A new measure for assessment of clustering based on kernel density estimation

Modak, Soumita

doi:10.1080/03610926.2022.2032168

Cited by 15 publications

(9 citation statements)

References 21 publications

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“…Conti et al proposed a resampling method that is easy to compute (Conti, Mecatti, & Nicolussi, 2022). Modak proposed a method to determine the number of cluster paths (Modak, 2022). Trafimow et al proposed a simple chart that can be used for group-by-group comparisons in marketing (Trafimow, Hyman, & Cong, 2022).…”

Section: Introductionmentioning

confidence: 99%

On Discrete Probability Distributions to Grasp the Number of Samples in a Population

Yabu¹

2023

Preprint

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In situations where there are multiple options, when the number of options selected is known, the discrete probability distribution of the number of options selected is mathematically defined, and properties such as expected value and variance are shown. By using the discrete probability distributions derived in this paper, we can find the most probable number of people trying to buy and the most probable number of sales of other people's products when we know the number of sales of our own product. Therefore, application in the field of economics can be expected.

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Section: Introductionmentioning

confidence: 99%

On Discrete Probability Distributions to Grasp the Number of Samples in a Population

Yabu¹

2023

Preprint

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“…A diverse variety of cluster validity indices is existing in the literature [18-24] . Measures like the classic Bayes’ Information Criterion, Bayes factor [25-28] are introduced in the environment of the parametric mixture models, while Sugar and James [29] implement a parametric model-based technique to find K.…”

Section: Introductionmentioning

confidence: 99%

Validity Index for Clustered Data in Non-negative Space

Modak

2023

Calcutta Statistical Association Bulletin

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We propose a novel nonparametric cluster validity index which can be used to evaluate the unknown number of existing clusters prevailing a data set, to assess the quality of classification for a clustered set of data members, or to compare the clustering output obtained from different algorithms. Our efficient measure depends only on the observation-wise distances of the non-negative clustered data from their origin given in an arbitrary dimensional space. Its fast implementation makes it appealing for big data analysis, whereas the high-dimensional applicability widens its usefulness. Easy interpretation, simple algorithm, speedy computation and great performance, shown in terms of data study, establish our advised validity index as a strong cluster accuracy measure among the acknowledged ones from the literature. AMS subject classification: 62H30

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“…Established literature give an overview of analyzing astronomical data sets in the classical multivariate set-up, be it time series or cross-sectional data (Matijevič et Modak 2021aModak , 2021bModak , 2022. In contrast, the novelty of our present work lies in dealing with time series not as a multivariate data set, where the variables are measured at discrete points ordered in time, but rather as continuous curves of time called functional data.…”

Section: Introductionmentioning

confidence: 99%

Clustering of eclipsing binary light curves through functional principal component analysis

Modak,

Chattopadhyay,

Chattopadhyay

2022

Preprint

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In this paper, we revisit the problem of clustering 1318 new variable stars found in the Milky way. Our recent work distinguishes these stars based on their light curves which are univariate series of brightness from the stars observed at discrete time points. This work proposes a new approach to look at these discrete series as continuous curves over time by transforming them into functional data. Then, functional principal component analysis is performed using these functional light curves. Clustering based on the significant functional principal components reveals two distinct groups of eclipsing binaries with consistency and superiority compared to our previous results. This method is established as a new powerful light curve-based classifier, where implementation of a simple clustering algorithm is effective enough to uncover the true clusters based merely on the first few relevant functional principal components. Simultaneously we discard the noise from the data study involving the higher order functional principal components. Thus the suggested method is very useful for clustering big light curve data sets which is also verified by our simulation study.

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A new measure for assessment of clustering based on kernel density estimation

Cited by 15 publications

References 21 publications

On Discrete Probability Distributions to Grasp the Number of Samples in a Population

On Discrete Probability Distributions to Grasp the Number of Samples in a Population

Validity Index for Clustered Data in Non-negative Space

Clustering of eclipsing binary light curves through functional principal component analysis

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