This paper presents a novel approach in Explainable AI (XAI), integrating contrastive explanations with differential privacy in clustering methods. For several basic clustering problems, including $k$-median and $k$-means, we give efficient differential private contrastive explanations that achieve essentially the same explanations as those that non-private clustering explanations can obtain. We define contrastive explanations as the utility difference between the original clustering utility and utility from clustering with a specifically fixed centroid. In each contrastive scenario, we designate a specific data point as the fixed centroid position, enabling us to measure the impact of this constraint on clustering utility under differential privacy. Extensive experiments across various datasets show our method's effectiveness in providing meaningful explanations without significantly compromising data privacy or clustering utility. This underscores our contribution to privacy-aware machine learning, demonstrating the feasibility of achieving a balance between privacy and utility in the explanation of clustering tasks.

翻译：本文提出了一种可解释人工智能（XAI）的新方法，将对比解释与差分隐私集成于聚类方法中。针对包括$k$-中位数与$k$-均值在内的若干基础聚类问题，我们给出了高效的差分隐私对比解释方案，其所能获得的解释效果与非隐私聚类解释方案基本一致。我们将对比解释定义为原始聚类效用与在特定固定质心约束下聚类效用之间的差值。在每个对比场景中，我们指定一个特定数据点作为固定质心位置，从而能够在差分隐私框架下度量该约束对聚类效用的影响。在不同数据集上的大量实验表明，我们的方法能够在不过度损害数据隐私或聚类效用的前提下提供有意义的解释。这凸显了我们在隐私感知机器学习方面的贡献，证明了在聚类任务解释中实现隐私与效用平衡的可行性。