000 & 3 & 7 & [22] \\ seg & 2310 & 7 & 18 & UCI (Image segmentation) \\ smo & 2855 & 3 & 8 & UCI (Attitude towards smoking restrictions) \\ snr & 208 & 2 & 60 & R library _mlbench_ (Sonar) \\ soy & 307 & 7 & 28 & [15] \\ spa & 4601 & 2 & 57 & UCI (Spambase) \\ spe & 267 & 2 & 44 & UCI (SPECTF heart) \\ thy & 7200 & 3 & 21 & UCI (Thyroid disease) \\ trn & 1000 & 2 & 10 & R library _mlbench_ (Threenorm) \\ twn & 1000 & 2 & 10 & R library _mlbench_ (Twonorm) \\ usn & 1302 & 3 & 27 & [23] \\ veh & 846 & 4 & 18 & UCI (StatLog vehicle silhouette) \\ vol & 1521 & 6 & 5 & [15] \\ vot & 435 & 2 & 16 & UCI (Congressional voting records) \\ vow & 990 & 11 & 10 & UCI (Vowel recognition) \\ wav & 3600 & 3 & 21 & UCI (Waveform) \\ zoo & 101 & 7 & 16 & R library _mlbench_ (Zoo) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The description of 58 datasets.