Wittgenstein's Family Resemblance Clustering Algorithm

2026-01-03

arXiv.org

AI Summary

This work proposes WFR, a novel graph-based nonlinear clustering algorithm inspired by Wittgenstein’s notion of “family resemblance,” which addresses the limitations of traditional clustering methods that often require a predefined number of clusters or impose strong assumptions on cluster shape. WFR formalizes the philosophical concept of family resemblance by constructing a similarity graph, applying thresholding, and analyzing connected components to automatically discover clusters of arbitrary shape without prior knowledge of the cluster count. The method is further extended via kernelization to Kernel WFR to capture complex nonlinear relationships. Experimental results on standard benchmarks demonstrate that WFR effectively uncovers intricate semantic structures and exhibits strong robustness to unknown cluster numbers and irregular cluster geometries.

Technology Category

• Machine Learning: Clustering
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
• Knowledge Representation and Reasoning: Nonmonotonic Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• Web Mining and Content Analysis: Normalization, clustering, classification, and summarization of Web text

Abstract

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.

Problem

• clustering
• family resemblance
• nonlinear clustering
• cluster shape assumption
• number of clusters

Innovation

• family resemblance
• graph-based clustering
• nonlinear clustering
• Wittgenstein
• kernel method