Explainable fuzzy cluster-based regression algorithm with gradient descent learning

Abstract

We propose an algorithm for n-dimensional regression problems with continuous variables. Its main property is explainability, which we identify as the ability to understand the algorithm's decisions from a human perspective. This has been achieved thanks to the simplicity of the architecture, the lack of hidden layers (as opposed to deep neural networks used for this same task), and the linguistic nature of its fuzzy inference system. First, the algorithm divides the joint input-output space into clusters that are subsequently approximated using linear functions. Then, we fit a Cauchy membership function to each cluster, therefore identifying them as fuzzy sets. The prediction of each linear regression is merged using a Takagi-Sugeno-Kang approach to generate the prediction of the model. Finally, the parameters of the algorithm (those from the linear functions and Cauchy membership functions) are fine-tuned using gradient descent optimization. In order to validate this algorithm, we considered three different scenarios: The first two are simple one-input and two-input problems with artificial data, which allow visual inspection of the results. In the third scenario, we use real data for the prediction of the power generated by a combined cycle power plant. The results obtained in this last problem (3.513 RMSE and 2.649 MAE) outperform the state of the art (3.787 RMSE and 2.818 MAE).

Keywords

Clustering algorithms / explainable artificial intelligence / fuzzy logic / gradient methods / Takagi-Sugeno model