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

Eraldo Pereira Marinho, Nelson Callegari Junior, Fabricio Aparecido Breve, Caetano Mazzoni Ranieri

Abstract

The dynamics of Saturn's satellite system offer a rich framework for studying orbital stability and resonance interactions. Traditional methods for analysing such systems, including Fourier analysis and stability metrics, struggle with the scale and complexity of modern datasets. This study introduces a machine learning-based pipeline for clustering approximately 22,300 simulated satellite orbits, addressing these challenges with advanced feature extraction and dimensionality reduction techniques. The key to this approach is using MiniRocket, which efficiently transforms 400 timesteps into a 9,996-dimensional feature space, capturing intricate temporal patterns. Additional automated feature extraction and dimensionality reduction techniques refine the data, enabling robust clustering analysis. This pipeline reveals stability regions, resonance structures, and other key behaviours in Saturn's satellite system, providing new insights into their long-term dynamical evolution. By integrating computational tools with traditional celestial mechanics techniques, this study offers a scalable and interpretable methodology for analysing large-scale orbital datasets and advancing the exploration of planetary dynamics.

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

Abstract

The dynamics of Saturn's satellite system offer a rich framework for studying orbital stability and resonance interactions. Traditional methods for analysing such systems, including Fourier analysis and stability metrics, struggle with the scale and complexity of modern datasets. This study introduces a machine learning-based pipeline for clustering approximately 22,300 simulated satellite orbits, addressing these challenges with advanced feature extraction and dimensionality reduction techniques. The key to this approach is using MiniRocket, which efficiently transforms 400 timesteps into a 9,996-dimensional feature space, capturing intricate temporal patterns. Additional automated feature extraction and dimensionality reduction techniques refine the data, enabling robust clustering analysis. This pipeline reveals stability regions, resonance structures, and other key behaviours in Saturn's satellite system, providing new insights into their long-term dynamical evolution. By integrating computational tools with traditional celestial mechanics techniques, this study offers a scalable and interpretable methodology for analysing large-scale orbital datasets and advancing the exploration of planetary dynamics.
Paper Structure (27 sections, 14 equations, 12 figures, 5 tables)

This paper contains 27 sections, 14 equations, 12 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Related work
  3. Methodology
  4. Machine Learning Pipeline
  5. Feature Extraction
  6. Dimensionality Reduction
  7. Principal Component Analysis (PCA)
  8. Uniform Manifold Approximation and Projection (UMAP)
  9. Alternative DR control (PaCMAP).
  10. Combining UMAP and PCA
  11. Clustering
  12. Distance Metrics
  13. Dynamic Time Warping (DTW):
  14. Alternative Metrics:
  15. Future Considerations:
  16. ...and 12 more sections

Figures (12)

  • Figure 1: Proposed pipeline for clustering time-series data. The data shape at each stage is shown to improve reproducibility. Feature extraction modules are optional and are enabled or disabled to form different feature subsets (ablation study). Only the selected subset is concatenated to build the final feature vector; see Table \ref{['tab:feature_dimensions']} for the evaluated configurations and best-performing pipelines.
  • Figure 2: Dynamical map representing the clustering of initial orbital conditions in the space of semi-major axis versus initial eccentricity for the angle $\varphi_1$. The colour bar indicates different clusters obtained through the K-Means algorithm, capturing distinct dynamical behaviours in the orbital phase space. The horizontal axis represents the semi-major axis, and the vertical axis represents the eccentricity. Outliers are evident throughout the dynamical map.
  • Figure 3: The same context of Figure \ref{['fig:dynamic_map_phi1']} with outliers repositioned using $K=24$ nearest neighbours.
  • Figure 4: As in Figure \ref{['fig:dynamic_map_phi1']} but for the angle $\varphi_2$.
  • Figure 5: The same context of Figure \ref{['fig:dynamic_map_phi2']} with outliers repositioned using $K=24$ nearest neighbours.
  • ...and 7 more figures