QC has a single main hyperparameter, which is the width sigma of the Gaussian distribution around each data point.
Developed by Marvin Weinstein and David Horn in 2009,[2] Dynamic Quantum Clustering (DQC) extends the basic QC algorithm in several ways.
DQC uses the same potential landscape as QC, but it replaces classical gradient descent with quantum evolution.
To do this, each data point is again represented by its individual wave function (a multidimensional Gaussian distribution with width sigma).
The time-dependent Schrödinger equation is then used to compute each wave function's evolution over time in the given quantum potential.
This non-locality creates the possibility of tunneling, where a point will seem to ignore or pass through a potential barrier on its way toward some lower minimum.
The biggest problem in non-convex gradient descent is often the existence of many small and uninteresting local minima where points can get stuck as they descend.
DQC introduces two new hyperparameters: the time step, and the mass of each data point (which controls the degree of tunneling behavior).
Whereas tuning of sigma is integral to understanding any new data set, both time step and mass can usually be left at reasonable default values and still produce useful results.
When needed, DQC addresses this problem by selecting a limited number of points from the data set to act as a basis (see next section).
The largest reasonable basis size depends on available computing resources, and on how long one is willing to wait for results.
As of 2020, without access to enterprise-level computing resources, the largest tractable basis size is typically in the range of 1,500–2,000 points.
The trajectories have the same dimensionality as the data space, which is often much larger than 3; the visualization is simply a 3D view into a higher-dimensional motion.
Second, they can be treated as regressions: position along the channel at a given time (or, equivalently, order of arrival at the cluster center) may be correlated with some metadata of interest.
Variants of QC have been applied to real-world data in many fields, including biology,[1][2][3][4][5][6] geology,[3][7] physics,[3][4][8] finance,[3] engineering,[4] and economics.
[9] With these applications, a comprehensive mathematical analysis to find all the roots of the quantum potential has also been worked out.