Quantum clustering
Quantum Clustering (QC) is a class of data-clustering algorithms that use conceptual and mathematical tools from quantum mechanics. QC belongs to the family of density-based clustering algorithms, where clusters are defined by regions of higher density of data points. QC was first developed by David Horn and Assaf Gottlieb in 2001. Original Quantum Clustering Algorithm Given a set of points in an n-dimensional data space, QC represents each point with a multidimensional Gaussian distribution, with width (standard deviation) sigma, centered at each point’s location in the space. These Gaussians are then added together to create a single distribution for the entire data set. (This step is a particular example of kernel density estimation, often referred to as a Parzen-Rosenblatt window estimator.) This distribution is considered to be the quantum-mechanical wave function for the data set. Loosely speaking, the wave function is a generalized description of where there are likely to be data points in the space. QC next introduces the idea of a quantum potential; using the time-independent Schrödinger equation, a potential surface is constructed which has the data set’s wave function as a stable solution. Details in the potential surface are more robust to changes in sigma (the width