# Online Streaming Feature Selection via Conditional Independence
## 5 Experiments and Analysis
### Comparison of ConInd with Two Online Algorithms
#### 5.3.3 Variation in the Number of Features and Running Time with the Increase of Feature Ratio  
To further observe the variation in of number of features and running time in every filtering phase with the increase of the feature size, we ran these algorithms by step by step increasing the features size in 14 datasets. In the experiment, the running time was reported as execution time only. For comparison, all datasets were executed once in the same environment. We observed the variation ratio of the feature number by continuing to increase the incoming features from 20% to 100%, as presented in Table 8.  
At a ratio of 100% for incoming features, the changes in the features by filtering for the cina0, sylva, lucap0, and reged1 datasets were \(106\to 57\to 30\), \(77\to 52\to 24\), \(94\to 49\to 40\), and \(541\to 16\to 13\) (Table 8). We observed that, from \(\#NIC\to\#SIC\to SF\), there was a low range in the number of features, and more than 10 features were selected. This means that the datasets have low redundancy and high relevance. Similarly, we observed that, in the datasets for leukemia and \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Dataset**} & \multirow{2}{*}{**Ratio**} & \multicolumn{4}{c}{**\#**} & \multicolumn{2}{c}{**Time**} \\ \cline{3-8}  & & \multicolumn{3}{c}{_ConIntd_} & \multicolumn{2}{c}{_OSFS_} & \multicolumn{1}{c}{_ConInd_} & \multicolumn{1}{c}{_OSFS_} \\ \cline{3-8}  & & \#NIC & _\#SIC_ & _SF_ & _SF_ & _Confind_ & _OSFS_ \\ \hline \multirow{3}{*}{ionosphere} & 25\% & 8 & 5 & 5 & 4 & 0.0222 & 0.0184 \\  & 50\% & 15 & 6 & 5 & 4 & 0.0855 & 0.0678 \\  & 75\% & 21 & 6 & 5 & 4 & 0.148 & 0.1078 \\  & 100\% & 25 & 7 & 5 & 4 & **0.2215** & **0.1315** \\ \hline \multirow{3}{*}{martil} & 25\% & 0 & 0 & 0 & 0 & 0.0235 & 0.0251 \\  & 50\% & 0 & 0 & 0 & 0 & 0.0446 & 0.0474 \\  & 75\% & 0 & 0 & 0 & 0 & 0.0673 & 0.0698 \\  & 100\% & 1 & 1 & 1 & **1** & **0.1063** & **0.1081** \\ \hline \multirow{3}{*}{leukemia} & 25\% & 488 & 21 & 5 & 3 & 74.3909 & 3.6738 \\  & 50\% & 914 & 28 & 6 & 3 & 143.903 & 5.8859 \\  & 75\% & 1521 & 35 & 8 & 4 & 356.6957 & 9.9276 \\  & 100\% & 2019 & 47 & 9 & **3** & **593.3249** & **12.7647** \\ \hline \multirow{3}{*}{arcene} & 25\% & 670 & 3 & 3 & 4 & 26.9589 & 1.6326 \\  & 50\% & 1354 & 8 & 5 & 4 & 111.864 & 6.8246 \\  & 75\% & 2017 & 11 & 6 & 3 & 259.0335 & 10.2471 \\  & 100\% & 2666 & 13 & 6 & **5** & **764.5764** & **20.8445** \\ \hline \multirow{3}{*}{cina0} & 25\% & 24 & 17 & 12 & 10 & 3.6124 & 3.8368 \\  & 50\% & 52 & 30 & 17 & 14 & 34.372 & 35.8382 \\  & 75\% & 81 & 47 & 28 & 23 & 157.9134 & 263.1822 \\  & 100\% & 106 & 57 & 30 & **22** & **407.7689** & **721.3638** \\ \hline \multirow{3}{*}{sylva} & 25\% & 22 & 17 & 12 & 10 & 4.3963 & 12.7006 \\  & 50\% & 36 & 24 & 15 & 13 & 13.3102 & 27.0316 \\  & 75\% & 55 & 39 & 22 & 18 & 53.8118 & 115.1798 \\  & 100\% & 77 & 52 & 24 & **18** & **189.8111** & **247.9366** \\ \hline \multirow{3}{*}{lucap0} & 25\% & 24 & 18 & 16 & 15 & 2.4505 & 10.5797 \\  & 50\% & 50 & 38 & 32 & 26 & 32.2265 & 147.5867 \\  & 75\% & 68 & 44 & 36 & 30 & 88.2781 & 416.6544 \\  & 100\% & 94 & 49 & 40 & **36** & **225.7368** & **1.43 \(\times\) 10\({}^{7}\)** \\ \hline \multirow{3}{*}{reged1} & 25\% & 6 & 1 & 1 & 2 & 0.0282 & 0.0299 \\  & 50\% & 15 & 3 & 3 & 4 & 0.0791 & 0.103 \\ \cline{1-1}  & 75\% & 22 & 5 & 5 & 6 & 0.1639 & 0.2067 \\ \cline{1-1}  & 100\% & 541 & 16 & 13 & **13** & **63.9082** & **121.2839** \\ \hline \hline \end{tabular} Ratio, ratio of feature space #, the number of selected features; Time, runtime; Ratio, Ratio of feature number; _SF_, selected feature of the algorithm; _#NIC_, # through the filtering of null-conditional dependence; _#SIC_, # through the filtering of single-conditional dependence.  
\end{table} 
Table 8: Variation in the number of selected features and running time with the ratio of feature space. features by filtering was \(2009\to 47\) (\(2.3\%\)) and \(2666\to 13\) (\(0.48\%\)). The number of features declined rapidly, meaning that the features are highly redundant.