# Context-Based Geodesic Dissimilarity Measure for Clustering Categorical Data
## 5 Discussion  
The results shown in Table 6 indicate that the proposed method shows better performance compared to the other measures, since it produces larger RI values than other measures for three of four datasets (Breast cancer, Soybean, and Lymphography), with the exception of the Mushroom dataset. That is, for Breast cancer, Soybean, and Lymphography datasets, the proposed method yields the highest scores 94.86%, 91.32%, and 63.33%, respectively. For the Mushroom dataset, various distance measures yield almost identical Rand indices with less than 1% point differences (GD 74.81%, AD 74.76%, GGD 74.16%, and the proposed method CGD 74.16%). This result demonstrates that the proposed measure generally facilitates the discovery of the natural groupings well compared to the other dissimilarity measures.  
Figure 4 presents a visual comparison using the result of the Rand index in Table 1 and categorization in Table 6. Except for the Mushroom dataset, in general, the dissimilarity measures with context-based method considering the correlation between categorical variables (such as AD and CGD) show better performances than others (such as GD and GGD). This result may indicate that since these three datasets (Breast cancer, Soybean, Lymphography) have highly correlated categorical variables (as shown in Table 4, that  
\begin{table}
\begin{tabular}{l c c c c} \hline \hline \multirow{2}{*}{**Data Set**} & \multicolumn{4}{c}{**Jaccard Index**} \\ \cline{2-5}  & **Gower Distance** & **Association-Based** & **Gower-Based** & **Proposed** \\  & **Distance (GD)** & **Dissimilarity** & **Geodesic Distance** & **Method** \\ \hline Breast cancer & 82.34\% & 85.36\% & 83.08\% & **90.97\%** \\ Soybean & 21.98\% & 34.81\% & 27.14\% & **35.22\%** \\ Lymphography & 24.60\% & 26.25\% & 29.80\% & **33.01\%** \\ Mushroom & **64.37\%** & 64.34\% & 63.92\% & 63.92\% \\ \hline \hline \end{tabular}
\end{table}
Table 6: _Cont._is, dependency factor (\(\rho(\mathbf{x})\)) for Breast cancer 100%, Soybean 61.18%, and Lymphography 47.76%), the context-based methods outperform the non-context-based methods. In addition, the dissimilarity measures that consider the concept of connectivity of data observations (such as GGD and CGD) perform better than those that do not (such as GD and AD). This result may also indicate that these three datasets have clusters of complex shapes in their manifold structure.  
In the case of the Mushroom dataset with a high value of dependency factor (97% as shown in Table 4), all four dissimilarity measures showed similar performances with slight differences. That is, the concept of context did not improve the performance of clustering. We might interpret it in a way that this dataset has many correlated variables but no high correlation between variables. The reason why the concept of connectivity was not effective in the performance of clustering for this dataset may also be interpreted in a way in which the dataset has significant noise and does not reveal complex shapes in a manifold structure.  
Overall, the proposed context-based geodesic dissimilarity (CGD) measure that considers the correlations among categorical variables and the concept of connectivity has, in general, better clustering quality when categorical variables are highly correlated and the dataset has clusters of complex shapes.