# Dependence Representation Learning with Convolutional Neural Networks and 2D Histograms
## 5 Conclusions  
We have proposed a dependence representation learning algorithm. Our method allows a neural network to extract dependence representations from visualizations of random variable pairs. Empirically, we showed that our CNNs can classify dependence types and predict correlations from 2D histogram inputs. We also visualized the learned dependence representation spaces. Finally, we applied our dependence representation learning algorithm to feature generation. Following experimental setup used in the previous AutoLearn, we show that our proposed method outperformed the AutoLearn in terms of average classification accuracy while generating half as many features. As future work, we plan to apply \begin{table}
\begin{tabular}{l l l l l} \hline \hline \multirow{2}{*}{} & Average & 94.44 & **95.24** & **95.24** \\ \cline{2-5}  & KNN & **94.44** & **94.44** & **94.44** \\  & LR & **94.44** & **94.44** & **94.44** \\  & SVM-L & 94.44 & **100.0** & 94.44 \\  & SVM-P & **100.0** & **100.0** & **100.0** \\  & RF & 94.44 & 94.44 & **100.0** \\  & AB & **100.0** & **100.0** & 94.44 \\  & DT & 83.33 & 83.33 & **88.89** \\ \hline \multirow{7}{*}{Spectf} & Average & 81.49 & 82.73 & **83.98** \\ \cline{2-5}  & KNN & 71.30 & 79.13 & **80.87** \\ \cline{1-1}  & LR & 86.09 & 85.22 & **86.96** \\ \cline{1-1}  & SVM-L & 86.96 & 85.22 & **87.83** \\ \cline{1-1}  & SVM-P & 71.30 & 73.04 & **74.78** \\ \cline{1-1}  & RF & **86.96** & **86.96** & 85.22 \\ \cline{1-1}  & AB & 84.35 & 83.48 & **87.83** \\ \cline{1-1}  & DT & 83.48 & **86.09** & 84.35 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: \(Cont.\) \begin{table}
\begin{tabular}{l l l l l} \hline \hline
**Dataset** & **Classifier** & **Original** & **AutoLearn** & **Proposed** \\ \hline \multirow{7}{*}{Leukaemia} & Average & 85.71 & 82.14 & **87.50** \\ \cline{2-5}  & KNN & **87.50** & **87.50** & **87.50** \\  & LR & **87.50** & **87.50** & **87.50** \\  & SVM-P & 62.50 & **75.00** & **75.00** \\  & RF & **87.50** & 75.00 & **87.50** \\  & AB & **100.0** & 75.00 & **100.0** \\  & DT & **87.50** & **87.50** & **87.50** \\ \hline \multirow{7}{*}{Arcene} & Average & 87.14 & **88.57** & 86.43 \\ \cline{1-1} \cline{2-5}  & KNN & 90.00 & 85.00 & **95.00** \\ \cline{1-1}  & LR & 85.00 & **90.00** & **90.00** \\ \cline{1-1}  & SVM-L & 85.00 & **90.00** & 85.00 \\ \cline{1-1}  & SVM-P & 90.00 & **95.00** & 90.00 \\ \cline{1-1}  & RF & 90.00 & **95.00** & 80.00 \\ \cline{1-1}  & AB & **90.00** & 80.00 & 80.00 \\ \cline{1-1}  & DT & 80.00 & 85.00 & **85.00** \\ \hline \multirow{7}{*}{Banknote} & Average & 99.17 & 99.48 & **99.69** \\ \cline{1-1} \cline{2-5}  & KNN & 99.28 & **100.0** & **100.0** \\ \cline{1-1}  & LR & 99.28 & 99.28 & **100.0** \\ \cline{1-1}  & SVM-L & 99.28 & **100.0** & **100.0** \\ \cline{1-1}  & SVM-P & 99.28 & 99.28 & **100.0** \\ \cline{1-1}  & RF & 99.28 & 98.55 & **100.0** \\ \cline{1-1}  & AB & 99.28 & **100.0** & 99.28 \\ \cline{1-1}  & DT & 98.55 & **99.28** & 98.55 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Performance comparison in terms of classification accuracy (3/3). our method to feature selection, which is the process of selecting an optimal subset of relevant features for use in constructing machine learning models. All authors made contributions to this work. H.-j.K. contributed to the organization of the research as well as the final manuscript preparation. T.K. proposed the original idea, conducted data processing, and wrote the original draft of this work. Conceptualization, T.K. and H.-j.K.; methodology, T.K. ; software, T.K. ; validation, T.K. and H.-j.K.; formal analysis, T.K. and H.-j.K.; investigation, T.K. ; resources, H.-j.K.; data curation, T.K. ; writing--original draft preparation, T.K. ; writing--review and editing, H.-j.K.; visualization, T.K. ; supervision, H.-j.K.; project administration, H.-j.K.; funding acquisition, H.-j.K. All authors have read and agreed to the published version of the manuscript.