Granular Elastic Network Regression with Stochastic Gradient Descent
Linear regression is the use of linear functions to model the relationship between a dependent variable and one or more independent variables. Linear regression models have been widely used in various fields such as finance, industry, and medicine. To address the problem that the traditional linear...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-07-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/15/2628 |
| _version_ | 1827602215221592064 |
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| author | Linjie He Yumin Chen Caiming Zhong Keshou Wu |
| author_facet | Linjie He Yumin Chen Caiming Zhong Keshou Wu |
| author_sort | Linjie He |
| collection | DOAJ |
| description | Linear regression is the use of linear functions to model the relationship between a dependent variable and one or more independent variables. Linear regression models have been widely used in various fields such as finance, industry, and medicine. To address the problem that the traditional linear regression model is difficult to handle uncertain data, we propose a granule-based elastic network regression model. First we construct granules and granular vectors by granulation methods. Then, we define multiple granular operation rules so that the model can effectively handle uncertain data. Further, the granular norm and the granular vector norm are defined to design the granular loss function and construct the granular elastic network regression model. After that, we conduct the derivative of the granular loss function and design the granular elastic network gradient descent optimization algorithm. Finally, we performed experiments on the UCI datasets to verify the validity of the granular elasticity network. We found that the granular elasticity network has the advantage of good fit compared with the traditional linear regression model. |
| first_indexed | 2024-03-09T05:13:06Z |
| format | Article |
| id | doaj.art-81a6cb3f460f4e9e8948e52e5a85354d |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T05:13:06Z |
| publishDate | 2022-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-81a6cb3f460f4e9e8948e52e5a85354d2023-12-03T12:47:33ZengMDPI AGMathematics2227-73902022-07-011015262810.3390/math10152628Granular Elastic Network Regression with Stochastic Gradient DescentLinjie He0Yumin Chen1Caiming Zhong2Keshou Wu3College of Computer Science and Technology, Xiamen University of Technology, Xiamen 361024, ChinaCollege of Computer Science and Technology, Xiamen University of Technology, Xiamen 361024, ChinaCollege of Science and Technology, Ningbo University, Ningbo 315211, ChinaCollege of Computer Science and Technology, Xiamen University of Technology, Xiamen 361024, ChinaLinear regression is the use of linear functions to model the relationship between a dependent variable and one or more independent variables. Linear regression models have been widely used in various fields such as finance, industry, and medicine. To address the problem that the traditional linear regression model is difficult to handle uncertain data, we propose a granule-based elastic network regression model. First we construct granules and granular vectors by granulation methods. Then, we define multiple granular operation rules so that the model can effectively handle uncertain data. Further, the granular norm and the granular vector norm are defined to design the granular loss function and construct the granular elastic network regression model. After that, we conduct the derivative of the granular loss function and design the granular elastic network gradient descent optimization algorithm. Finally, we performed experiments on the UCI datasets to verify the validity of the granular elasticity network. We found that the granular elasticity network has the advantage of good fit compared with the traditional linear regression model.https://www.mdpi.com/2227-7390/10/15/2628granular computinggranular regressionelastic networkregression |
| spellingShingle | Linjie He Yumin Chen Caiming Zhong Keshou Wu Granular Elastic Network Regression with Stochastic Gradient Descent Mathematics granular computing granular regression elastic network regression |
| title | Granular Elastic Network Regression with Stochastic Gradient Descent |
| title_full | Granular Elastic Network Regression with Stochastic Gradient Descent |
| title_fullStr | Granular Elastic Network Regression with Stochastic Gradient Descent |
| title_full_unstemmed | Granular Elastic Network Regression with Stochastic Gradient Descent |
| title_short | Granular Elastic Network Regression with Stochastic Gradient Descent |
| title_sort | granular elastic network regression with stochastic gradient descent |
| topic | granular computing granular regression elastic network regression |
| url | https://www.mdpi.com/2227-7390/10/15/2628 |
| work_keys_str_mv | AT linjiehe granularelasticnetworkregressionwithstochasticgradientdescent AT yuminchen granularelasticnetworkregressionwithstochasticgradientdescent AT caimingzhong granularelasticnetworkregressionwithstochasticgradientdescent AT keshouwu granularelasticnetworkregressionwithstochasticgradientdescent |