# Enhanced Label Noise Filtering with Multiple Voting
## 5 Experimental Work
### Experimental Investigation  
Next, the experimental results of each dataset will be presented. Table 3 shows the comparisons of each filter in terms of cost on the Heart dataset. This table consists of three parts corresponding to three noise ratios (10%, 20%, and 30%). Under each noise ratio, the experiments were based on nine different cost matrices. Here, it was assumed that \(C_{00}=C_{11}=0\), so only \(C_{01}\) and \(C_{10}\) were needed to define a cost matrix. For example, in the second row of Table 3, 1:1 means \(C_{01}=C_{10}=1\), while 1:20 means \(C_{01}=1,C_{10}=20\). The last column in Table 3, Ave., represents the average cost of each filter based on all nine cost matrices. Table 3 shows that for all three noise ratios, CF\({}_{ODP}\) had the lowest average cost among all the CF based filters. Likewise, MF\({}_{ODP}\) was the best one among all the MF based filters. Moreover, under all the noise ratios and cost matrices, CF\({}_{ODP}\) and MF\({}_{ODP}\) outperformed other filters in most cases. This was in contrast to the other filters that heavily depend on cost matrices. For example, CF\({}_{CF}\) showed outstanding performance when \(C_{01}>C_{10}\), but its performance decreased dramatically when \(C_{10}\) increased. When the correlation between the cost and noise ratio was considered, we found that the cost of all the filters increased with noise ratio growth. However, compared with other filters, the cost increases of CF\({}_{ODP}\) and MF\({}_{ODP}\) were slow. In detail, when the noise ratio grew from 10% to 30%, the cost increase of CF\({}_{ODP}\) was 44, MF\({}_{ODP}\) was 12, while the cost increase of other filters was fast (for example, 97 for CF\({}_{1}\) and 102 for MF\({}_{1}\)). By further comparing CF\({}_{ODP}\) and MF\({}_{ODP}\), we found that under this dataset, CF\({}_{ODP}\) had a smaller average cost value. However, with the noise ratio increasing, the performance difference between them became small. Table 4 shows the cost comparisons of each filter based on the Wdbcdataset. The experimental conclusions in Table 4 are similar to those of Table 3. In most cases (under different noise ratios and cost matrices), CF\({}_{ODP}\) and MF\({}_{ODP}\) were the winners. In addition, their advantages were more obvious when the noise ratio and cost value increased. When the noise ratio was 10%, CF\({}_{ODP}\) outperformed MF\({}_{ODP}\). However, they showed similar performance when the noise ratio grew. Table 5 presents the experimental results based on the Wpbc dataset. Similar to the experimental conclusions from Tables 3 and 4, our approach could effectively improve the performance of the MF and CF based filters. In addition, CF\({}_{ODP}\) and MF\({}_{ODP}\) consistently worked well in different cases. Except for CF\({}_{ODP}\) and MF\({}_{ODP}\), the performance of the other filters usually had a dramatic decline when the noise ratio increased. Moreover, other filters had obvious performance changes when the relationship of \(C_{01}\) and \(C_{10}\) changed. For example, MF\({}_{MF}\) worked well when \(C_{10}>C_{01}\), but its performance became poor when \(C_{01}>C_{10}\). Tables 6-8 show the experimental results on the datasets of Spect, Spect1, and Promoter. Similar to the above analysis, these three tables clearly indicate the superiority of CF\({}_{ODP}\) and MF\({}_{ODP}\). ==ERROR: No output for this page== \begin{table} \
\begin{tabular}{c c c c c c c c c c c} \hline \hline  & & & & & & & & & & & \\ \hline  & 1:1 & 1:3 & 1:5 & 1:10 & 1:20 & 3:1 & 5:1 & 10:1 & 20:1 & Ave. \\ \hline CF & 10 & 19 & 29 & 52 & 99 & 20 & 31 & 57 & 109 & 47 \\ \hline CF\({}_{1}\) & 23 & 26 & 29 & 38 & 54 & 65 & 107 & 212 & 422 & 108 \\ \hline CF\({}_{MF}\) & 8 & 19 & 29 & 54 & 106 & 15 & 22 & 38 & 72 & 40 \\ \hline CF\({}_{CF}\) & 7 & 22 & 37 & 73 & 147 & 7 & 7 &\end{tabular}\end{table} 
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Several important conclusions can be drawn by summarizing the above evaluation results:  
(1) Selecting the optimal decision point by our approach could effectively improve the performance of an MVFilter.