Next, we used cosine similarity (cos) to describe how similar patches are to each other in their underlying relative combination of features based on their location (Figure 5a).  We found that across HVs, homotopic patches (in the same location on the cortical sheet) appeared more similar than randomly selected patches (\(cos=0.45\pm 0.28\) for homotopic versus \(cos=0.00\pm 0.29\) for heterotopic random patches, \(p<0.001\)\(d=1.57\)).  Despite their differing locations, FCD patches were more similar to each other in their features (\(cos=0.29\pm0.29\)) than to random HV cortical patches (FCD vs heterotopic patches \(cos=0.006\pm0.29\)\(p<0.001\)\(d=0.97\)), and also appeared quite similar to homotopic patches in HVs (FCD vs homotopic patches \(cos=0.24\pm0.31\)\(p=1.78\)\(d=0.17\)), consistent with the fact that these often subtle lesions have a fairly typical appearance for their given location. 

Local Normalization

While FCDs can be found in nearly any cortical region, normal cortical outlier regions by definition have fairly consistent spatial locations across HVs.  Local normalization allows for detection of differences from the expected appearance at any given cortical location.  Following local normalization, as expected, we found that patches in the outlier ROIs appeared more "typical" for their location, now with a similar Mahalanobis distance to randomly selected cortical patches (random cortex MD = \(1.86\pm0.52\) versus precentral MD = \(1.92\pm0.52\)\(d=0.10\), and insula MD = \(1.59\pm0.36\)\(d=0.63\)).  In contrast, following local normalization, FCDs remained as significant outliers (MD = \(3.55\pm0.81\)) compared to both normal cortex and the previously outlying ROIs (versus normal cortex  \(d=2.81\),  precentral \(d=2.78\), insula \(d=4.09\)) (Figure 5a).  Cosine similarity between FCD patches also became significantly higher following local normalization (\(0.40\pm 0.26\)) compared to non-lesional patches at any location (to homotopic patches \(cos=0.00\pm 0.30\)\(p<0.001\)\(d=1.40\), and to heterotopic patches \(cos=0.00\pm 0.28\)\(p<0.001\)\(d=1.44\), with no difference between the two, \(p=0.54\), ) (Figure 5a, left).  Local normalization, therefore, not only aids with global outlier detection by decreasing the "outlierness" of normal cortical regions, but also local outlier detection, by further distancing FCDs from the expected appearance at their location in the cortical sheet.