Statistical Analysis of Dwarf Galaxies and Their Globular Clusters in the Local Volume

Chattopadhyay, Tanuka; Шарина, М. Е.; Karmakar, Pradip

doi:10.1088/0004-637x/724/1/678

Cited by 11 publications

(10 citation statements)

References 44 publications

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“…K-means cluster analysis (CA) is a multivariate unsupervised machine learning technique, basically applied for finding coherent groups in a data set (Chattopadhyay et al 2007(Chattopadhyay et al , 2010(Chattopadhyay et al , 2012(Chattopadhyay et al , 2019Das et al 2015). The main objective of this method is to find K clusters such that all the objects are distributed among those K clusters with the following two properties :…”

Section: K-means Cluster Analysismentioning

confidence: 99%

Structural properties and classification of variable stars: A study through unsupervised machine learning techniques

Sabatier¹,

Chattopadhyay²

2022

Preprint

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The advancement in the field of data science especially in machine learning along with vast databases of variable star projects like the Optical Gravitational Lensing Experiment (OGLE) encourages researchers to analyse as well as classify light curves of different variable stars automatically with efficiency. In the present work, we have demonstrated the relative performances of principal component analysis (PCA) and independent component analysis (ICA) applying to huge databases of OGLE variable star light curves after obtaining 1000 magnitudes between phase 0 to 1 with step length 0.001 for each light curves in identifying resonances for fundamental mode (FU) and first overtone (FO) Cepheids and in the classification of variable stars for Large Magellanic Cloud (LMC), Small Magellanic Cloud (SMC) as well as Milky Way (MW). We have seen that the performance of ICA is better for finding resonances for Cepheid variables as well as for accurately classifying large data sets of light curves than PCA. Using K-means clustering algorithm (CA) with respect to independent components (ICs), we have plotted periodluminosity diagrams and colour-magnitude diagrams separately for LMC, SMC and MW and found that ICA along with K-means CA is a very robust tool for classification as well as future prediction on the nature of light curves of variable stars.

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Section: K-means Cluster Analysismentioning

confidence: 99%

Structural properties and classification of variable stars: A study through unsupervised machine learning techniques

Sabatier¹,

Chattopadhyay²

2022

Preprint

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“…Presently there is no good method available for the determination of the optimum number of ICs. In this work, the optimum number of ICs have been chosen by the optimum number of Principal Components (PCs) (Albazzaz & Wang 2004;Chattopadhyay et al 2013;Eloyan & Ghosh 2013), to find m (m << p) (Chattopadhyay & Chattopadhyay 2007;Babu et al 2009;Fraix-Burnet et al 2010;Chattopadhyay et al 2010Chattopadhyay et al , 2013. We have first performed PCA to find the significant number of ICs.…”

Section: Independent Component Analysismentioning

confidence: 99%

Unsupervised Classification of Galaxies. I. Independent Component Analysis Feature Selection

Chattopadhyay

Fraix-Burnet

Mondal³

2019

PASP

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Subjective classification of galaxies can mislead us in the quest of the origin regarding formation and evolution of galaxies since this is necessarily limited to a few features. The human mind is not able to apprehend the complex correlations in a manyfold parameter space, and multivariate analyses are the best tools to understand the differences among various kinds of objects. In this series of papers, an objective classification of 362,923 galaxies from the Value Added Galaxy Catalogue (VAGC) is carried out with the help of two methods of multivariate analysis. First, Independent Component Analysis (ICA) is used to determine a set of derived independent components that are linear combinations of 47 observed features (viz. ionized lines, Lick indices, photometric and morphological properties, star formation rates etc.) of the galaxies. Subsequently, a K-means cluster analysis is applied on the nine independent components to obtain ten distinct and homogeneous groups. In this first paper, we describe the methods and the main results. It appears that the nine Independent Components represent a complete physical description of galaxies (velocity dispersion, ionisation, metallicity, surface brightness and structure). We find that our ten groups can be essentially placed into traditional and empirical classes (from colour-magnitude and emission-line diagnostic diagrams, early-vs late-types) despite the classical corresponding features (colour, line ratios and morphology) being not significantly correlated with the nine Independent Components. More detailed physical interpretation of the groups will be performed in subsequent papers.

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“…In this paper, the number of ICs is determined by the number of Principal Components (PCs) chosen (Albazzaz and Wang, 2004). To reduce the number of components Si from p to m (m<<p), one is to perform PCA (Babu et al 2009;Chattopadhyay & Chattopadhyay 2007;Fraix Burnet et al 2010;Chattopadhyay et al 2010). In this method also Yi's (i=1,2,...,p) vectors are found, which are linear combinations of Xi's (i=1,2,...,p) such that Yi's are uncorrelated.…”

Section: Independent Component Analysismentioning

confidence: 99%

“…Since only a few (say, m ≪ p ) of the IC components may explain a larger percentage of variation in the data, one can take only those m components instead of all p components. Then the GCs are classified on the basis of those m ICs using another exploratory data analytic method, namely K -means CA (Chattopadhyay et al 2009; Chattopadhyay, Sharina, & Karmakar 2010; Chattopadhyay et al 2012; Chattopadhyay & Karmakar 2013; Chattopadhyay, Mondal, & Chattopadhyay 2013) to find the homogeneous groups. In the end, the properties of the homogeneous groups of GCs allow us to propose a possible scenario for the formation of the GCs and their host galaxy.…”

Section: Introductionmentioning

confidence: 99%

Multivariate Analysis of the Globular Clusters in M87

Das

Chattopadhayay

Davoust

2015

Publ. Astron. Soc. Aust.

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An objective classification of 147 globular clusters in the inner region of the giant elliptical galaxy M87 is carried out with the help of two methods of multivariate analysis. First independent component analysis is used to determine a set of independent variables that are linear combinations of various observed parameters (mostly Lick indices) of the globular clusters. Next K-means cluster analysis is applied on the independent components, to find the optimum number of homogeneous groups having an underlying structure. The properties of the four groups of globular clusters thus uncovered are used to explain the formation mechanism of the host galaxy. It is suggested that M87 formed in two successive phases. First a monolithic collapse, which gave rise to an inner group of metal-rich clusters with little systematic rotation and an outer group of metal-poor clusters in eccentric orbits. In a second phase, the galaxy accreted low-mass satellites in a dissipationless fashion, from the gas of which the two other groups of globular clusters formed. Evidence is given for a blue stellar population in the more metal rich clusters, which we interpret by Helium enrichment. Finally, it is found that the clusters of M87 differ in some of their chemical properties (NaD, TiO1, light element abundances) from globular clusters in our Galaxy and M31.

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Statistical Analysis of Dwarf Galaxies and Their Globular Clusters in the Local Volume

Cited by 11 publications

References 44 publications

Structural properties and classification of variable stars: A study through unsupervised machine learning techniques

Structural properties and classification of variable stars: A study through unsupervised machine learning techniques

Unsupervised Classification of Galaxies. I. Independent Component Analysis Feature Selection

Multivariate Analysis of the Globular Clusters in M87

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