Spatial variability of electronic transport in BiFeO3-CoFe 2O4 (BFO-CFO) self-assembled heterostructures is explored using spatially resolved first-order reversal curve (FORC) current voltage (IV) mapping. Multivariate statistical analysis of FORC-IV data classifies statistically significant behaviors and maps characteristic responses spatially. In particular, regions of grain, matrix, and grain boundary responses are clearly identified. k-Means and Bayesian demixing analysis suggest the characteristic response be separated into four components, with hysteretic-type behavior localized at the BFO-CFO tubular interfaces. The conditions under which Bayesian components allow direct physical interpretation are explored, and transport mechanisms at the grain boundaries and individual phases are analyzed. This approach conjoins multivariate statistical analysis with physics-based interpretation, actualizing a robust, universal, data-driven approach to problem solving, which can be applied to exploration of local transport and other functional phenomena in other spatially inhomogeneous systems.