Clustering methods are an important tool to enumerate and describe the different coherent kinds of Gamma Ray Bursts (GRBs). But their performance can be affected by a number of factors such as the choice of clustering algorithm and inherent associated assumptions, the inclusion of variables in clustering, nature of initialization methods used or the iterative algorithm or the criterion used to judge the optimal number of groups supported by the data. We analyzed GRBs from the BATSE 4Br catalog using k-means and Gaussian Mixture Models-based clustering methods and found that after accounting for all the above factors, all six variables -different subsets of which have been used in the literature -and that are, namely, the flux duration variables (T 50 , T 90 ), the peak flux (P 256 ) measured in 256-millisecond bins, the total fluence (F t ) and the spectral hardness ratios (H 32 and H 321 ) contain information on clustering. Further, our analysis found evidence of five different kinds of GRBs and that these groups have different kinds of dispersions in terms of shape, size and orientation. In terms of duration, fluence and spectrum, the five types of GRBs were characterized as intermediate/faint/intermediate, long/intermediate/soft, intermediate/intermediate/intermediate, short/faint/hard and long/bright/intermediate.

Determining the kinds of gamma-ray bursts (GRBs) has been of interest to astronomers for many years. We analyzed 1599 GRBs from the Burst and Transient Source Experiment (BATSE) 4Br catalogue using t-mixtures-model-based clustering on all nine observed parameters (T 50 , T 90

Understanding the physical and evolutionary properties of Hot Stellar Systems (HSS) is a major challenge in astronomy. We studied the dataset on 13 456 HSS of Misgeld & Hilker (2011, MNRAS, 414, 3 699) that includes 12 763 candidate globular clusters using stellar mass ( $M_s$ ), effective radius ( $R_e$ ) and mass-to-luminosity ratio ( $M_s/L_\nu$ ), and found multi-layered homogeneous grouping among these stellar systems. Our methods elicited eight homogeneous ellipsoidal groups at the finest sub-group level. Some of these groups have high overlap and were merged through a multi-phased syncytial algorithm motivated from Almodóvar-Rivera & Maitra (2020, JMLR, 21, 1). Five groups were merged in the first phase, resulting in three complex-structured groups. Our algorithm determined further complex structure and permitted another merging phase, revealing two complex-structured groups at the highest level. A nonparametric bootstrap procedure was also used to estimate the confidence of each of our group assignments. These assignments generally had high confidence in classification, indicating great degree of certainty of the HSS assignments into our complex-structured groups. The physical and kinematic properties of the two groups were assessed in terms of $M_s$ , $R_e$ , surface density and $M_s/L_\nu$ . The first group consisted of older, smaller and less bright HSS while the second group consisted of brighter and younger HSS. Our analysis provides novel insight into the physical and evolutionary properties of HSS and also helps understand physical and evolutionary properties of candidate globular clusters. Further, the candidate globular clusters (GCs) are seen to have very high chance of really being GCs rather than dwarfs or dwarf ellipticals that are also indicated to be quite distinct from each other.