# Two-Stage Dimensionality Reduction for Social Media Engagement Classification
## 4 Experimental Results
### Benchmark Datasets  
The selected datasets, as listed in Table 1, are well-suited to this application as they exhibit a range of attributes including varying numbers of labels and features. The distribution of instances among classes is also a critical aspect to consider when evaluating the performance of a method. High-dimensional datasets and simpler ones were both intentionally included in order to assess the impact of dimensionality reduction in both scenarios. The results shown in this section are those in which the value of \(d\) provided the highest level of accuracy for the classification methods. The parameter values of the methods for each dataset are also displayed in Table 1.  
It was observed that the best classification results were obtained when the TSDR approach was used as a preprocessor on the datasets with the highest number of attributes, as demonstrated in Table 2. The results indicate that dimensionality reduction has a positive impact on the final results. In certain cases, the accuracy achieved by the proposed built-in discriminator function for classification was even comparable to that of the MLP, which is widely recognized for its strong generalization ability. As a matter of fact, considering that all datasets contain two classes and, therefore, that reduced subsets contain only two dimensions, the results are particularly positive because they possess comparable accuracy with much smaller datasets. In contrast, when \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Dataset** & **Features** & **Labels** & **Individuals** & **\(k\)** & **Stage 1 \(d\)** & **Stage 2 \(d\)** \\ \hline cancer\_dataset & 9 & 2 & [458, 241] & 26 & 7 & 2 \\ crab\_dataset & 6 & 2 & [100, 100] & 14 & 5 & 2 \\ glass\_dataset & 9 & 2 & [51, 163] & 15 & 7 & 2 \\ ovarian\_dataset & 100 & 2 & [121, 95] & 15 & 21 & 2 \\ \hline \hline \end{tabular} Note: \(d\) refers to the number of dimensions at the end of each stage.  
\end{table} 
Table 1: Selected benchmark datasets. the original datasets had low dimensionality, the classification methods performed better on the original datasets [25]. Another important performance indicator is the F1 score, calculated as the harmonic mean of precision (a measure of the number of correctly identified positive cases from all predicted positive cases) and recall (a measure of the number of correctly identified positive cases from all actual positive cases). This is a popular performance measure for classification when data are unbalanced, and provides a better measure of incorrectly classified cases than the accuracy metric [26]. As demonstrated in Tables 2 and 3, overall, the use of the TSDR discriminator as a classifier leads to an improved accuracy and F1 score compared to the original datasets. Both _k_-NN and MLP show considerable increases in accuracy when the TSDR subsets are used for classification. However, a comprehensive evaluation of the proposed method should also consider the training time required to reach the final results [27]. It is important to note that the use of the TSDR approach requires additional computational time, as it involves solving two major optimization problems. However, the larger the dataset is, the smaller the overall time for classification becomes. For instance, the MLP requires an average of 67 s to train on the original ovarian_dataset, whereas it only requires an average of 0.1 s to train on the TSDR subset. Considering that it takes 31 s on average to obtain the final subset, the MLP can produce a result in no more than 32 s when using the reduced subset, which is much faster than the time required for the original dataset. An analysis of the silhouette coefficient was also conducted in this study. The initial coefficient values for each dataset were calculated, as well for the subsets generated by the first (TSDR-1) and second (TSDR-2) stages of the proposed method.