A comparative study of Euclidean and spherical clustering techniques for BATSE gamma-ray burst data

ABSTRACT This study investigates the classification of gamma-ray bursts (GRBs) using spherical clustering techniques, focusing on the burst and transient source experiment (BATSE) data set with features T90, hardness, and F1. Spherical k-means and von Mises–Fisher model-based clustering effectively recover the long, short, and intermediate GRB classes, achieving high adjusted Rand index (ARI) of 0.65 and normalized mutual information (NMI) of 0.50, with silhouette scores of 0.70–0.74 and linear discriminant analysis (LDA) accuracies of 0.97–0.98. These methods outperform traditional Euclidean approaches, such as Gaussian mixture model-based clustering (GMMBC) and standard k-means, which yield accuracies of 72.38 per cent and 68.57 per cent, respectively, compared to 97.92 per cent for von Mises–Fisher and 90.11 per cent for spherical k-means. The optimal number of clusters, determined to be three using elbow and curvature-based methods, supports the tripartite classification proposed by Horváth. Spherical clustering’s robustness to magnitude variations, driven by cosine similarity, mitigates biases from cosmological and instrumental effects, providing clearer class separation. The intermediate GRB class, particularly well-defined by the von Mises–Fisher method, exhibits unique spectral and directional properties, potentially linked to neutron star-white dwarf mergers, as supported by observations like GRB 170817A. Exploratory analysis of galactic coordinates hints at spatial clustering, possibly reflecting cosmic structure. These findings challenge the traditional GRB dichotomy and advocate for incorporating the intermediate class into physical models. Future work will integrate redshift measurements and multiwavelength observations to further validate and refine these classifications.