mlsanityData to 7 Oct 2026

Curse of Dimensionality for TSK Fuzzy Neural Networks: Explanation and Solutions

arXiv 2102.04271 ↗First posted 8 Feb 2021cs.LGcited by 12

Not on the map. Why?

Abstract (arXiv)

Takagi-Sugeno-Kang (TSK) fuzzy system with Gaussian membership functions (MFs) is one of the most widely used fuzzy systems in machine learning. However, it usually has difficulty handling high-dimensional datasets. This paper explores why TSK fuzzy systems with Gaussian MFs may fail on high-dimensional inputs. After transforming defuzzification to an equivalent form of softmax function, we find that the poor performance is due to the saturation of softmax. We show that two defuzzification operations, LogTSK and HTSK, the latter of which is first proposed in this paper, can avoid the saturation. Experimental results on datasets with various dimensionalities validated our analysis and demonstrated the effectiveness of LogTSK and HTSK.

Key facts. Cited by 12 papers in the map (data through 7 Oct 2026). Builds on 13 of its 31 references that are in the map. First posted on arXiv 8 Feb 2021.

Builds on

13 of 31 references.

References · 13

  1. 2017Attention Is All You Needcited by 59,932
  2. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  3. 2015Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classificationcited by 3,590
  4. 2018How Does Batch Normalization Help Optimization?cited by 355
  5. 2019Adaptive Gradient Methods with Dynamic Bound of Learning Ratecited by 181
  6. 2017Relief-Based Feature Selection: Introduction and Reviewcited by 38
  7. 2017Noisy Softmax: Improving the Generalization Ability of DCNN via Postponing the Early Softmax Saturationcited by 21
  8. 2019Optimize TSK Fuzzy Systems for Regression Problems: Mini-Batch Gradient Descent with Regularization, DropRule and AdaBound (MBGD-RDA)cited by 9
  9. 2019Recommendations on Designing Practical Interval Type-2 Fuzzy Systemscited by 6
  10. 2019On the Functional Equivalence of TSK Fuzzy Systems to Neural Networks, Mixture of Experts, CART, and Stacking Ensemble Regressioncited by 5
  11. 2020Distilling a Deep Neural Network into a Takagi-Sugeno-Kang Fuzzy Inference Systemcited by 4
  12. 2019Concise Fuzzy System Modeling Integrating Soft Subspace Clustering and Sparse Learningcited by 3
1 more
  1. 2020Supervised Enhanced Soft Subspace Clustering (SESSC) for TSK Fuzzy Classifierscited by 2

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 2; 2023: 0; 2024: 4; 2025: 3; 2026: 3.

12 papers.

  1. 2022An Adaptive Neuro-Fuzzy System with Integrated Feature Selection and Rule Extraction for High-Dimensional Classification Problemscited by 3
  2. 2025FAME: Introducing Fuzzy Additive Models for Explainable AIcited by 3
  3. 2022PyTSK: A Python Toolbox for TSK Fuzzy Systemscited by 2
  4. 2024Semantic-Preserving Feature Partitioning for Multi-View Ensemble Learningcited by 2
  5. 2024Enhancing Interval Type-2 Fuzzy Logic Systems: Learning for Precision and Prediction Intervalscited by 1
  6. 2024Zadeh's Type-2 Fuzzy Logic Systems: Precision and High-Quality Prediction Intervalscited by 0
  7. 2024A Self-Constructing Multi-Expert Fuzzy System for High-dimensional Data Classificationcited by 0
  8. 2025Gradient-Based Neuroplastic Adaptation for Concurrent Optimization of Neuro-Fuzzy Networkscited by 0
  9. 2025An Integrated Fusion Framework for Ensemble Learning Leveraging Gradient Boosting and Fuzzy Rule-Based Modelscited by 0
  10. 2026Alternating Bi-Objective Optimization for Explainable Neuro-Fuzzy Systemscited by 0
  11. 2026Explainable machine learning workflows for radio astronomical data processingcited by 0
  12. 2026SoftTri: Smooth Triangular Membership Functions for Adaptive Fuzzy Inference Systemscited by 0