Mutual k-Nearest Neighbor Graph for Data Analysis: Application to Metric Space Clustering

Edgar Chávez, Stéphane Marchand-Maillet, Adolfo J. Quiroz

Abstract: In this paper, we delve into the Mutual k-Nearest Neighbor Graph ( $$m$$ k $$NN G$$ ) and its significance in clustering and outlier detection. We present a rigorous mathematical framework elucidating its application and highlight its role in the success of various clustering algorithms. Building on Brito et al.’s findings, which link the connected components of the $$m$$ k $$NN G$$ to clusters under specific density bounds, we explore its relevance in the context of a wide range of density functions.