A novel adversarial deep TSK fuzzy classifier with its inverse-free fast training

Abstract Deep learning is one of the most popular machine learning methods, and has been used in many applications. However, conventional deep learning is a fully deterministic model that has difficulty reducing data uncertainty while shedding no light on model transparency. To this end, a novel adv...

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Main Authors: Limin Mao, Hangming Shi, Yongxin Chou, Jinliang Cong, Mingli Lu, Zekang Bian, Suhang Gu
Format: Article
Language:English
Published: Springer 2025-05-01
Series:Complex & Intelligent Systems
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Online Access:https://doi.org/10.1007/s40747-025-01928-3
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author Limin Mao
Hangming Shi
Yongxin Chou
Jinliang Cong
Mingli Lu
Zekang Bian
Suhang Gu
author_facet Limin Mao
Hangming Shi
Yongxin Chou
Jinliang Cong
Mingli Lu
Zekang Bian
Suhang Gu
author_sort Limin Mao
collection DOAJ
description Abstract Deep learning is one of the most popular machine learning methods, and has been used in many applications. However, conventional deep learning is a fully deterministic model that has difficulty reducing data uncertainty while shedding no light on model transparency. To this end, a novel adversarial deep Takagi–Sugeno–Kang (TSK) fuzzy classifier (AD-TSK), which is characterized by its novel stacked structure and inverse-free fast training, is proposed in this paper. After taking the TSK fuzzy classifier as the subclassifier in each layer of AD-TSK, proactive adversarial example learning is designed based on the adversarial attacks on both the features and labels of the inputs for each subclassifier to generate the adversarial TSK fuzzy classifier (ATSK) with increased robustness to noise. Moreover, the generalization capability of AD-TSK can be guaranteed by its novel stacked structure constructed using the dropout-based gradients of each ATSK to update the original inputs along the stacked structure in a layer-by-layer manner. In particular, by sharing the merits of the Schur complement and Sherman–Morrison formula, the consequent parameters of all fuzzy rules in each ATSK can be determined without the matrix inversion operation, and the corresponding optimal number of fuzzy rules can be optimized based on the previous consequent parameters of all fuzzy rules. This can facilitate the inverse-free fast deep learning algorithm of AD-TSK while maintaining interpretability. Extensive experiments on fourteen benchmark datasets from the UCI and KEEL data repositories and the corresponding statistical test results demonstrate the effectiveness of the proposed AD-TSK as well as its inverse-free fast training. The source code of AD-TSK classifier can be downloaded from https://github.com/gusuhang10/AD-TSK .
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spelling doaj-art-99f2dabfc24b4cb1b07861897701f99f2025-08-20T03:22:57ZengSpringerComplex & Intelligent Systems2199-45362198-60532025-05-0111712210.1007/s40747-025-01928-3A novel adversarial deep TSK fuzzy classifier with its inverse-free fast trainingLimin Mao0Hangming Shi1Yongxin Chou2Jinliang Cong3Mingli Lu4Zekang Bian5Suhang Gu6School of Electrical Engineering and Automation, Changshu Institute of TechnologySchool of Intelligent Manufacturing, Changzhou UniversitySchool of Electrical Engineering and Automation, Changshu Institute of TechnologySchool of Electrical Engineering and Automation, Changshu Institute of TechnologySchool of Electrical Engineering and Automation, Changshu Institute of TechnologySchool of AI and Computer Science, Jiangnan UniversitySchool of Electrical Engineering and Automation, Changshu Institute of TechnologyAbstract Deep learning is one of the most popular machine learning methods, and has been used in many applications. However, conventional deep learning is a fully deterministic model that has difficulty reducing data uncertainty while shedding no light on model transparency. To this end, a novel adversarial deep Takagi–Sugeno–Kang (TSK) fuzzy classifier (AD-TSK), which is characterized by its novel stacked structure and inverse-free fast training, is proposed in this paper. After taking the TSK fuzzy classifier as the subclassifier in each layer of AD-TSK, proactive adversarial example learning is designed based on the adversarial attacks on both the features and labels of the inputs for each subclassifier to generate the adversarial TSK fuzzy classifier (ATSK) with increased robustness to noise. Moreover, the generalization capability of AD-TSK can be guaranteed by its novel stacked structure constructed using the dropout-based gradients of each ATSK to update the original inputs along the stacked structure in a layer-by-layer manner. In particular, by sharing the merits of the Schur complement and Sherman–Morrison formula, the consequent parameters of all fuzzy rules in each ATSK can be determined without the matrix inversion operation, and the corresponding optimal number of fuzzy rules can be optimized based on the previous consequent parameters of all fuzzy rules. This can facilitate the inverse-free fast deep learning algorithm of AD-TSK while maintaining interpretability. Extensive experiments on fourteen benchmark datasets from the UCI and KEEL data repositories and the corresponding statistical test results demonstrate the effectiveness of the proposed AD-TSK as well as its inverse-free fast training. The source code of AD-TSK classifier can be downloaded from https://github.com/gusuhang10/AD-TSK .https://doi.org/10.1007/s40747-025-01928-3TSK fuzzy classifierInterpretabilityDeep fuzzy systemDeep learningFast learning
spellingShingle Limin Mao
Hangming Shi
Yongxin Chou
Jinliang Cong
Mingli Lu
Zekang Bian
Suhang Gu
A novel adversarial deep TSK fuzzy classifier with its inverse-free fast training
Complex & Intelligent Systems
TSK fuzzy classifier
Interpretability
Deep fuzzy system
Deep learning
Fast learning
title A novel adversarial deep TSK fuzzy classifier with its inverse-free fast training
title_full A novel adversarial deep TSK fuzzy classifier with its inverse-free fast training
title_fullStr A novel adversarial deep TSK fuzzy classifier with its inverse-free fast training
title_full_unstemmed A novel adversarial deep TSK fuzzy classifier with its inverse-free fast training
title_short A novel adversarial deep TSK fuzzy classifier with its inverse-free fast training
title_sort novel adversarial deep tsk fuzzy classifier with its inverse free fast training
topic TSK fuzzy classifier
Interpretability
Deep fuzzy system
Deep learning
Fast learning
url https://doi.org/10.1007/s40747-025-01928-3
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