A modified inertial viscosity extragradient type method for equilibrium problems application to classification of diabetes mellitus: Machine learning methods

Suthep Suantai; Watcharaporn Yajai; Pronpat Peeyada; Watcharaporn Cholamjiak; Petcharaporn Chachvarat; Suthep Suantai; Watcharaporn Yajai; Pronpat Peeyada; Watcharaporn Cholamjiak; Petcharaporn Chachvarat

doi:10.3934/math.2023055

AIMS Mathematics

2023, Volume 8, Issue 1: 1102-1126. doi: 10.3934/math.2023055

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Research article

A modified inertial viscosity extragradient type method for equilibrium problems application to classification of diabetes mellitus: Machine learning methods

1.
Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand
2.
School of Science, University of Phayao, Phayao 56000, Thailand
3.
Faculty of Medicine at University of Phayao, Phayao 56000, Thailand

Received: 30 June 2022 Revised: 29 September 2022 Accepted: 09 October 2022 Published: 17 October 2022
MSC : 65K15, 47H05, 49M37

Diabetes is one of the four major types of noncommunicable diseases (cardiovascular disease, diabetes, cancer and chronic respiratory diseases). It is chronic condition that occurs when the body does not produce enough insulin therefore results in raised blood sugar levels. Insulin is a hormone that regulates the blood sugar when food consumption. If the proper treatment is not received organs of the body like kidneys, nervous system and eyes can deteriorate. Therefore, it is better to predict diabetes as early as possible because lead to serious damage to many of the body's systems. In this paper, we modify extragradient method with an inertial extrapolation step and viscosity-type method to solve equilibrium problems of pseudomonotone bifunction operator in real Hilbert spaces. Strong convergence result is obtained under the assumption that the bifunction satisfies the Lipchitz-type condition. Moreover, we show choosing stepsize parameter in many ways, this shows that our algorithm is flexible using. Finally, we apply our algorithm to solve the diabetes mellitus classification in machine learning and show the algorithm's efficiency by comparing with existing algorithms.
- equilibrium problems,
- extragradient algorithm,
- Hilbert spaces,
- viscosity method,
- classification
Citation: Suthep Suantai, Watcharaporn Yajai, Pronpat Peeyada, Watcharaporn Cholamjiak, Petcharaporn Chachvarat. A modified inertial viscosity extragradient type method for equilibrium problems application to classification of diabetes mellitus: Machine learning methods[J]. AIMS Mathematics, 2023, 8(1): 1102-1126. doi: 10.3934/math.2023055

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Abstract

Diabetes is one of the four major types of noncommunicable diseases (cardiovascular disease, diabetes, cancer and chronic respiratory diseases). It is chronic condition that occurs when the body does not produce enough insulin therefore results in raised blood sugar levels. Insulin is a hormone that regulates the blood sugar when food consumption. If the proper treatment is not received organs of the body like kidneys, nervous system and eyes can deteriorate. Therefore, it is better to predict diabetes as early as possible because lead to serious damage to many of the body's systems. In this paper, we modify extragradient method with an inertial extrapolation step and viscosity-type method to solve equilibrium problems of pseudomonotone bifunction operator in real Hilbert spaces. Strong convergence result is obtained under the assumption that the bifunction satisfies the Lipchitz-type condition. Moreover, we show choosing stepsize parameter in many ways, this shows that our algorithm is flexible using. Finally, we apply our algorithm to solve the diabetes mellitus classification in machine learning and show the algorithm's efficiency by comparing with existing algorithms.

References

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