## 4 Result and Discussion  
Evaluating encoded features is vital for assessing autoencoder performance, as it reveals the quality of the data transformations and their impact on downstream tasks. This analysis helps determine how effectively the autoencoder compresses and represents the data, influencing the training efficiency and model accuracy. Comparing the correlation matrices of original and encoded features provides insight into the autoencoder's success in reducing redundancy and capturing the essential data structure, which informs future model and preprocessing choices. The encoded features, following preprocessing and transformation by the autoencoder, exhibit a notably distinct correlation matrix compared to the original data (Figure 4). The preprocessing phase has regularized the relationships between variables, as evidenced by the more uniform and moderated correlation coefficients. In the original dataset, variables demonstrate significant positive and negative correlations, reflective of the inherent interdependencies in raw environmental data. In contrast, the encoded features reveal a correlation structure. Figure 5 indicates a transformation towards a space where variables are more orthogonal or independent from one another. Figure 5 displays the correlation matrix for the encoded features, essential for understanding the interrelationships among variables in the dataset. Each matrix cell indicates  
Figure 5: Correlation matrix for encoded feature. the correlation between features, with 1 representing a perfect positive correlation and \(-1\) a perfect negative correlation. The shades of gray illustrate the strength of these correlations. This matrix is crucial for identifying highly correlated features that may be redundant, thereby aiding in feature selection and dimensionality reduction. This phase enhances the model's efficiency and accuracy by thoroughly analyzing the encoded features, ensuring that only the most relevant and independent features are utilized for training. This new structure within the encoded features implies a significant dimensional reduction and a distillation of the raw data into a form where the overlapping information is minimized. The correlation matrix from the encoded features, typically the output from an autoencoder's bottleneck layer, would show the relationship between each pair of encoded variables. In a well-trained autoencoder, especially one created to produce disentangled representations, we would expect to see a correlation matrix with lower off-diagonal values. This indicates that the encoded features are less correlated with each other, meaning the autoencoder has learned a representation that separates the underlying factors of the data. This is desirable because it suggests that each encoded feature captures a unique aspect of the input data, reducing redundancy and potentially improving the performance of downstream tasks. Furthermore, the correlation matrices of the original and encoded features serve as compelling visual evidence of the impact of preprocessing. Where the original data's correlation matrix shows extensive correlation coefficients and the encoded data's matrix demonstrates a more subdued variance, signaling a more refined feature set. The practical implications of these improvements are significant. In anomaly detection, models trained on less correlated and more disentangled features are likely to respond more to deviations from standard patterns, thereby enhancing their detection capabilities. In forecasting, the refined features can contribute to models that generalize more effectively from the training data to new, unseen data, leading to more accurate and reliable predictions. This enhanced ability to capture and represent the underlying structure of the data translates into better performance across various analytical tasks. The numerical research serves two purposes: (1) comparing fitting speed of different models; (2) testing regression model performance based on different models.