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

astro-ph.EPMar 13, 2026

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

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

Organizations: Institute of Geosciences and Exact Sciences (IGCE), Unesp, Rio Claro, Brazil.

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.

Figures & tables

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 1 for the evaluated configurations and best-performing pipelines.

Feature Extraction Method	Feature Dimensions
MiniRocket	(22,288, 9,996)
FFT	(22,288, 201)
Wavelet Transform	(22,288, 401)
TSFresh	(22,288, 794)
Combined Features	(22,288, 11,375)

Table 1: Feature dimensions at each extraction step.

Features	Method	PCA	UMAP	Silhouette	DB	CH	Clusters
minirocket, wavelet, tsfresh	K-means	2	55	0.6830	0.4176	115173.8695	C0:9671, C1:4452, C2:2528, C3:5637
minirocket, tsfresh	Agglomerative	3	50	0.6830	0.4424	52505.8749	C0:7847, C1:10152, C2:2527, C3:1762
minirocket, fft, tsfresh	GMM	2	90	0.6810	0.4612	95632.9438	C0:9316, C1:5582, C2:4893, C3:2497
minirocket, tsfresh	K-means	2	20	0.6809	0.4338	109598.8835	C0:5618, C1:9647, C2:2528, C3:4495
minirocket, fft, tsfresh	K-means	2	60	0.6722	0.4334	106145.4625	C0:9685, C1:5625, C2:2525, C3:4453
minirocket, wavelet, tsfresh	GMM	2	50	0.6650	0.4308	104599.3775	C0:6254, C1:2528, C2:9208, C3:4298

Table 2: Pipeline Benchmark Table

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 2 with outliers repositioned using $K=24$ nearest neighbours.

Figure 4: As in Figure 2 but for the angle $\varphi_{2}$ .

Figure 5: The same context of Figure 4 with outliers repositioned using $K=24$ nearest neighbours.

Figure 6: Entropy map in the $(a,e)$ plane for $\varphi_{1}$ , computed from PCC-based soft labels using Eq. ( 4 ). The field is shown as the entropy per $(a,e)$ bin.

Figure 7: Entropy map in the $(a,e)$ plane for $\varphi_{2}$ , computed from PCC-based soft labels using Eq. ( 4 ). The field is shown as the entropy per $(a,e)$ bin.

Angle	Relabelled	ARI	NMI	Homogeneity	Completeness	V-measure
$\varphi_{1}$	$978$ (4.39%)	0.881	0.850	0.850	0.850	0.850
$\varphi_{2}$	$998$ (4.48%)	0.875	0.850	0.849	0.850	0.850

Table 3: Summary of ORG-D impact on the dynamical maps for

\varphi_{1}

and

\varphi_{2}

. For each angle we report the fraction of relabelled orbits and several agreement indices between pre– and post–ORG-D cluster assignments.

	Post 0	Post 1	Post 2	Post 3
Pre 0	9315	367	3	0
Pre 1	262	5222	129	12
Pre 2	4	137	4312	0
Pre 3	1	63	0	2461

Table 4: Confusion matrix between pre– and post–ORG-D labels for

\varphi_{1}

. Rows correspond to the original K-Means clusters and columns to the PCC-based ORG-D labels.

	Post 0	Post 1	Post 2	Post 3
Pre 0	8804	369	1	9
Pre 1	355	5248	82	12
Pre 2	0	112	4795	0
Pre 3	14	44	0	2443

Table 5: Confusion matrix between pre– and post–ORG-D labels for

\varphi_{2}

. Rows correspond to the original K-Means clusters and columns to the PCC-based ORG-D labels.

Angle	Feature Configuration	Silhouette	Davies–Bouldin	Calinski–Harabasz
$\varphi_{1}$	MiniRocket	0.5656	0.6593	42851.35
$\varphi_{1}$	MiniRocket + FFT	0.5761	0.6466	43808.21
$\varphi_{1}$	MiniRocket + FFT + Wavelet	0.5601	0.6695	35547.92
$\varphi_{1}$	Full Feature Stack	0.5186	0.6979	33617.59
$\varphi_{2}$	MiniRocket	0.6228	0.5108	89090.91
$\varphi_{2}$	MiniRocket + FFT	0.6191	0.5155	89704.76

Table 6: Controlled feature ablation under fixed DR and clustering hyperparameters for

\varphi_{1}

and

\varphi_{2}

Figure 8: Dynamical map obtained using the reversed DR ordering (PCA→UMAP) for $\varphi_{1}$ . Although this configuration yields slightly higher internal validation indices, the chaotic transition region exhibits increased fragmentation and irregular cluster boundaries. This illustrates that improved geometric compactness in the embedding space does not necessarily correspond to enhanced dynamical coherence.

Figure 9: Level curves of the Hamiltonian ( 10 ). Pink, green, and yellow indicate areas of the phase space corresponding to distinct regimes of motion: oscillation (pink), prograde circulation (yellow), and retrograde circulation (green). The red curves indicate the separatrix between the oscillatory and circulating regimes. Here, $m=l=1$ and $g=9.8$ (arbitrary units).

Figure 10: The resulting K-Means clustering, K = 3, for the simple pendulum time series, which is numerically computed in Figure 9

Figure 11: Dynamical maps representing the clustering of initial orbital conditions in the space of semi-major axis versus initial eccentricity. The top and bottom panels show the mapping for $\varphi_{1}$ and $\varphi_{2}$ , respectively. The colour-coded regions indicate different clusters obtained through the K-Means algorithm, capturing distinct dynamical behaviours indicated by C, L, Ch, and NP, meaning corotation resonance, Lindblad resonance, chaotic motion, and non-physical meaning, respectively. At the top panel, four coloured symbols of the initial conditions of representative temporal series of each region are shown (see Figure 12 ).

Figure 12: Time variations of the critical angles $\varphi_{1}$ and $\varphi_{2}$ corresponding to the initial conditions indicated the symbols given in Figure 11 . From top to bottom: full circle, star, rectangle, crux. The corresponding initial values of the semi-major axis and the eccentricity of each orbit are given at the top of the panels.

Dynamical Systems

Dynamical systems studies how states evolve over time, including stability, feedback, chaos, and transitions in physical, biological, and engineered systems.

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Satellite orbit prediction, which aims to forecast future orbital trajectories from historical observations, is important for collision warning and safe space operations. With advances in time-series forecasting, learning-based methods have emerged as a promising solution for satellite prediction. In orbital dynamics, a satellite state is typically described by position and velocity, where position characterizes trajectory geometry and velocity reflects its instantaneous direction and rate of change. However, most existing methods mainly focus on temporal dependencies within position sequences while rarely exploiting the intrinsic coupling between position and velocity, which is essential for modeling satellite motion. To this end, we propose OrbitNet, a velocity-aware representation learning method for accurate satellite orbit prediction. It lifts conventional position-sequence forecasting to a position-velocity coupled representation learning paradigm by exploiting relationships among satellite state variables. Specifically, we develop a velocity-coupled representation refinement strategy to enhance positional representations through cross-variable interactions between position and velocity. We further introduce orbital segment modeling, which partitions historical trajectories into temporal segments and performs segment-level temporal learning to capture local motion variations and long-range evolution patterns. Extensive experiments show that OrbitNet outperforms large time-series foundation models and representative general forecasting methods under both in-domain evaluation on Starlink and zero-shot evaluation across six unseen satellite constellations. We expect this work to encourage further exploration of satellite-aware representation learning for trajectory time-series forecasting.

Abstract

Dynamical Systems

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