Multivariate t-Mixtures-Model-based Cluster Analysis of BATSE Catalog Establishes Importance of All Observed Parameters, Confirms Five Distinct Ellipsoidal Sub-populations of Gamma Ray Bursts

Chattopadhyay, Souradeep; Maitra, Ranjan

doi:10.1093/mnras/sty1940

Cited by 14 publications

(29 citation statements)

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“…Early results indicate each of these strategies lead to comparable results in most cases. The use of k-means and Euclidean distances for applications such as in the case of clustering of GRBs [18], [20] is not always appropriate. Therefore, appropriate adjustments are required for handling non-spherically dispersed groups of data or datasets with unequal variances.…”

Section: Discussionmentioning

confidence: 99%

“…Hybrid methods of these two deletion schemes also exist. Yet another whole-data strategy [19], [20] clusters the complete records and classifies the incomplete records with rules based on the obtained grouping and a partial distance or marginal posterior probability approach. This scheme inherently assumes a missing-completely-at-random (MCAR) mechanism for the unobserved records and features.…”

Section: Introductionmentioning

confidence: 99%

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An efficientk‐means‐type algorithm for clustering datasets with incomplete records

Lithio

Maitra

2018

Statistical Analysis

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The k-means algorithm is arguably the most popular nonparametric clustering method but cannot generally be applied to datasets with incomplete records. The usual practice then is to either impute missing values under an assumed missing-completelyat-random mechanism or to ignore the incomplete records, and apply the algorithm on the resulting dataset. We develop an efficient version of the k-means algorithm that allows for clustering in the presence of incomplete records. Our extension is called kmmeans and reduces to the k-means algorithm when all records are complete. We also provide initialization strategies for our algorithm and methods to estimate the number of groups in the dataset. Illustrations and simulations demonstrate the efficacy of our approach in a variety of settings and patterns of missing data. Our methods are also applied to the analysis of activation images obtained from a functional Magnetic Resonance Imaging experiment. Index TermsAMELIA, CARP, FMRI, IMPUTATION, JUMP STATISTIC, k-MEANS++, k-POD, MICE, SOFT CONSTRAINTS, SDSS arXiv:1802.08363v2 [stat.ML] 8 Sep 2018 algorithm using partial distances. However, the repeated application of k-means at every iteration is computationally expensive. The literature is also sparse on estimating the number of groups K for data with incomplete records. This paper develops an efficient k-means-type clustering algorithm called k m -means that accommodates incomplete records and generalizes the algorithm of [38] that is popular in the statistical literature and software. Expressions for the objective function and its changes following the cluster reassignment of an observation play central roles in our generalization of the [38] algorithm. Section II also provides an initialization strategy for k m -means and an adaptation of the jump statistic [39] for estimating the number of groups. Section III comprehensively evaluates our methodology through a series of large-scale simulation experiments for datasets of different clustering complexities, sizes, numbers of groups, and with different missingness mechanisms and proportions. Section IV uses our methods to find the types of activated cerebral regions from several singletask functional Magnetic Resonance Imaging (fMRI) experiments. We conclude with some discussion in Section V. This paper also has an online supplement having additional illustrations on performance evaluations and other preliminary data analysis. Figures in the supplement referred to in this paper have the prefix "S-".

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

An efficientk‐means‐type algorithm for clustering datasets with incomplete records

Lithio

Maitra

2018

Statistical Analysis

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“…Chattopadhyay et al (2007) using k-means partitioning method and the Dirichlet process of mixture modelling with also the same six parameters (T 50 , T 90 , F t , H 32 , H 321 and P 256 ) found also three kind of GRBs. Chattopadhyay & Maitra (2017) carried out multidimensional analysis of the BATSE data with six parameters but only for 1599 GRBs because of the assumption that if F 4 is missing the F t variable cannot be used (in a recent paper they published similar results (Chattopadhyay & Maitra 2018)). Because of the same reason, all 1929 bursts was analyzed only in a five-parameter space.…”

Section: Discussionmentioning

confidence: 99%

Gaussian-mixture-model-based cluster analysis of gamma-ray bursts in the BATSE catalog

Tóth

Rácz

Horváth

2019

Monthly Notices of the Royal Astronomical Society

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Clustering is an important tool to describe gamma-ray bursts (GRBs). We analyzed the Final BATSE Catalog using Gaussian-mixture-models-based clustering methods for six variables (durations, peak flux, total fluence and spectral hardness ratios) that contain information on clustering. Our analysis found that the five kinds of GRBs previously found by other authors are only the cut groups of the previously well-known three types (short, long and intermediate in duration). The two short and intermediate duration groups differ mostly in the peak flux. Therefore, the reanalysis of the BATSE data finds similar group structures than previously. Because the brightness distribution is asymmetric and not correlated with durations or hardnesses the Gaussian mixture model cuts the Short and the Intermediate duration groups into two subgroups, the dim ones and the bright ones.

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“…On this data set, K ‐means with the Jump statistic was initially shown to find three groups but careful reapplication found K to be indeterminate. MBC found five ellipsoidally dispersed groups in the log 10 ‐transformed data set. Rather than applying K ‐means on the log 10 ‐transformed features, we investigate a data‐driven approach to choose feature‐specific transformations before applying K ‐means.…”

Section: Introductionmentioning

confidence: 99%

“…These analyses used only a few of the available features. The 25‐year‐old controversy between two or three GRB types is perhaps academic because careful model‐based clustering (MBC) and variable selection showed all available features as necessary. These studies also found five kinds of GRBs.…”

Section: Introductionmentioning

confidence: 99%

TiK‐means: Transformation‐infusedK‐means clustering for skewed groups

Berry

Maitra

2019

Statistical Analysis

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The K-means algorithm is extended to allow for partitioning of skewed groups. Our algorithm is called TiK-means and contributes a K-means-type algorithm that assigns observations to groups while estimating their skewness-transformation parameters. The resulting groups and transformation reveal general-structured clusters that can be explained by inverting the estimated transformation. Further, a modification of the jump statistic chooses the number of groups. Our algorithm is evaluated on simulated and real-life data sets and then applied to a long-standing astronomical dispute regarding the distinct kinds of gamma ray bursts. K E Y W O R D SBATSE, gamma ray bursts, inverse hyperbolic sine transformation, jump selection plot, K-means INTRODUCTIONClustering observations into distinct groups of homogeneous observations [19,24,36,37,49,56,61,64,67] is important for many applications, for example, taxonomical classification [53], market segmentation [28], color quantization of images [10,46], and software management [43]. The task is generally challenging with many heuristic [19,20,33,34,36,42] or more formal statistical model-based [24,50,51,65] approaches. However, the K-means algorithm [27,41,42] that finds partitions locally minimizing the within-sums-of-squares (WSS) is the most commonly used method. This algorithm depends on good initialization [10,44] and ideally suited to find homogeneous spherically dispersed groups. Further, K-means itself does not provide the number of groups K, for which many methods [26,36,39,46,54,59,62] exist. Nevertheless, it is used (in fact, more commonly abused) extensively because of its computational speed and simplicity. Many adaptations of K-means exist. The algorithm was recently modified for partially observed data sets [16,40]. The K-medoids algorithm [35,58] is a robust alternative that decrees each cluster center to be a medoid (or exemplar) that is an observation in the data set. The K-median Stat Anal Data Min: The ASA Data Sci Journal. 2019;12:223-233.wileyonlinelibrary.com/sam

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Multivariate t-Mixtures-Model-based Cluster Analysis of BATSE Catalog Establishes Importance of All Observed Parameters, Confirms Five Distinct Ellipsoidal Sub-populations of Gamma Ray Bursts

Abstract: 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

Cited by 14 publications

References 44 publications

An efficientk‐means‐type algorithm for clustering datasets with incomplete records

An efficientk‐means‐type algorithm for clustering datasets with incomplete records

Gaussian-mixture-model-based cluster analysis of gamma-ray bursts in the BATSE catalog

TiK‐means: Transformation‐infusedK‐means clustering for skewed groups

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