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

2021/02/08 by Yuqi Cui, Dongrui Wu, Cui, Yuqi +3 · 2 citations
Computer Science · #FOS: Computer and information sciences #Face and Expression Recognition #Fuzzy Logic and Control Systems #Machine Learning (cs.LG) #Neural Networks and Applications

paper · pdf · doi:10.48550/arxiv.2102.04271

openalex publication_date 2021/02/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Cited by

• An Integrated Fusion Framework for Ensemble Learning Leveraging Gradient Boosting and Fuzzy Rule-Based Models
• Deep Fuzzy Optimization for Batch-Size and Nearest Neighbors in Optimal Robot Motion Planning

Related

• Efficient NTK using Dimensionality Reduction
• Can Shallow Neural Networks Beat the Curse of Dimensionality? A mean field training perspective
• Depth Separations in Neural Networks: Separating the Dimension from the Accuracy
• The Limitations of Large Width in Neural Networks: A Deep Gaussian Process Perspective
• Networks with Finite VC Dimension: Pro and Contra