Dynamic quantum clustering: a method for visual exploration of structures in data

TL;DR

This paper introduces a dynamic quantum clustering method using a time-dependent Schrödinger equation and Gaussian wave functions to explore data structures visually and identify clusters effectively.

Contribution

It extends quantum clustering into a dynamic framework with an analytic approach using Gaussian states, enabling better exploration of data relationships.

Findings

Enables visualization of data structures through quantum dynamics.

Provides an analytic method for evolving data points in feature space.

Facilitates exploration of data relationships via dynamical distances.

Abstract

A given set of data-points in some feature space may be associated with a Schrodinger equation whose potential is determined by the data. This is known to lead to good clustering solutions. Here we extend this approach into a full-fledged dynamical scheme using a time-dependent Schrodinger equation. Moreover, we approximate this Hamiltonian formalism by a truncated calculation within a set of Gaussian wave functions (coherent states) centered around the original points. This allows for analytic evaluation of the time evolution of all such states, opening up the possibility of exploration of relationships among data-points through observation of varying dynamical-distances among points and convergence of points into clusters. This formalism may be further supplemented by preprocessing, such as dimensional reduction through singular value decomposition or feature filtering.