The extended Kullback-Leibler divergence measure in the unknown probability density function cases and applications

Lê, Hòa; Truong, Hoang Van; Bao, Pham The

doi:10.1504/ijiids.2021.118555

Cited by 2 publications

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“…The Kullback–Leibler divergence between two probability density functions f ( x ) and g ( x ) is determined by the formula ( 5 ) 30 : We use the extended Kullback–Leibler divergence be determined by the formula ( 6 ) 31 : in which is the empirical probability of data. In this context, it is important to note that the samples are arranged in ascending order, as indicated by the notation .…”

Section: Estimate the Parameters Of The Component Probability Distrib...mentioning

confidence: 99%

The fuzzy Kullback–Leibler divergence for estimating parameters of the probability distribution in fuzzy data: an application to classifying Vietnamese Herb Leaves

Le,

Sang,

Lam Thuy

et al. 2023

Sci Rep

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In this paper, we address the challenge of estimating probability distributions which are typically represented by parameter-based values. However, this estimation is prone to errors and does not comprehensively capture the nature of real-world data. Additionally, real-world data often follows a mixed form of probability distributions, where sub-datasets may contain incomplete information. To enhance flexibility, especially in classification problems, we propose a new method for describing parameters estimated through Bayesian statistics. Our method introduces fuzzy parameters and assesses the similarity between probability distributions using the fuzzy extended Kullback–Leibler divergence. We demonstrate the practical application of our approach in Vietnamese Herb Leaves classification. By incorporating fuzzy parameters and leveraging Bayesian statistics, our method provides more robust estimations of probability distributions and enables improved flexibility in classification tasks.

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Section: Estimate the Parameters Of The Component Probability Distrib...mentioning

confidence: 99%

The fuzzy Kullback–Leibler divergence for estimating parameters of the probability distribution in fuzzy data: an application to classifying Vietnamese Herb Leaves

Le,

Sang,

Lam Thuy

et al. 2023

Sci Rep

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show abstract

“…Step 2 Calculate the extended Kullback -Leibler divergence values 11 , for the difference of each probability distribution compared to data. Output The probability distribution is best suited to the sub-dataset corresponding to the probability distribution with the smallest extended Kullback -Leibler divergence.…”

Section: Estimate the Parameters Of The Component Probability Distrib...mentioning

confidence: 99%

A new approach to estimating parameters of the probability distribution in fuzzy data – an application to classifying Vietnamese Herb Leaf

Le,

Bao,

et al. 2022

Preprint

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The probability distribution of data are parameter-based and typically formatted as script numbers. However, these values areusually estimated experimentally, leading to selecting only one value is error-prone. Moreover, the real data often follows amixed form of probability distributions, in which sub-datasets are often incomplete data. It is possible to use parameters forensuring flexibility, especially in classification problems. Therefore, in this paper, we propose a new method for describingparameters estimated through Bayesian statistics; the new similarity between two probability distributions with the fuzzyparameters, through the fuzzy extended Kullback – Leibler divergence. The paper also applied the proposed methods in leaf classification.

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The extended Kullback-Leibler divergence measure in the unknown probability density function cases and applications

Cited by 2 publications

References 0 publications

The fuzzy Kullback–Leibler divergence for estimating parameters of the probability distribution in fuzzy data: an application to classifying Vietnamese Herb Leaves

The fuzzy Kullback–Leibler divergence for estimating parameters of the probability distribution in fuzzy data: an application to classifying Vietnamese Herb Leaves

A new approach to estimating parameters of the probability distribution in fuzzy data – an application to classifying Vietnamese Herb Leaf

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