Several PET studies have explored the relationship between β-amyloid load and tau uptake at the early stages of Alzheimer's disease (AD) progression. Most of these studies have focused on the linear relationship between β-amyloid and tau at the local level and their synergistic effect on different AD biomarkers. We hypothesize that patterns of spatial association between β-amyloid and tau might be uncovered using alternative association metrics that account for linear as well as more complex, possible nonlinear dependencies. In the present study, we propose a new Canonical Distance Correlation Analysis (CDCA) to generate distinctive spatial patterns of the cross-correlation structure between tau, as measured by [18F]flortaucipir PET, and β-amyloid, as measured by [18F]florbetapir PET, from the Alzheimer's Disease Neuroimaging Initiative (ADNI) study. We found that the CDCA-based β-amyloid scores were not only maximally distance-correlated to tau in cognitively normal (CN) controls and mild cognitive impairment (MCI), but also differentiated between low and high levels of β-amyloid uptake. The most distinctive spatial association pattern was characterized by a spread of β-amyloid covering large areas of the cortex and localized tau in the entorhinal cortex. More importantly, this spatial dependency varies according to cognition, which cannot be explained by the uptake differences in β-amyloid or tau between CN and MCI subjects. Hence, the CDCA-based scores might be more accurate than the amyloid or tau SUVR for the enrollment in clinical trials of those individuals on the path of cognitive deterioration.