An automatic unsupervised classification of 1318 light curves of variable stars, including eclipsing binaries along with some possible pulsating stars, has been performed using k-medoids clustering method. This separates the stars according to their geometrical configuration in a more scientific way compared to the subjective traditional classification scheme. The light curves in the Galaxy, subjectively grouped in four categories (EA, EB, EW, PUL) in Miller et al. (2010), have been found to consist of two optimum groups containing primarily eclipsing binaries corresponding to bright, massive systems and fainter, less massive systems. Our technique has been assessed in terms of clustering accuracy measure the Average Silhouette Width, which shows the resulting clustering pattern is quite good.

We consider the problem related to clustering of gamma-ray bursts (from "BATSE" catalogue) through kernel principal component analysis in which our proposed kernel outperforms results of other competent kernels in terms of clustering accuracy and we obtain three physically interpretable groups of gamma-ray bursts. The effectivity of the suggested kernel in combination with kernel principal component analysis in revealing natural clusters in noisy and nonlinear data while reducing the dimension of the data is also explored in two simulated data sets.keywords: clustering; gamma ray bursts; kernel principal component analysis; positive definite kernel.

Area of study is the formation mechanism of the present-day population of elliptical galaxies, in the context of hierarchical cosmological models accompanied by accretion and minor mergers. The present work investigates the formation and evolution of several components of the nearby massive early-type galaxies (ETGs) through cross-correlation function (CCF), using the spatial parameters right ascension (RA) and declination (DEC), and the intrinsic parameters mass (M * ) and size. According to the astrophysical terminology, here these variables, namely mass, size, RA and DEC are termed as parameters, whereas the unknown constants involved in the kernel function are called hyperparameters. Throughout this paper, the parameter size is used to represent the effective radius (R e ). Following Huang et al. (2013a), each nearby ETG is divided into three parts on the basis of its R e value. We study the CCF between each of these three components of nearby massive ETGs and the ETGs in the high redshift range, 0.5 < z ≤ 2.7. It is found that the innermost components of nearby ETGs are highly correlated with ETGs in the redshift range, 2 < z ≤ 2.7, known as 'red nuggets'. The intermediate and the outermost parts have moderate correlations with ETGs in the redshift range, 0.5 < z ≤ 0.75. The quantitative measures are highly consistent with the two phase formation scenario of nearby massive ETGs, as suggested by various authors, and resolve the conflict raised in a previous work (De, Chattopadhyay, & Chattopadhyay 2014) suggesting other possibilities for the formation of Soumita Modak

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