# On the Influence of Data Imbalance on Supervised Gaussian Mixture Models
## 6 Conclusions  
Class imbalance can pose a significant challenge in many classification problems. In this paper, we investigated the effect of imbalanced data on supervised Gaussian mixture models (SGMMs) in classification problems. It has been established that this imbalance significantly hampers the performance of SGMMs, emphasizing the need for effective mitigation strategies.  
This study specifically focuses on imbalanced two-class data, where the minority class is of primary importance, within the framework of Gaussian mixtures. The investigation centers on two prominent SGMMs, namely EDDA and MclustDA models. Additionally, a range of approaches to tackle class imbalance were presented, including threshold-based methods and sampling-based techniques.  
The empirical results provide substantial insights into the necessity of addressing class imbalance for both the EDDA and MclustDA models. Notably, both threshold-based and sampling-based approaches exhibit marked improvements in classification accuracy for the minority class. Among these strategies, threshold-based adjustments, particularly those derived from cost-sensitive learning, stand out as highly recommended. This is due to their ability to enhance performance without necessitating model re-estimation, avoiding the loss of valuable training data, as in downsampling, or the artificial creation of data, as in oversampling techniques.  
Table 7 offers a concise overview of various techniques explored in this paper for handling imbalanced data. Several crucial aspects deemed relevant in practical applications are considered, and a raw qualitative assessment is provided.  
The contributions of this paper collectively serve as a valuable resource for practitioners and researchers, offering effective strategies to enhance the performance of supervised Gaussian mixtures in scenarios characterized by class imbalance.  
\begin{table}
\begin{tabular}{l l l l l l l} \hline \hline
**Techniques** & **Accuracy** & \begin{tabular}{l} **Computational** \\ **Speed** \\ \end{tabular} & \
\begin{tabular}{l} **Ease of** \\ **Implementation** \\ \end{tabular} &
\begin{tabular}{l} **Hyperparameter** \\ **Tuning** \\ \end{tabular} & **Scalability** & **Parallelization** \\ \hline costSens & \(\star\star\star\) & \(\star\star\star\) & \(\star\star\star\) & \(\star\star\star\) & — \\ adjPriorThreshold & \(\star\) & \(\star\star\) & \(\star\) & \(\star\star\) & \(\star\star\) & \(\star\star\) \\ optThreshold & \(\star\star\star\) & \(\star\) & \(\star\star\) & \(\star\) & \(\star\star\) & \(\star\star\) \\ downSamp & \(\star\star\star\) & \(\star\star\) & \(\star\star\) & — & \(\star\star\) & — \\ upSamp & \(\star\star\) & \(\star\star\) & \(\star\star\) & — & \(\star\star\) & — \\ smote & \(\star\star\) & \(\star\star\) & \(\star\star\) & — & \(\star\) & — \\ \hline \hline \end{tabular}
\end{table}
Table 7: Summary of specific techniques for handling imbalanced two-class data in supervised GMMs (higher number of \(\star\) indicates better rating; — indicates not applicable).  
Figure 4: Performance outcomes for various models and methods addressing class imbalance on the hypothyroid dataset.  
**Funding:** This research received no external funding.  
**Data Availability Statement:** All the analyses have been conducted in R [16] using the mclust package [14; 15]. Code to reproduce the analyses is available in a GitHub repository at [[https://github.com/luca-scr/SGMM_Class_Imbalance](https://github.com/luca-scr/SGMM_Class_Imbalance)]([https://github.com/luca-scr/SGMM_Class_Imbalance](https://github.com/luca-scr/SGMM_Class_Imbalance)) (accessed on 15 October 2023).  
**Conflicts of Interest:** The author declares no conflict of interest.