A Comprehensive Analysis of Quantum Clustering : Finding All the Potential Minima

Quantum clustering (QC), is a data algorithm based on quantum mechanics which accomplished by substituting each point in given dataset with Gaussian. The width of the Gaussian σ value, hyper-parameter can be manually defined and manipulated to suit application. Numerical methods are used find all minima potential as they correspond cluster centers. Herein, we investigate mathematical task expressing finding roots exponential polynomial corresponding two-dimensional potential. This an outstanding because normally such expressions impossible solve analytically. However, prove that if points included square region size σ, there only one minimum. bound not useful number solutions look for, numerical means, it allows propose new approach “per block”. technique decreases particles approximating some groups weighted particles. These findings problem but also for polynomials encountered chemistry, Solid-state Physics other applications.