This paper, introducing a novel method in philomatics, draws on Wittgenstein's concept of family resemblance from analytic philosophy to develop a clustering algorithm for machine learning. According to Wittgenstein's Philosophical Investigations (1953), family resemblance holds that members of a concept or category are connected by overlapping similarities rather than a single defining property. Consequently, a family of entities forms a chain of items sharing overlapping traits. This philosophical idea naturally lends itself to a graph-based approach in machine learning. Accordingly, we propose the Wittgenstein's Family Resemblance (WFR) clustering algorithm and its kernel variant, kernel WFR. This algorithm computes resemblance scores between neighboring data instances, and after thresholding these scores, a resemblance graph is constructed. The connected components of this graph define the resulting clusters. Simulations on benchmark datasets demonstrate that WFR is an effective nonlinear clustering algorithm that does not require prior knowledge of the number of clusters or assumptions about their shapes.

翻译：本文引入了一种哲学数学的新方法，借鉴分析哲学中维特根斯坦的家族相似性概念，发展出一种适用于机器学习的聚类算法。根据维特根斯坦在《哲学研究》（1953）中的论述，家族相似性认为概念或范畴的成员通过重叠的相似性而非单一界定属性相互关联。因此，一个实体家族形成了一条共享重叠特征的链式结构。这一哲学思想自然适用于机器学习中的图方法。据此，我们提出了维特根斯坦家族相似性聚类算法及其核变体——核WFR。该算法计算相邻数据实例之间的相似性得分，经过阈值处理后构建相似性图。该图的连通分量即构成最终聚类。在基准数据集上的仿真实验表明，WFR是一种有效的非线性聚类算法，无需预先获知聚类数量，也无需对聚类形状进行假设。