Clustering Astronomical Orbital Synthetic Data Using Advanced Feature Extraction and Dimensionality Reduction Techniques

The analysis of orbital dynamics in celestial mechanics has traditionally relied on numerical simulations and stability metrics, such as those derived from Fourier analysis. These methods have proven effective for understanding resonance structures and stability zones, particularly in planetary systems like Saturn's satellite system. However, their computational cost and inability to scale with large datasets pose significant challenges in the era of modern astronomical simulations. Recent advances in machine learning have paved the way for more efficient and scalable approaches to analyzing high-dimensional time series data. Feature extraction techniques like TSFresh and the introduction of random convolutional kernels for time series analysis and clustering represent a further step in improving scalability and efficiency. These methods leverage randomly initialized convolutional filters to extract meaningful patterns without the need for extensive training, offering competitive performance in clustering tasks. Similarly, MiniRocket has established itself as a state-of-the-art feature extractor, transforming raw time series data into a high-dimensional feature space that captures both local and global temporal dynamics with exceptional efficiency.

The orbital dynamics of Saturn's satellite system offer a rich framework for studying orbital stability and resonance interactions. However, traditional analysis methods, such as Fourier analysis and stability metrics, struggle with the scale and complexity of modern datasets. To address these challenges, this study introduces a machine learning-based pipeline for clustering approximately 22,300 simulated satellite orbits. The key is using MiniRocket, which efficiently transforms 400 timesteps into a 9,996-dimensional feature space, capturing intricate temporal patterns. Combined with TSFresh automated feature extraction and dimensionality reduction techniques, the study achieves robust clustering analysis.

The core innovations of this study include applying MiniRocket for high-dimensional time series data feature extraction, combined with TSFresh and dimensionality reduction techniques for effective clustering analysis of complex orbital data. MiniRocket uses random convolutional kernels to transform raw time series data into a high-dimensional feature space, capturing both local and global temporal dynamics. TSFresh automates the extraction of interpretable features, combined with dimensionality reduction techniques like PCA and UMAP for comprehensive clustering analysis. These methods reveal stability regions and resonance structures in Saturn's satellite system.

• �� Use MiniRocket for feature extraction, transforming 400-step time series data into a 9,996-dimensional feature space.
• �� Use TSFresh to automate the extraction of interpretable features, combined with dimensionality reduction techniques like PCA and UMAP for comprehensive clustering analysis.
• �� Use clustering algorithms like K-means, Agglomerative, and GMM to validate the method's effectiveness.
• �� Under various feature combinations and dimensionality reduction configurations, the experimental results demonstrate efficient clustering capability on orbital data.

The experimental design includes using techniques such as MiniRocket, TSFresh, PCA, and UMAP, combined with clustering algorithms like K-means, Agglomerative, and GMM, to validate the method's effectiveness. Under various feature combinations and dimensionality reduction configurations, the experimental results demonstrate efficient clustering capability on orbital data, particularly achieving a Silhouette score of 0.6830, indicating effective clustering capability on orbital data.

The experimental results show that using features extracted by MiniRocket and TSFresh, combined with PCA and UMAP dimensionality reduction techniques, the K-means clustering algorithm achieved a Silhouette score of 0.6830, demonstrating effective clustering capability on orbital data. The clustering analysis identified four major dynamic regions in Saturn's satellite system, each corresponding to different resonance and stability characteristics. Experiments under various feature combinations and dimensionality reduction configurations validated MiniRocket's efficiency and accuracy in high-dimensional feature extraction, significantly outperforming traditional methods.

This methodology can be directly applied to other planetary systems' orbital data analysis, offering scalable analytical tools for future planetary exploration missions. By revealing stability and resonance structures in Saturn's satellite system, the research provides new insights into planetary dynamics' long-term evolution.

The study faces some limitations, such as UMAP's parameter selection significantly impacting results when handling nonlinear dynamic relationships, requiring further optimization. Additionally, the current clustering analysis does not fully integrate physical labels and dynamical diagnostics, limiting comprehensive understanding of orbital behavior. Future research directions include further optimizing UMAP and PCA parameter configurations to enhance clustering accuracy and stability; exploring the integration of more physical labels and dynamical diagnostics into clustering analysis; extending the methodology to other planetary systems' orbital data analysis.