## 4 Results and Discussion
### Evaluation of All Investigated Dimensionality Reduction Methods for Clustering Based on MoD Data
The convergence of learning error for the ANN model based on 2D-dimensional convolution layers can be seen in Figure 8. The initial training dataset augmented with synthetic samples by 3% for each cluster and 10% for the afternoon cluster can improve the convergence of the learning curve. Improvement in learning convergence for the ANN model based on 2-dimensional convolutions is only noticeable with the initial training dataset augmented with a lower percentage of synthetic samples. This suggests that artefacts generated within synthetic samples are not consistent with outlier regions in samples generated by real-world MoD-based data. Thus, this slows down the learning convergence since convolution layers had to learn more features for the outlier regions based on real-world MoD data and ones caused by artefacts in synthetic samples. The hidden abnormalities and artefacts in spatial features within synthetic samples slow down the learning convergence only if they are present in a higher percentage for each cluster. Thus, a higher synthetic sample percentage for each cluster requires more time to fit artefacts in their spatial features with samples generated by real-world MoD-based data. This increase in synthetic samples for each cluster combined with the initial training dataset reduces the speed of learning convergence over the entire learning process but still avoids _overfitting_. Figure 7: Convergence of learning error in the case of shallow ANN model based on FC layers. The initial training dataset is generated by real-world samples based on MoD data. The augmented training datasets represent combined initial datasets with the different percentages of samples from three clusters (morning, afternoon, and evening) generated by the proposed Conv2D VAEs framework. The augmentation of the largest afternoon clusters with synthetic samples improves the speed of learning convergence. It is possible to conclude that the proposed Conv2D VAE framework accurately learns the spatial features of this cluster. This largest afternoon cluster contains four hourly subclusters while all other clusters contain only two hourly subclusters. This suggests that the Conv2D VAE framework had more samples to learn from for the afternoon cluster. Thus, the proposed framework has produced high accuracy in generating spatial features for synthetic samples in the afternoon cluster. It is possible to notice that all other augmentations of specific clusters with higher percentages of synthetic samples have produced satisfying learning convergence results without causing _overfitting_. This proves that the proposed Conv2D VAE framework has learned a sufficiently accurate representation of spatial features for particular clusters based on which synthetic samples are generated. The augmentation of specific clusters with synthetic samples increases the differentiation between other clusters generated only using real-world MoD-based data. Simultaneously, all training datasets with synthetic samples for a particular cluster induce similar final learning errors. The augmentation of the initial training dataset for a particular cluster with synthetic samples containing features, which accurately approximate their real-world counterparts, tackles the negative effects of outlier samples on learning convergence. The 2-dimensional convolution layers use those outlier samples for a non-linear function approximation of all samples for classification tasks through the learning process. This attempt to fit the outlier samples consequently results in a longer and fluctuating learning convergence. The augmentation of particular clusters with synthetic samples with an accurate representation of these cluster spatial features can reduce the impact of those outlier samples on the learning process. This is especially noticeable in the case of clusters with a larger number of samples, e.g., afternoon cluster, and batch-oriented learning approaches.