# Online Streaming Feature Selection via Conditional Independence
## 5 Experiments and Analysis
### Number of Features through Filtering of Conditional Dependence in the ConInd Algorithm  
To observe the variation of number of features through every filtering phases, i.e., null-conditional independence, single-conditional independence, and multi-conditional independence, Table 4 summarizes the variation of number of features with the three-layer filtering of conditional independence in _ConInd_ algorithm.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Datasets**} & \multicolumn{4}{c}{**Number of Features (\#)**} \\ \cline{2-5}  & \#IFS & \#NIC & \#SIC & \#MIC (SF) \\ \hline wdbc & 30 & 24 & 6 & 3 \\ colon & **2000** & **359** & **5** & **3** \\ lucas0 & 11 & 9 & 4 & 4 \\
**sylva** & **216** & **77** & **52** & **24** \\ ionosphere & 34 & 25 & 7 & 5 \\
**cina0** & **132** & **106** & **57** & **30** \\
**lucap0** & **143** & **94** & **49** & **40** \\ marti1 & 1024 & 1 & 1 & 1 \\
**reged1** & **999** & **541** & **16** & **13** \\ Lung & 3312 & 2318 & 212 & 35 \\ prosate\_GE & 5966 & 3182 & 24 & 4 \\ leukemia & 7066 & 2019 & 47 & 8 \\ arcene & 10,000 & 2666 & 13 & 6 \\ Smk\_can\_187 & 19,993 & 4924 & 55 & 9 \\ \hline \hline \end{tabular} \#, the number of selected features; \#IFS, the number of initial feature space; \#NIC, \# via the filtering of Null-conditional dependence; \#SIC, \# through the filtering of Single-conditional dependence; \#MIC, \# through the filtering of Multi-conditional dependence; SF; selected feature of running algorithm.  
\end{table}
Table 4: The number of features in filtering conditional independence.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Datasets** & \# & **Size** & **Dataset** & \# & **Size** \\ \hline wdbc & 30 & 569 & marti1 & 1024 & 500 \\ colon & 2000 & 62 & reged1 & 999 & 500 \\ lucas0 & 11 & 2000 & lung & 3312 & 203 \\ sylva & 216 & 13,086 & prosate\_GE & 5966 & 102 \\ ionosphere & 34 & 351 & leukemia & 7066 & 72 \\ cina0 & 132 & 16,033 & arcene & 10,000 & 100 \\ lucap0 & 143 & 2000 & Smk\_can\_187 & 19,993 & 187 \\ \hline \hline \end{tabular} \#, the number of features, Size, the number of instances.  
\end{table}
Table 3: Summary of the benchmark datasets.  
In Table 4, we can observe that the elements of the candidate feature set gradually decrease under the three-layer filtering of conditional dependence. The filtering efficiency of _ConInd_ increases with variation of feature number in the _CFS_. Moreover, the higher the dimension is, the more obvious the effect of _ConInd_ is because, with the increase of feature scale, irrelevant features and redundant features will rapidly increase. For the five datasets of sylva, cina0, lucap0, reged1, and Lung, the number of selected features in the _SF_ is greater than 10. This is because there are many features that are strongly relevant with class attribute in these datasets. For such datasets, the _ConInd_ algorithm often has shorter running time than _OSFS_, especially for the datasets highlighted in bold. The reason is that most of the features have been filtered by the filtering of single-conditional independence. In the multi-conditional filtering phase, the size of filtering condition is relatively smaller than _OSFS_. We discuss the details in Section 5.3.2.