# A Visual Mining Approach to Improved Multiple-Instance Learning
## 4 Visual Multiple-Instance Learning
### Creating a Multiple-Instance Tree (MILTree)
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & **MT-Med** & **MT-SI** & **MI-SVM** & **mi-SVM** & **EMDD** & **DD-SVM** & **MILES** & **MILED** \\ \hline MT-Med & 0.000 & 1.112 & 12.94 & 8.693 & 12.05 & 5.450 & 4.530 & 2.825 \\ \hline MT-SI & \(-\)1.112 & 0.000 & 11.83 & 7.580 & 10.94 & 4.338 & 3.418 & 1.713 \\ \hline MI-SVM & \(-\)12.94 & \(-\)11.83 & 0.000 & \(-\)4.250 & \(-\)0.895 & \(-\)7.492 & \(-\)8.412 & \(-\)10.12 \\ \hline mi-SVM & \(-\)8.693 & \(-\)7.580 & 4.250 & 0.000 & 3.355 & \(-\)3.242 & \(-\)4.163 & \(-\)5.867 \\ \hline EMDD & \(-\)12.05 & \(-\)10.94 & 0.895 & \(-\)3.355 & 0.000 & \(-\)6.597 & \(-\)7.518 & \(-\)9.222 \\ \hline DD-SVM & \(-\)5.450 & \(-\)4.338 & 7.492 & 3.242 & 6.597 & 0.000 & \(-\)0.920 & \(-\)2.625 \\ \hline MILES & \(-\)4.530 & \(-\)3.418 & 8.412 & 4.163 & 7.518 & 0.920 & 0.000 & \(-\)1.705 \\ \hline MILDE & \(-\)2.825 & \(-\)1.713 & 10.12 & 5.867 & 9.222 & 2.625 & 1.705 & 0.000 \\ \hline \hline \end{tabular}
\end{table} 
Table 16: Contrast Estimation between the methods on each row with respect to the methods on each column, considering different datasets. Positive values indicate that the method in the row presented higher average accuracy than the method in the column. The proposed methods are MILTree-Med (MT-Med) and MILTree-SI (MT-SI). \begin{table}
\begin{tabular}{c c c} \hline \hline \(i\) & **Method** & **[PERSON]** & **[PERSON]** \\ \hline
7 & MI-SVM & **0.001** & **0.022** \\
6 & EMDD & **0.001** & **0.022** \\
5 & mi-SVM & **0.001** & **0.022** \\
4 & DD-SVM & **0.010** & **0.022** \\
3 & MILTree-SI & 0.354 & **0.022** \\
2 & MILES & 0.413 & **0.022** \\
1 & MILLE & 0.585 & 0.050 \\ \hline \hline \end{tabular} Bold values indicate the methods that present statistically lower accuracies when compared to MILTree-Med.

\end{table} 
Table 17: [PERSON]’s and [PERSON]’s test results for \(\alpha=0.05\) (Friedman). [PERSON]’s procedure rejects those hypotheses for \(p\leq 0.01\); [PERSON]’s procedure rejects those hypotheses for \(p\leq 0.022\). \begin{table}
\begin{tabular}{c c} \hline \hline
**Method** & **Ranking** \\ \hline MILTree-Med & 2.3571 \\ MILDE & 3.0714 \\ MILES & 3.4285 \\ MILTree-SI & 3.5714 \\ DD-SVM & 4.5714 \\ mi-SVM & 5.5714 \\ EMDD & 6.2142 \\ MI-SVM & 7.2142 \\ \hline \hline \end{tabular}
\end{table} 
Table 15: Average rankings. [PERSON] statistic 23.5 according to \(\chi\)-square with 7 degrees of freedom; \(p=0.0014\). Besides producing comparable or better accuracy with respect to state-of-the-art methods, our MILTree-based techniques allow the user to take part in every step of the multiple-instance classification process, such as data exploration, sampling for training, model updating (both automatic and manual) and validating the classification model. The method has been tested on datasets of various sizes, and users have found positive aspects of the approach, as well as limitations, mainly related to interactive functions in the current prototype system. Our methods and techniques combined are, to the best of our knowledge, the first complete set of visual tools to support MIL learning. Because we deal with data that are organized in multiple levels (bag and instance levels in the case of MIL), future work can explore related tasks, such as hierarchical clustering or learning from label proportions [44; 45], in which the data are organized in groups that can be viewed as bags, and only the proportion of each class in each bag is known. An alternative high precision way of organizing the samples in bags might be to use multidimensional projections. While we would lose the hierarchical organization, there might be benefits in the precision of the display. This is a venue worth pursuing. A visual alternative for very large datasets is also an expected development from this work. Conceptualization, methodology, formal analysis and writing: S.C., M.P. and R.M. ; software and adaptation of visualization, S.C.; supervision and project administration, M.P. and R.M. ; funding acquisition, R.M.