Data Mining Graphene: Correlative Analysis of Structure and Electronic   Degrees of Freedom in Graphenic Monolayers with Defects
  The link between changes in the material crystal structure and its mechanical, electronic, magnetic, and optical functionalities - known as the structure-property relationship - is the cornerstone of the contemporary materials science research. The recent advances in scanning transmission electron and scanning probe microscopies (STEM and SPM) have opened an unprecedented path towards examining the materials structure-property relationships on the single-impurity and atomic-configuration levels. Lacking, however, are the statistics-based approaches for cross-correlation of structure and property variables obtained in different information channels of the STEM and SPM experiments. Here we have designed an approach based on a combination of sliding window fast Fourier transform, Pearson correlation matrix, and linear and kernel canonical correlation, to study a relationship between lattice distortions and electron scattering from SPM data on graphene with defects. Our analysis revealed that the strength of coupling to strain is altered between different scattering channels, which can explain coexistence of several quasiparticle interference patterns in nanoscale regions of interest. In addition, the application of kernel functions allowed us to extract a non-linear component of the relationship between the lattice strain and scattering intensity in graphene. The outlined approach can be further utilized towards analyzing correlations in various multi-modal imaging techniques where the information of interest is spatially distributed and generally has a complex multidimensional nature. 
Maxim Ziatdinov, Shintaro Fujii, Manabu Kiguchi, Toshiaki Enoki,   Stephen Jesse, Sergei Kalinin
cond-mat.mtrl-sci