Agglomerative clustering and collectiveness measure via exponent generating function

TL;DR

This paper introduces a novel agglomerative clustering method that uses path integral and exponent generating functions to define affinity measures, effectively capturing the collectiveness of moving systems like crowds.

Contribution

It proposes a new affinity measure based on path integral descriptors and exponent generating functions, with a physical interpretation as a collectiveness measure.

Findings

Effective in measuring collectiveness in moving systems

Path integral descriptor has desirable properties

Validated using Self-driven particle (SDP) model

Abstract

The key in agglomerative clustering is to define the affinity measure between two sets. A novel agglomerative clustering method is proposed by utilizing the path integral to define the affinity measure. Firstly, the path integral descriptor of an edge, a node and a set is computed by path integral and exponent generating function. Then, the affinity measure between two sets is obtained by path integral descriptor of sets. Several good properties of the path integral descriptor is proposed in this paper. In addition, we give the physical interpretation of the proposed path integral descriptor of a set. The proposed path integral descriptor of a set can be regard as the collectiveness measure of a set, which can be a moving system such as human crowd, sheep herd and so on. Self-driven particle (SDP) model is used to test the ability of the proposed method in measuring collectiveness.