Interpretability-Oriented Adjustment of K-Means: A Multiple-Objective Particle Swarm Optimization Framework

Clustering is an unsupervised machine learning technique used to partition unlabeled data into different groups. However, traditional clustering methods only provide a set of results without any explanations. While numerous methods in the literature attempt to explain clustering results, the explanation rules provided by these models are fixed and sacrificing clustering quality for the sake of making the rules easier to understand. To address this, this paper proposes a feature selection model to balance the interpretability and clustering quality. The model consists of two stages. In the first stage, the concept of explanatory radius is defined, and the explanatory radius of each cluster in the initial clustering results is calculated. In the second stage, a feature subspace is selected, and the dataset is re-clustered in this subspace using a proposed formula to obtain a new clustering result. Three objective functions are designed to evaluate the performance of the new clustering results in terms of cluster quality and interpretability. Subsequently, the model utilizes a multi-objective optimization framework to optimize the three objective functions in the solution space formed by different feature subspaces, resulting in a set of Pareto solutions. Each solution in the Pareto set represents a trade-off between clustering quality and interpretability. Finally, the contribution of features during the generation process of each cluster is used to represent the interpretability of each cluster’s result. The proposed method is validated on both artificial datasets and real-world datasets, and comparative analyses are conducted with the latest explainable clustering algorithms in the literature. The analysis results demonstrate the effectiveness of the proposed method.