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As a global measure of the concordance between two parcellations, we used the Adjusted Rand Index (ARI) and a new similarity index developed for this application.
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To address the global similarity or concordance of two parcellations we first applied the Adjusted Rand Index (ARI; [32]).
While the above results revealed both simple and highly complex correspondences between region definitions owing to multiple atlasing methods, we additionally sought to provide a single scalar-valued index of global concordance between two parcellations.
These graph-based depictions as shown in Figure 6(B) provide a simple, straight-forward means for understanding the major spatial relationships between two parcellations.
The ordering of regions in each parcellation as depicted in Figure 3(A) is somewhat arbitrary, and thus visually determining the degree of correspondence between two parcellations is difficult.
Figure 6(A) shows the initial bipartite representation of the correspondence between two parcellations based on probabilistic atlases of similar scope, the Harvard-Oxford (H-O) and the LPBA40 atlases.
Although our SVD-based approach (shown in Figure 5A) does not necessarily yield the optimal solution, in general, lower resulting bandwidth is indicative of better correspondence between the two parcellations.
The alignment of two parcellations that would, theoretically, enable mapping between the constituent regions with the highest degree of certainty occurs when every region from one parcellation corresponds directly and exclusively to one region from the other.
For any pair of parcellations, we define a weighted bipartite graph B = (V1+V2, E) where edges E are weighted as:
The above measures are each defined with respect to two parcellations.
This is useful to impose a meaningful order on the sets of region labels when comparing two parcellations.
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CEO of Professional Science Editing for Scientists @ prosciediting.com