Figure 1.
Principle of support vector machines.
(a) The algorithm tries to find a boundary that maximises the distance between groups. When the input data is viewed in two-dimensions it cannot be separated by a straight line. However, if the two-dimensional space is transformed into a three dimensional space, then it is possible to separate the data using a hyperplane. (b) The SVM tries to find a boundary that maximizes the distance between groups. The data that are closest to the maximum margin hyperplane are called support vectors. A unique set of support vectors defines the maximum margin hyperplane for the learning problem.
Table 1.
Demographic and Cognitive Characteristics of the Sample Groups.
Figure 2.
Boxplots showing the distribution of diffusion tensor MRI indices for the global WM ROI in control (CON), non-amnestic MCI (MCIna) and amnestic MCI (MCIa).
The boxplots represent the interquartile ranges, which contain 50% of individual subjects' values. The whiskers are lines that extend from the box to the highest and lowest values. A line across the box indicates the median values. * p<0.05 on post-hoc Tukey test.
Figure 3.
Paradigmatical reduced datasets.
Following reduction of the full dataset containing diffusion values from the 130,394 voxels in the white matter skeleton, to the top 500 voxels that distinguishes between control, MCIna and MCIa subjects, this figure shows representative scatter plots from one control subject (green), one MCIna subject (orange) and one MCIa subject (red). The diffusion values for the top 500 voxels from each diffusion index are plotted. Loess regression lines (span = 2/3, polynomial degree = 1) have been fitted through each subject's dataset. For FA, the loess regression line through the data points of the control subject are seen as higher than the loess lines through the data points from MCIa or MCIna subjects. The reverse is the case for DA, DR and MD, with the loess lines through MCIa subjects indicating higher values than the lines through MCIna or control loess lines. Outliers are excluded from these graphs. For the loess line, the span which determines smoothness was set to 0.66.
Figure 4.
Sensitivity, specificity, accuracy and the area under the curve for a receiver operating characteristic curve (ROC AUC) for control and MCI classification.
The values indicated are weighted averages for the two classes under consideration; i.e. control and MCI. Results are shown for 7 datasets – 100 voxels, 250 voxels, 500 voxels, 750 voxels, 1000 voxels, 2000 voxels and 3000 voxels. The voxels comprising these reduced datasets were selected by the ReliefF algorithm.
Figure 5.
ROC curve for control and MCI classification.
True positives refer to MCI volumes that are correctly classified as MCI, and false positives refer to volumes that are incorrectly labelled as MCI.
Figure 6.
Sensitivity, specificity, accuracy and the area under the curve for a receiver operating characteristic curve (ROC AUC) for Control, MCIna and MCIa classification.
The values indicated are weighted averages for the three classes under consideration; control, MCIna and MCIa. Results are shown for the 7 datasets – 100 voxels, 250 voxels, 500 voxels, 750 voxels, 1000 voxels, 2000 voxels and 3000 voxels. The voxels comprising these reduced datasets were selected by the ReliefF algorithm.
Figure 7.
ROC curve for control, MCIna and MCIa classification.
True positives refer to MCIna volumes that are correctly classified as MCIna, and false positives refer to volumes that are incorrectly labelled as MCIna.
Figure 8.
ROC curve for control, MCIna and MCIa classification.
True positives refer to MCIa volumes that are correctly classified as MCIa, and false positives refer to volumes that are incorrectly labelled as MCIa.
Figure 9.
Top 500 voxels selected for classification by the Relieff algorithm.
(a) Classification of control and MCI groups. The highest accuracy for this classification was achieved by the FA index. Here we show a cluster of voxels selected by the algorithm which is located in the forceps major. (b) Classification of control, MCIna and MCIa groups. For this classification of three groups, the highest accuracy was again achieved with the FA index. Here we show two significant clusters of voxels selected by Relieff. Similar to the two group classification, the forceps major was also implicated in three group classification. An additional significant cluster is located in the fronto-occipital fasciculus. Both (a) and (b) show the same sagittal slice in the right hemisphere (x = 29).