Robustness Analysis of USmorph: I. Generalization Efficiency of Unsupervised Strategies and Supervised Learning in Galaxy Morphological Classification

TL;DR

This study provides a rigorous robustness analysis of the USmorph galaxy morphology framework, which integrates unsupervised feature extraction and clustering with supervised CNN classification. By systematically tuning the CAE (latent dimension $d=40$, $5\times5$ kernels), APCT for rotational invariance, and a bagging clustering set at $K=50$, the authors establish a stable pipeline whose labels are validated against low-dimensional structure (t-SNE) and physics-based parameter spaces. The supervised stage using GoogLeNet achieves $\sim$94% accuracy with consistent performance across data partitions, demonstrating reliable morphology classification suitable for upcoming surveys like CSST. Collectively, the work provides practical guidance on architectural choices and validation strategies to enable robust, scalable galaxy morphology analysis in large, unlabeled astronomical datasets.

Abstract

We conduct a systematic robustness analysis of the hybrid machine learning framework \texttt{USmorph}, which integrates unsupervised and supervised learning for galaxy morphological classification. Although \texttt{USmorph} has already been applied to nearly 100,000 $I$-band galaxy images in the COSMOS field ($0.2 < z < 1.2$, $I_{\mathrm{mag}} < 25$), the stability of its core modules has not been quantitatively assessed. Our tests show that the convolutional autoencoder (CAE) achieves the best performance in preserving structural information when adopting an intermediate network depth, $5\times5$ convolutional kernels, and a 40-dimensional latent representation. The adaptive polar coordinate transform (APCT) effectively enhances rotational invariance and improves the robustness of downstream tasks. In the unsupervised stage, a bagging clustering number of $K=50$ provides the optimal trade-off between classification granularity and labeling efficiency. For supervised learning, we employ GoogLeNet, which exhibits stable performance without overfitting. We validate the reliability of the final classifications through two independent tests: (1) the t-distributed stochastic neighbor embedding (t-SNE) visualization reveals clear clustering boundaries in the low-dimensional space; and (2) the morphological classifications are consistent with theoretical expectations of galaxy evolution, with both true and false positives showing unbiased distributions in the parameter space. These results demonstrate the strong robustness of the \texttt{USmorph} algorithm, providing guidance for its future application to the China Space Station Telescope (CSST) mission.

Figures (10)

• Figure 1: The distribution in the $I_{\rm{mag}}$--redshift ($z$) parameter space of galaxies in the COSMOS field. Marginalized number distributions along the $I_{\rm{mag}}$ and $z$ dimensions are projected at the top margin and right margin, respectively. The subsample satisfying the selection criteria $0.2 < z < 1.2$ and $I_{\rm{mag}} < 25$ is highlighted in red.
• Figure 2: CAE architecture with symmetric encoder-decoder structure. Encoder: $100\times100$ input undergoes two $5\times5$ convolutional layers (16 channels throughout) interleaved with max pooling, producing $25\times25\times16$ features. The resulting feature maps are flattened to a 40-dimensional vector that encodes galaxy features.
• Figure 3: Denoising results using filters of different sizes. From left to right, the images show: the original noisy images; images denoised using Gaussian filtering ($\sigma = 1$ and $2$); images denoised with CAE filters of sizes $3\times 3$, $5\times 5$, and $7\times 7$; and images denoised using only a single convolutional layer. The denoising performance of the $5\times 5$ and $7\times 7$ filter sizes is quite similar; however, some small and faint structures in galaxies may be overlooked when using the $7\times 7$ filter, as indicated by the arrows. The white bar in the first panel indicates an angular scale of $1\hbox{$^{\prime\prime}$}$ ($\approx 33$ pixels).
• Figure 4: Denoising results obtained with different configurations. The first column shows raw images of five randomly selected galaxies; the second column shows the denoising results with the configuration used in this manuscript ( Hidden dim=40); the third column shows the denoising results when the hidden dimension is reduced to 16; the fourth column shows the denoising results when 15 more training epochs are added; the fifth column shows the denoising results when using the binary cross-entropy loss function.
• Figure 5: Left: Distribution of mean pixel-value differences for galaxy images before and after $90^\circ$ rotation, comparing cases with (blue) and without (grey) APCT. Each value represents the per-galaxy average of absolute differences $|\Delta I(x,y)|$ across all pixel positions. APCT results in near-zero differences, demonstrating strong rotational invariance. In contrast, non-APCT images exhibit significant deviations due to imperfect centrosymmetry. Right: Example galaxy processed with APCT under rotations of $0^\circ$, $90^\circ$, $180^\circ$, and $270^\circ$, showing that the APCT-processed images remain nearly unchanged, regardless of the rotation of the original input.