# Optimize TSK Fuzzy Systems for Classification Problems: Mini-Batch Gradient Descent with Uniform Regularization and Batch Normalization

## TL;DR

This paper introduces a mini-batch gradient descent algorithm for TSK fuzzy classifiers, incorporating uniform regularization and batch normalization to enhance training efficiency and classification accuracy on large, high-dimensional datasets.

## Contribution

The paper proposes a novel training algorithm for TSK fuzzy systems that combines uniform regularization and batch normalization, improving scalability and performance.

## Key findings

- UR and BN individually improve classification accuracy.
- Integrating UR and BN further enhances performance.
- The method is effective on diverse UCI datasets.

## Abstract

Takagi-Sugeno-Kang (TSK) fuzzy systems are flexible and interpretable machine learning models; however, they may not be easily optimized when the data size is large, and/or the data dimensionality is high. This paper proposes a mini-batch gradient descent (MBGD) based algorithm to efficiently and effectively train TSK fuzzy classifiers. It integrates two novel techniques: 1) uniform regularization (UR), which forces the rules to have similar average contributions to the output, and hence to increase the generalization performance of the TSK classifier; and, 2) batch normalization (BN), which extends BN from deep neural networks to TSK fuzzy classifiers to expedite the convergence and improve the generalization performance. Experiments on 12 UCI datasets from various application domains, with varying size and dimensionality, demonstrated that UR and BN are effective individually, and integrating them can further improve the classification performance.