## 3 Materials and Methods
### Cluster Analysis
#### 3.3.2 Cluster Analysis Using Unsupervised Artificial Models  
For the clustering analysis, we used three AI-based methods, including Autoencoder-Based Deep Clustering (ABDC) [50], Self-Organizing Maps (SOM) [51], and Deep Embedded Clustering (DEC) [52], to detect complex patterns and clusters that traditional algorithms like k-means often fail to capture, particularly in cases involving non-spherical or highly overlapping clusters.  
ABDC integrates unsupervised learning with deep neural networks to extract meaningful compact feature representation from high-dimensional data. In this framework, an autoencoder is first trained to compress the input into a low-dimensional latent space that captures the underlying structure and key patterns of the dataset. Once the latent representation is learned, the k-means algorithm is applied to this reduced feature space to identify initial cluster assignments. The model iteratively refines the learned features and the cluster assignments, by minimizing both reconstruction error and clustering loss. This feedback loop continuously aligns the learned feature space with the clustering task, leading to more coherent and accurate cluster formation. As a result, the approach is particularly effective for complex, nonlinear data where traditional clustering algorithms may struggle.  
SOM is an artificial neural network model, particularly well-suited for clustering and visualizing high-dimensional data. It projects complex data onto a low-dimensional, typically two-dimensional, grid, while preserving the topological relationships of the input space. The algorithm organizes input data based on similarity, so that neighboring nodes (or neurons) on the grid respond similarly to similar inputs, effectively mapping intricate data patterns into an interpretable spatial layout. This spatial organization enables SOM to reveal intrinsic structures and relationships within complex datasets, making them highly effective for exploratory data analysis and pattern recognition. Additionally, SOM are robust to noise and capable of capturing nonlinear relationships, allowing them to identify subtle clusters and data transitions.  
DEC is an advanced AI-based clustering method that integrates deep learning with unsupervised clustering. DEC begins by training an autoencoder to learn a compact, low-dimensional latent representation of the input data, effectively capturing complex and nonlinear patterns that traditional feature extraction methods may miss. Unlike conventional clustering algorithms that operate on raw data or fixed features, DEC simultaneously refines both the feature space and the cluster assignments through an iterative optimization process. DEC uses a soft assignment approach based on the Student's t-distribution, which assigns data points to clusters probabilistically rather than through hard assignments. This probabilistic approach allows the model to express uncertainty and subtle cluster memberships, improving robustness and flexibility. Through repeated iterations, DEC minimizes a clustering loss function that encourages the latent feature space to align more closely with the evolving cluster structure. This joint learning framework enables DEC to excel at clustering high-dimensional and complex datasets where conventional clustering methods often struggle.