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

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.

💡 Research Summary

The paper presents a scalable machine‑learning pipeline for clustering a large synthetic dataset of Saturnian satellite orbits (≈22,300 time‑series, each 400 steps long). Traditional dynamical analysis—Fourier spectra, stability indices, or dynamical maps—struggles with such volume and dimensionality. To overcome these limitations, the authors combine several modern time‑series feature extraction methods, dimensionality‑reduction techniques, and unsupervised clustering algorithms.

Feature extraction is the cornerstone of the approach. MiniRocket, a state‑of‑the‑art random convolutional kernel method originally designed for classification, is employed to transform each 400‑step series (two angular variables φ₁ and φ₂) into a 9,996‑dimensional vector. MiniRocket’s fixed set of carefully dilated kernels captures both local and global temporal patterns while remaining computationally cheap (up to 75× faster than its predecessor). Complementary extractors—Fast Fourier Transform (FFT), Discrete Wavelet Transform (DWT), and TSFresh—are also evaluated. FFT provides a compact frequency representation, DWT adds time‑frequency localization, and TSFresh automatically computes 794 statistical, entropy‑based, and distributional features. Prior to each extraction step, per‑series Z‑score normalization is applied to eliminate scale differences and focus the downstream distance metrics on shape rather than magnitude.

Because the concatenated feature space can exceed 11,000 dimensions, the authors apply a two‑stage dimensionality reduction. Principal Component Analysis (PCA) first reduces linear redundancy, preserving the bulk of variance while shrinking the dimensionality to a few hundred components. Uniform Manifold Approximation and Projection (UMAP) then maps the PCA‑reduced data onto a 2‑ or 3‑dimensional manifold, preserving both local neighborhoods and global topology. As a robustness check, PaCMAP is substituted for UMAP in a limited set of experiments, yielding comparable results.

Clustering is performed with three algorithms: K‑means, Agglomerative Hierarchical Clustering, and Gaussian Mixture Models (GMM). Hyper‑parameters (number of clusters, PCA variance retained, UMAP neighbor count, etc.) are tuned via exhaustive grid search. The best configuration—MiniRocket + TSFresh features, PCA + UMAP reduction, followed by K‑means with k = 4—achieves a Silhouette score of 0.683, Davies‑Bouldin index of 0.418, and Calinski‑Harabasz index of ~115 000, outperforming pipelines that omit MiniRocket or use only FFT.

Interpretation of the clusters reveals physically meaningful structures. Two of the clusters correspond to the Corotation and Lindblad resonances (specific ranges of φ₁ and φ₂), representing long‑term stable zones where test satellites remain trapped. Other clusters capture non‑resonant or chaotic regions with higher orbital element variability. These findings mirror classic dynamical maps but are obtained automatically, allowing rapid analysis of thousands of simulated orbits without manual parameter sweeps.

Ablation studies demonstrate that MiniRocket alone already yields high-quality clusters; however, adding FFT and TSFresh refines the separation of subtle dynamical regimes. The authors also discuss computational efficiency: processing the full dataset through MiniRocket, PCA, UMAP, and K‑means takes on the order of minutes on a standard workstation, a stark contrast to the hours or days required for traditional spectral‑analysis pipelines.

In summary, the work showcases how recent advances in time‑series representation learning (MiniRocket, TSFresh) and manifold learning (UMAP) can be integrated into a reproducible, end‑to‑end workflow for astronomical dynamics. The methodology is not limited to Saturn’s moons; it can be extended to other planetary systems, asteroid families, or any large‑scale N‑body simulation where orbital elements evolve over time. By bridging machine learning with celestial mechanics, the paper opens a path toward more automated, scalable, and insightful exploration of planetary system evolution.