Abstract
A given set of data points in some feature space may be associated with a Schrödinger 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 Schrödinger 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.
2 More- Received 17 August 2009
DOI:https://doi.org/10.1103/PhysRevE.80.066117
©2009 American Physical Society