Systems and methods for determining optimal parameters for dynamic quantum clustering analyses
In the present work, quantum clustering is extended to provide a dynamical approach for data clustering using a time-dependent Schrödinger equation. To expedite computations, we can approximate the time-dependent 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 and/or feature filtering. Additionally, the parameters of the analysis can be modified in order to improve the efficiency of the dynamic quantum clustering processes.
1. A method for data clustering, comprising:
obtaining a set of source data using a dynamic quantum clustering server system, where the set of source data comprises a data dimensionality;
assigning a subset of the set of source data to a representational space using the dynamic quantum clustering server system, where the representational space allows a distance between pieces of data in the set of source data to be measured;
constructing a potential function based on the representational space and the set of source data using the dynamic quantum clustering server system;
computing a set of frames of animation for the set of source data over a time interval using the dynamic quantum clustering server system wherein computing a frame of animation includes:
associating data points from the set of source data with states, where the states include initial wave functions;
computing kinetic and potential energies for each initial wave function;
determining updated wave functions based on the kinetic and potential energies of each initial wave function;
determining at least one trajectory for the time interval based on the updated wave functions; and
constructing the frame of animation based on the at least one trajectory;
evaluating the computed set of frames of animation for the set of source data using the dynamic quantum clustering server system, where the evaluation identifies data clusters comprising a subset of the set of source data within the computed set of frames of animation:
when a cluster threshold is reached:
generating a representation of the computed set of frames of animation using the dynamic quantum clustering server system; and
transmitting the generated representation to a client device displaying the generated representation by providing an interactive visual animation of point positions at one or more selected times; and
when the cluster threshold is not reached, iteratively:
identifying strongly clustered data in the computed set of frames of animation using the dynamic quantum clustering server system;
filtering the strongly clustered data from the set of source data to generate a set of filtered data using the dynamic quantum clustering server system; and
computing a second set of frames of animation for the set of filtered data using the dynamic quantum clustering server system.
2. The method of claim 1 , further comprising labeling the data clusters using the dynamic quantum clustering server system.
3. The method of claim 2 , wherein the data clusters are labeled with color information using the dynamic quantum clustering server system.
4. The method of claim 1 , further comprising preprocessing the set of source data points to reduce the dimensionality of the set of source data using the dynamic quantum clustering server system.
5. The method of claim 4 , wherein the set of source data is preprocessed using singular value decomposition.
6. The method of claim 1 , wherein the potential function is determined such that a quantum mechanical ground state of the potential function is equal to the sum of the initial states of the potential function.
7. The method of claim 6 , wherein the potential function is constructed as a sum of Gaussian functions centered at each data point in the set of source data.
8. The method of claim 6 , wherein computing a set of frames of animation comprises computing an expectation value of a quantum mechanical position operator using the dynamic quantum clustering server system.
9. The method of claim 1 , further comprising displaying the generated representation by providing an interactive visual display of point positions at one or more selected times using the dynamic quantum clustering server system.
10. The method of claim 1 , further comprising transmitting the generated representation to a client device configured to provide an interactive visual display of the generated representation.
11. The method of claim 1 , further comprising obtaining labeling data using the dynamic quantum clustering server system, where the labeling data identifies one or more features of the data clusters.
12. The method of claim 1 , wherein the representational space comprises a Hilbert space.
13. The method of claim 1 , wherein the potential function satisfies a time-independent Schrödinger equation.
14. The method of claim 1 , further comprising generating a matrix representation of the obtained source data using the dynamic quantum clustering server system, where the matrix representation is utilized in place of the obtained source data.
15. The method of claim 1 , wherein:
the potential function comprises a set of initial states; and
the cardinality of the set of initial states is based on the number of data points in the set of source data.
16. The method of claim 1 , further comprising:
generating the filtered data based on the strongly clustered data using the dynamic quantum clustering server system, where the filtered data comprises the strongly clustered data; and
computing the second set of frames of animation for the set of filtered data using the dynamic quantum clustering server system, where the second set of frames of animation comprises a set of frames of animation of the strongly clustered data.
17. The method of claim 1 , wherein the strongly clustered data is centered around a local minimum in the representational space.
18. The method of claim 1 , further comprising:
identifying when at least one piece of strongly clustered data becomes less strongly clustered using the dynamic quantum clustering server system; and
cease iteratively computing the second set of frames of animation using the dynamic quantum clustering server system.