Table 1. Performance of the method using real-world datasets.

Cohort	Demographics	Brain Regions (Number of coefficients)	Misclassification Rates				Sensitivity & Specificity (adjusted)	Positive Predictive Value (adjusted)	Comments & Figure
			LOO (Entire Cohort)	Split Half (10 Training & 10 Test Samples)	LOO Split (20 Split Half Samples)	Adjusted (Entire Cohort)
ADHD Children; Healthy Children	41 participants, 33 males, 12.6±3.18 years; 42 participants, 18 males, 10.5±2.43 years	L&R AMY, L HC, L CN, L&R GP, R PUT, L TH (44)	0.024; 0.0952	0.11±0.11; 0.16±0.10	0.07±0.1; 0.14±0.14	0.064; 0.115	93.6% and 88.5%	0.89	Fig. 1
TS Children; ADHD Children	71 participants, 59 males, 11.19±2.2 years; 41 participants, 33 males, 12.6±3.18 years	L&R AMY, L&R HC, L CN, L&R GP, L&R PUT, L&R TH (141)	0.014; 0	0.0105±0.018; 0.005±0.0158	0.0256±0.021; 0±0	0.0017; 0·005	99.83% and 99.5%	0.997	PPV for predicting TS child (Fig. 1)
SZ Adults; BD Adults	65 participants, 41 males, 42.16±8.71 years 26 participants, 11 males, 37.66±10.36 years	L&R AMY, L&R HC, LH &RH (93)	0; 0	0.012±0.022; 0±0	0.0108±0.017; 0±0	0.001; 0	99.999% and 100%	1	PPV for predicting SZ adult (Fig. 2)
BD Adults; Healthy Adults	26 participants, 11 males, 37.66±10.36 years; 40 participants, 22 males, 32.42±10.7 years	L&R AMY, L HC, RH (82)	0; 0·025	0.044±0.048; 0.043±0.07	0.044±0.07; 0.031±0.033	0; 0.036	100% and 96.4%	0.95	Fig. 2
SZ Adults; TS Adults	65 participants, 41 males, 42.16±8.71 years; 36 participants, 21 males, 37·34±10·9 years	L&R AMY, L&R HC, LH & RH (196)	0; 0	0.003±0.009; 0±0	0±0; 0±0	0.003; 0	99.997% and 100%	1	PPV for predicting SZ adult (Fig. 2)
SZ Adults; Healthy Adults	65 participants, 41 males, 42.16±8.71 years; 40 participants, 22 males, 32.42±10.7 years	L&R AMY, L&R HC, LH &RH (119)	0.015; 0.025	0.106±0.047; 0.04±0.0459	0.0525±0.045; 0.01±0.02108	0.069; 0.055	93.1%; 94.5%	0.963	Fig. 2
TS Adults; Healthy Adults	36 participants, 21 males, 37.34±10.9 years; 40 participants, 22 males, 32.42±10.7 years	R HC (6)	0.11; 0.025	0.15±0.077; 0.18±0.193	0.09±0.09; 0.10±0.1	0·168; 0·10	83.2% and 90%	0.91	Fig. 3
TS Children Healthy Children	71 participants, 59 males, 11.19±2.2 years 42 participants, 18 males, 10.5±2.43 years	R HC, R GP (14)	0.014 0.19	0.13±0.177 0.29±0.17	0.09±0.15 0.31±0.15	0.054 0.21	94.6% and 79%	0.90	Fig. 3
High Risk; Low Risk	66 participants, 31 males, 33.30±12.90 years; 65 participants, 30 males, 24.79±13.14 years	L&R Cortical Thickness (26)	0.181; 0.246	0.15±0.11; 0.45±0.145	0.142±0.11; 0.4±0.143	0.19; 0.29	81% and 71%	0.74	Fig. 4
SZ Adults; TS Adults; Healthy Adults	65 participants, 41 males, 42.16±8.71 years; 36 participants, 21 males, 37.34±10.9 years; 40 participants, 22 males, 32.42±10.7 years	L&R AMY, L&R HC, LH & RH (253)	0.0153;0.22; 0.625	0.08±0.14; 0.533±0.28; 0.49±0.31	0.028±0.045; 0.64±0.31; 0.035±0.27	0.067; 0.11; 0.737			Classifying an individual among 3 groups: (1) SZ adult, (2) TS adult, or (3) healthy adult (Fig. S7)
			0.0153; 0	0.015±0.036; 0.011±0.019	0.006±0.01; 0.01±0.019	0.0245; 0.001	97.76% and 99.999%	0.999	Classifying an individual among two groups: (1) SZ adult, and (2) healthy or TS adult.
SZ Adults; BD Adults; Healthy Adults	65 participants, 41 males, 42.16±8.71 years; 26 participants, 11 males, 37.66±10.36 years; 40 participants, 22 males, 32.42±10.7 years	L&R AMY, L&R HC, LH & RH (112)	0.015; 0.11; 0	0.73±0.177; 0.28±0.24; 0.0515±0.057	0.078±0.10; 1±0; 0.097±0.133	0.80; 0.83; 0.046			Classifying an individual among 3 groups: (1) SZ adult, (2) BD adult, or (3) healthy adult (Fig. S7)
			0.14; 0	0.167±0.079; 0.0121±0.022	0.165±0.092; 0.011±0.04	0.14; 0	86% and 100%	1	Classifying an individual among two groups: (1) SZ adult or BD adult, and (2) healthy adult.

We applied our method for discriminating the brains of persons with a specific neuropsychiatric disorder from those of healthy persons or persons with other neuropsychiatric disorders. The misclassification rates were computed by applying (1) leave-one-out (LOO) analysis to the entire cohort of participants, (2) split-half analysis to10 pairs of training and test samples, each sample with half the total number of brains in the entire cohort, and (3) LOO analysis to each of the 10 test and 10 training samples used for the split half analyses. The differences in the misclassification rates computed in (2) and (3) were added to the misclassification rates computed for the entire cohort to compute the adjusted misclassification rates. These adjusted rates were then used to calculate the sensitivity and specificity of our method for discriminating brains. In addition, we computed the Positive Predictive Value (PPV) that measures the proportion of individuals having the illness (true positives) among all individuals classified by the method as having that illness (true positives+false positives). The PPV gives the likelihood that a person diagnosed with an illness using the classification algorithm actually has the illness and was close to 1 in most of the datasets. Because procedures classified individuals with high sensitivity and specificity, multiple and independent split-half analyses provided strong evidence that the procedures were robust to variations in the sampling of participants who generated the classification algorithm. The performance of three-way classifications was poor, however, suggesting an iterative approach with nested two-way classifications for the accurate discrimination of the brains among three clinical conditions. Using the iterative approach for classifying an adult as healthy, with BD, or with SZ, the misclassification rates were 0 for healthy adult, 0·14 for BD adult, and 0·14 for SZ adult. Similarly, for the iterative approach for classifying an adult as healthy, with TS, or with SZ, the misclassification rates were 0.10 for healthy adult, 0.168 for TS adult, and 0.0245 for SZ adult.

Brain Regions: these were the regions for which scaling coefficients differed significantly between diagnostic groups at a p-value<10⁻⁷ and that subsequently were submitted for hierarchical clustering. This column also lists the total number of coeffcients from all brain regions used in each classification.

ADHD: Attention Deficit/Hyperactivity Disorder; HC: Healthy children; TS: Tourette Syndrome; SZ: Schizophrenia; BD: bipolar disorder; HA: healthy adults; L: left; R: right; LH: Left Hemisphere; RL, Right Hemisphere; AMY: Amygdala; HC: Hippocampus; GP: Globus Pallidus; PUT: Putamen; TH: Thalamus; CN, Caudate Nucleus; PPV: positive predictive value.