动态量子聚类：一种可视化探索数据结构的方法
Dynamic quantum clustering: a method for visual exploration of structures in data
摘要：
在某些特征空间中的一组给定的数据点可以与薛定谔方程相关联，薛定谔方程的电势由数据确定。这是已知的，导致良好的集群解决方案。在这里，我们将这种方法扩展到一个成熟的动力学计划，使用一个时间依赖的薛定谔方程。此外，我们近似这个哈密顿形式主义的截断计算内的一组高斯波函数（相干态）围绕原始点为中心。这允许分析评估所有这些状态的时间演变，通过观察点之间的动态距离和点到集群的收敛，打开了探索数据点之间的关系的可能性。这种形式可以通过预处理进一步补充，例如通过奇异值分解或特征滤波进行降维。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
