Dynamic Quantum Clustering
Dynamic Quantum Clustering (DQC) is a visual method that was developed by David Horn and Marvin Weinsten, and it is a method to help extract information in a multi-dimentisonal data set. This method is able to discover small but valuable subsets of data, and it also can reveal the interesting structure of data which other conventional clustering methods might skip.
Dynamic Quantum Clustering creates a search strategy for a user to search for unknown information, even if the user is not sure that the information is in the set of data. The strategy begins with connecting the data points from their initial position to the nearest region of higher density, and steps after this are referred to as evolution of data. One unique characteristic of DQC is that it is able to characterize hidden data before it starts analyzing data. Thus, it allows the user to see the unexpected structure of a very complex data set because it does not assume that there is a data structure to be found. The algorithm of DQC is quite similar to the algorithms of quantum mechanics, and then it uses quantum evolution to move a point to the nearest point in higher density. Then, after it forms a cluster of data points, it derives the structure of the data.
Applications of DQC
Nano-Chemistry (TXM - XANES)
DQC has the ability to analyze spectroscopic data, which is essential for X-ray absorption spectroscopy used by chemists. DQC is proficient at grouping a large number of raw spectra which have different shapes without making assumptions about the substances. The method is able to demonstrate the complicated filamentary structures hidden in the large data set.
Pump probe experiment
The SLAC Linear Coherent Light Source pump-probe experiment is another large and complex data set, and it is important to detect if the clean data have equilibrium phonon dynamics. DQC revealed unexpected filamentary structures.
Finance
This dataset consists of S&P 500 data, and DQC is able to reveal a surprising structure after analyzing how the stocks correlated with one another.
References
- Weinstein, M.; Mierer, F.; Hume, A.; Sciau, Ph.; Shaked, G.; Hofstetter, E.; Persi, E.; Mehta, A.; Horn, D. (October 17, 2019). "Analyzing Big Data with Dynamic Quantum Clustering". arXiv:1310.2700.
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