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Bridging Density Functional Theory and Big Data Analytics with Applications

  • Chien-Chang Chen
  • Hung-Hui Juan
  • Meng-Yuan Tsai
  • Henry Horng-Shing Lu
Chapter
Part of the Springer Handbooks of Computational Statistics book series (SHCS)

Abstract

The framework of the density functional theory (DFT) reveals both strong suitability and compatibility for investigating large-scale systems in the Big Data regime. By technically mapping the data space into physically meaningful bases, the chapter provides a simple procedure to formulate global Lagrangian and Hamiltonian density functionals to circumvent the emerging challenges on large-scale data analyses. Then, the informative features of mixed datasets and the corresponding clustering morphologies can be visually elucidated by means of the evaluations of global density functionals. Simulation results of data clustering illustrated that the proposed methodology provides an alternative route for analyzing the data characteristics with abundant physical insights. For the comprehensive demonstration in a high dimensional problem without prior ground truth, the developed density functionals were also applied on the post-process of magnetic resonance imaging (MRI) and better tumor recognitions can be achieved on the T1 post-contrast and T2 modes. It is appealing that the post-processing MRI using the proposed DFT-based algorithm would benefit the scientists in the judgment of clinical pathology. Eventually, successful high dimensional data analyses revealed that the proposed DFT-based algorithm has the potential to be used as a framework for investigations of large-scale complex systems and applications of high dimensional biomedical image processing.

Keywords

Density functional theory (DFT) Big data High dimensional data analysis Image analysis 

Notes

Acknowledgements

We would like to acknowledge the supports from National Science Council, National Center for Theoretical Sciences, Shing-Tung Yau Center, Center of Mathematical Modeling and Scientific Computing at National Chiao Tung University in Taiwan.

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Chien-Chang Chen
    • 1
    • 2
  • Hung-Hui Juan
    • 2
  • Meng-Yuan Tsai
    • 3
  • Henry Horng-Shing Lu
    • 3
    • 4
    • 2
  1. 1.Bio-MicroSystems Integration Laboratory, Department of Biomedical Sciences and EngineeringNational Central UniversityTaoyuan CityTaiwan
  2. 2.Shing-Tung Yau CenterNational Chiao Tung UniversityHsinchu CityTaiwan
  3. 3.Institute of StatisticsNational Chiao Tung UniversityHsinchu CityTaiwan
  4. 4.Big Data Research CenterNational Chiao Tung UniversityHsinchu CityTaiwan

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