Galaxy Morphological Classification with Manifold Learning

We address the problem of morphological classification of galaxies from the Galaxy Zoo DECaLS dataset using classical machine learning techniques. Our approach employs a dimensionality reduction method followed by a classical classifier to categorize galaxies based on shape (cigar/in-between/round; edge-on/face-on) and texture (smooth/featured). We evaluate various dimensionality reduction methods, including Locally Linear Embedding (LLE), Isomap, Uniform Manifold Approximation and Projection (UMAP), t-SNE, and Principal Component Analysis (PCA). Our results demonstrate that most classical classifiers achieve their highest performance when combined with LLE, attaining accuracy comparable to that of simple neural networks. Moreover, in the case of shape classification, the three-dimensional representation remains interpretable, in contrast to the commonly observed loss of interpretability following nonlinear transformations. Additionally, we explore dimensionality reduction followed by k-means clustering to assess whether the data exhibits a natural tendency toward a specific number of clusters. We evaluate clustering performance using silhouette, elbow, Dunn, and Davies-Bouldin scores. While the Davies-Bouldin score indicates a slight preference for four clusters (closely aligning with classifications made by human astronomers) the other metrics do not support a distinct clustering structure.