Overview of the Canonical Correlation Analysis (CCA) technique in the context of β-amyloid and tau PET datasets. CCA searches for brain weights or loadings that maximize the correlation between linear combinations of the β-amyloid and tau variables. The linear combination or weighted sum of the PET datasets results in β-amyloid and tau scores for each individual subject. The scores can be combined to show how the amyloid-tau association is expressed across the whole sample.
We have constructed a multi-modality metric to assess nonlinear spatial associations between datasets of β-amyloid and tau PET images. Our method generalizes a well-known technique, called Canonical Correlation Analysis, to a broader scenario in which the classical Pearson’ correlation coefficient is no longer the underlying associative metric.
The diagram summarizes the fundamentals of the Canonical Correlation Analysis technique within the framework of brain images.
Given two datasets, let’s say amyloid and tau PET images, the CCA produces individual scores in a latent space that express a maximum correlation between all possible linear combinations or weighted sums of the corresponding brain image voxels. Hence, once in the latent space, the scores can be combined to assess the amyloid-tau linear association across the whole sample. Additionally, the weights or loadings provide useful spatial information about the set of voxels with a higher contribution to the maximum-correlated scores.