# Online Streaming Feature Selection via Conditional Independence
## 5 Experiments and Analysis
### Comparison of ConInd with Two Online Algorithms
#### 5.3.2 The Number of Selected Features and Running Time  
To further analyze the performance of the three algorithms in the number of selected features and running time, Table 6 presents their performances in the 14 datasets. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & & \multicolumn{6}{c}{**Algorithms**} \\ \cline{2-7}
**Datasets** & \multicolumn{2}{c}{_Alpha-investing_} & \multicolumn{2}{c}{_OSFS_} & \multicolumn{2}{c}{_ConInd_} \\ \cline{2-7}  & \# & **Time** & **\#** & **Time** & **\#** & **Time** \\ \hline wdbc & 20 & 0.0138 & 3 & 0.1577 & 3 & 0.2201 \\ colon & 1 & 0.0663 & 3 & 0.6778 & 3 & 8.6637 \\ lucas0 & 4 & 0.0008 & 4 & 0.0142 & 4 & 0.0304 \\
**sylya** & 70 & 1.6717 & **18** & **247.9366** & **24** & **189.8111** \\ ionosphere & 10 & 0.0147 & 4 & 0.1315 & 5 & 0.2215 \\
**cina0** & 8 & 0.1046 & **22** & **721.3638** & **30** & **407.7689** \\
**lucap0** & 10 & 0.0197 & **36** & **1.67 \(\times\) 10\({}^{3}\)** & **40** & **225.7368** \\ marti1 & 28 & 0.116 & 1 & 0.1081 & 1 & 0.1063 \\
**reged1** & 1 & 0.0417 & 13 & **121.2839** & **13** & **63.9082** \\ lung & 45 & 0.7523 & 11 & 420.5678 & 35 & \(3.48\times 10^{4}\) \\ prostate\_GE & 12 & 0.4308 & 3 & 7.7915 & 4 & \(4.72\times 10^{4}\) \\ leukemia & 1 & 0.4346 & 3 & 12.7647 & 8 & 593.3249 \\ arcene & 8 & 1.4139 & 5 & 20.8445 & 6 & 764.5764 \\ Smk\_can\_187 & 6 & 2.7929 & 4 & 42.8323 & 9 & 327.1579 \\ \hline \hline \end{tabular} \#, the number of selected features; Time, running time; \(\sum\#_{A}\) and \(\sum\#_{C}\), respectively, the sum of \# of Alpha-investing and _ConInd_.  
\end{table} 
Table 6: The number of selected features and running time. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Algorithms**} & \multicolumn{3}{c}{**Average Accuracy for Classifiers in 14 the Datasets (\%)**} & \multicolumn{2}{c}{**Average Accuracy (\%)**} \\ \hline \multirow{6}{*}{_OSFS_} & Complex & Medium & Simple & Linear & Quadratic & \multirow{2}{*}{Cubic SVM} \\  & Tree & Tree & SVM & SVM & & \\  & 88.22 & 88.58 & 88.62 & 90.44 & 87.60 & 87.64 \\  & Decision & Tree average: & 88.47 & & SVM average: 88.56 & 88.44 \\ \cline{2-7}  & Fine & Medium & Cubic & Bagged & Subspace & RUSBoosted \\  & KNN & KNN & KNN & Trees & discriminant & Trees \\  & 87.83 & 90.22 & 87.41 & 89.89 & 90.27 & 84.54 \\  & & KNN: 88.49 & & & ENSEMBLE: 88.23 & \\ \hline \multirow{6}{*}{_ConInd_} & Complex & Medium & Simple & Linear & \multirow{2}{*}{QuadraticSVM} & \multirow{2}{*}{Cubic SVM} \\  & Tree & Tree & Tree & SVM & & \\  & 89.14 & 89.19 & 88.05 & 90.94 & 87.50 & 87.46 \\ \cline{1-1}  & Decision & Tree average: & 88.79 & & SVM average: 88.63 & 88.95 \\ \cline{1-1} \cline{2-7}  & Fine & Medium & Cubic & Bagged & Subspace & RUSBoosted \\ \cline{1-1}  & KNN & KNN & KNN & Trees & discriminant & Trees \\ \cline{1-1}  & 88.79 & 90.42 & 90.07 & 90.05 & 90.63 & 85.14 \\ \cline{1-1}  & KNN & average: 89.76 & & & ENSEMBLE average: 88.61 & \\ \hline \hline \end{tabular}
\end{table} 
Table 5: _Cont._* _A summary of the number of selected features of the algorithms_ As shown in Figure 7, we observed that the prediction accuracy of _ConInd_ is higher than that of _Alpha-investing_ and _OSFS_ for most of the datasets. However, in Table 6, it is obvious that the number of selected features is greater in _Alpha-investing_ than in _ConInd_ and _OSFS_ for many datasets. In the 14 datasets, the ratio of the average number of features for _Alpha-investing_ is 242% higher than that for _ConInd_. The can be attributed to the following reasons: 1. The predictive accuracy of _Alpha-investing_ is low. This means that a part of the elements in _Markov blanket_ cannot be obtained. 2. For the _OSFS_ algorithm, during the redundant feature analysis phase, it is possible that non-redundant features are discarded under the condition of redundant features, resulting in low predictive accuracy and fewer features being selected. 3. For the _ConInd_ algorithm, there are two aspects that account for the large number of selected features.