  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.
