PMC

Discriminative patterns of the healthy control group 2 (HC₂) vs at-risk mental state (ARMS) with disease transition (ARMS-T) vs ARMS without disease transition (ARMS-NT) classification analysis. A, HC₂ vs ARMS-T. B, HC₂ vs ARMS-NT. C, ARMS-T vs ARMS-NT. See the “Methods” section for an explanation of the visualization technique. Warm and cool colors represent volumetric reductions and increments, respectively, in the second vs the first group of the binary classifier.

Schematic representation of nonlinear support vector machine (SVM) classification (A) and large-margin classification (B). A, At left, 2 groups of individuals (red and green shapes) cannot be separated in the input space by a linear classifier because the relationship between the data instances and their class labels is nonlinear (black circle). At right, With the use of radial basis functions, the data can be mapped into a high-dimensional space where the groups can be separated by means of linear classification. The shaded shapes represent the support vectors that define the optimal separating hyperplane (OSH) (yellow). B, At left, infinite separating boundaries (dotted lines) may exist between 2 classes (red and green circles). At right, the SVM algorithm determines the OSH by maximizing the margin between the nearest data instances of opposite classes.

Discriminative patterns of the healthy control group 1 (HC₁) vs at-risk mental state, early (ARMS-E) vs at-risk mental state, late (ARMS-L) classification analysis. See the “Methods” section for an explanation of the visualization technique. Warm and cool colors represent volumetric reductions and increments, respectively, in the second vs the first group of the binary classifier. The units are gray matter volume residuals (after removing the effects of age and sex by means of partial correlation analysis and after scaling to a range of [−1, 1]). The gray matter volume reduction scales differed between HC₁ vs ARMS-E (A), HC₁ vs ARMS-L (B), and ARMS-E vs ARMS-L (C), with the largest effects being observed in the HC₁ vs ARMS-L classifier and the most subtle differences being present in the discriminative pattern of ARMS-E vs ARMS-L.