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The link between changes in the material crystal structure and itsmechanical, electronic, magnetic, and optical functionalities - known as thestructure-property relationship - is the cornerstone of the contemporarymaterials science research. The recent advances in scanning transmissionelectron and scanning probe microscopies (STEM and SPM) have opened anunprecedented path towards examining the materials structure-propertyrelationships on the single-impurity and atomic-configuration levels. Lacking,however, are the statistics-based approaches for cross-correlation of structureand property variables obtained in different information channels of the STEMand SPM experiments. Here we have designed an approach based on a combinationof sliding window fast Fourier transform, Pearson correlation matrix, andlinear and kernel canonical correlation, to study a relationship betweenlattice distortions and electron scattering from SPM data on graphene withdefects. Our analysis revealed that the strength of coupling to strain isaltered between different scattering channels, which can explain coexistence ofseveral quasiparticle interference patterns in nanoscale regions of interest.In addition, the application of kernel functions allowed us to extract anon-linear component of the relationship between the lattice strain andscattering intensity in graphene. The outlined approach can be further utilizedtowards analyzing correlations in various multi-modal imaging techniques wherethe information of interest is spatially distributed and generally has acomplex multidimensional nature.

Data Mining Graphene: Correlative Analysis of Structure and Electronic Degrees of Freedom in Graphenic Monolayers with Defects