Data analysis on the extrasolar planets using robust clustering

Jiang, Ing-Guey; Yeh, Li-Chin; Hung, Wen-Liang; Yang, Miin-Shen

doi:10.1111/j.1365-2966.2006.10580.x

Cited by 26 publications

(12 citation statements)

References 23 publications

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“…It turns out that they are not able to find structures for EPs. This is in agreement with the analysis of Jiang et al (2006), although it was performed with a very different approach to that adopted here. The main problem of these hierarchies is that either they produce just one or two big clusters and some outliers, or the solution is so nested that the definition of cutoff is too arbitrary and meaningless.…”

Section: Finding the Best Solutionsupporting

confidence: 76%

Extrasolar Planet Taxonomy: A New Statistical Approach

Marchi

2007

ApJ

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In this paper we present the guidelines for an extrasolar planet taxonomy. The discovery of an increasing number of extrasolar planets showing a vast variety of planetary parameters, such as Keplerian orbital elements, and environmental parameters, such as stellar masses, spectral types, and metallicity, prompts the development of a planetary taxonomy. In this work, via principal component analysis followed by hierarchical clustering analysis, we report the definition of five robust groups of planets. We also discuss the physical relevance of such analysis, which may provide a valid basis for disentangling the role of the several physical parameters involved in the processes of planet formation and subsequent evolution. For instance, we were able to divide the hot Jupiters into two main groups on the basis of their stellar masses and metallicities. Moreover, for some groups, we find strong correlations among metallicity, semimajor axis, and eccentricity. The implications of these findings are discussed.

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Section: Finding the Best Solutionsupporting

confidence: 76%

Extrasolar Planet Taxonomy: A New Statistical Approach

Marchi

2007

ApJ

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“…The study of correlations within sub-groups in the cluster analysis done by Jiang et al (2006) and Marchi (2007) also confirms the mass-period correlation. Thus, strictly speaking, the mass and period functions are not two independent power laws.…”

Section: Introductionsupporting

confidence: 64%

“…On the other hand, as pointed in Jiang et al (2006) and in Marchi (2007), the correlation of each group of exoplanets identified in the clustering analysis might be linked with the physical mechanisms more easily. The overall correlations could be more difficult to explain.…”

Section: Mass-period Correlation Coefficientsmentioning

confidence: 83%

On the Fundamental Mass-Period Functions of Extrasolar Planets

Jiang

Yeh

Chang

et al. 2009

ApJS

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Employing a catalog of 175 extrasolar planets (exoplanets) detected by the Doppler-shift method, we constructed the independent and coupled mass-period functions. It is the first time in this field that the selection effect is considered in the coupled mass-period functions. Our results are consistent with those of Tabachnik and Tremaine in 2002, with the major difference that we obtain a flatter mass function but a steeper period function. Moreover, our coupled mass-period functions show that about 2.5% of stars would have a planet with mass between Earth Mass and Neptune Mass, and about 3% of stars would have a planet with mass between Neptune Mass and Jupiter Mass.

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“…This confirms that there is a strong eccentricity-period correlation in Cluster Pe1, that is, the planets with larger orbital periods might have larger eccentricities. Furthermore, the characteristics of clusters Pe1 might be related to the tidal interaction based on the clustering results of Jiang et al [10]. However, in Cluster Pe2, there is no eccentricity-period correlation.…”

Section: Application To Extrasolar Planetsmentioning

confidence: 97%

“…However, there is no intracluster correlation in Cluster PM3. According to the clustering results of Jiang et al [10], the characteristics of clusters PM1 and PM2 might relate to the tidal and disc interactions.…”

Section: Application To Extrasolar Planetsmentioning

confidence: 98%

Learning-based EM algorithm for normal-inverse Gaussian mixture model with application to extrasolar planets

Hung

Chang-Chien

2016

Journal of Applied Statistics

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Karlis and Santourian [14] proposed a model-based clustering algorithm, the expectation-maximization (EM) algorithm, to fit the mixture of multivariate normal-inverse Gaussian (NIG) distribution. However, the EM algorithm for the mixture of multivariate NIG requires a set of initial values to begin the iterative process, and the number of components has to be given a priori. In this paper, we present a learning-based EM algorithm: its aim is to overcome the aforementioned weaknesses of Karlis and Santourian's EM algorithm [14]. The proposed learning-based EM algorithm was first inspired by Yang et al. [24]: the process of how they perform self-clustering was then simulated. Numerical experiments showed promising results compared to Karlis and Santourian's EM algorithm. Moreover, the methodology is applicable to the analysis of extrasolar planets. Our analysis provides an understanding of the clustering results in the ln P−ln M and ln P−e spaces, where M is the planetary mass, P is the orbital period and e is orbital eccentricity. Our identified groups interpret two phenomena: (1) the characteristics of two clusters in ln P−ln M space might be related to the tidal and disc interactions (see [9]); and (2) there are two clusters in ln P−e space. ARTICLE HISTORY

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Data analysis on the extrasolar planets using robust clustering

Cited by 26 publications

References 23 publications

Extrasolar Planet Taxonomy: A New Statistical Approach

Extrasolar Planet Taxonomy: A New Statistical Approach

On the Fundamental Mass-Period Functions of Extrasolar Planets

Learning-based EM algorithm for normal-inverse Gaussian mixture model with application to extrasolar planets

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