15. Bridging Density Functional Theory and Big Data Analytics with Applications

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.