Cluster networks and Bruhat-Tits buildings

TL;DR

This paper explores a clustering method using a family of metrics, resulting in a classification network, and discusses its relation to Bruhat-Tits buildings and the dimension of cluster systems.

Contribution

It introduces a clustering framework based on multiple metrics, leading to classification networks, and connects this approach to Bruhat-Tits buildings and cluster system dimensions.

Findings

Development of a clustering procedure with metric families

Establishment of classification networks as an alternative to trees

Discussion of the relation to Bruhat-Tits buildings and cluster dimensions

Abstract

Clustering procedure for the case where instead of a fixed metric one applies a family of metrics is considered. In this case instead of a classification tree one obtains a classification network (a directed acyclic graph with non directed cycles). Relation to Bruhat-Tits buildings is discussed. Dimension of a general cluster system is considered.