278 J. Zelenty et al.
different phases present in the data set and determine the most probable phase of each precipitate. Furthermore, by adapting GEMA into a Bayesian approach the user could incorporate prior knowledge regarding phases commonly found within the material, as well as their level of certainty. Finally, the algorithm could be extended to learn across
APT data sets. One could, in principle, have a hierarchical model that learns the differences between materials at the top-level; differences between regions of the same material at the mid-level; and then, finally, run GEMA within each APT data set while leveraging this information. Such hierarchical models are ubiquitous in the world of “big data” and extremely useful. As such, GEMA provides a small but crucial first step toward integrating the trillions of data points generated from thousands of APT runs to make broad claims about the structure of many disparate materials.
SUMMARY
In this paper, a new clustering algorithm, GEMA, was pre- sented, which utilizes aGMMto probabilistically distinguish clusters from random fluctuations in the matrix. This machine learning approach maximizes the data likelihood via EM: given atomic positions, the algorithm learns the position, size, and width of each cluster. A key advantage of GEMA is that atoms are probabilistically assigned to clusters, thus reflecting scientifically meaningful uncertainty regarding atoms located near precipitate/matrix interfaces. It was demonstrated that GEMA can outperform the maximum separation method in cluster detection accuracy when applied to realistically simulated data. Lastly, GEMA was successfully applied to real APT data.
ACKNOWLEDGMENTS
The EPSRC is kindly acknowledged for financial support under the grant EP/M022803/1.
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