## 4 Quantitative Methods for the Detection of AD
### Support Vector Machines
The radial basis function (RBF)  
\[RBF\big{(}\mathbf{x},\mathbf{x}^{\prime}\big{)}=\exp\left[-\frac{|\mathbf{x}-\mathbf{x}^{ \prime}|^{2}}{2\sigma^{2}}\right], \tag{28}\]  
is a very common choice for this purpose since it may express data over a continuous range and therefore as infinite effective dimensionality [123]. Choice of kernel for exploiting the \"kernel trick\" is sensitive to the nature of the data and results can vary. SVMs are quite amenable to incorporating regularization methods into the optimization process. They may also undergo \(k\)-fold cross-validation. Both regularization and cross-validation can help prevent overfitting [85]. SVMs may, however, be easily confounded by overlapping or noisy datasets and may underperform when the number of features is larger than the number of training samples. Noisy datasets may, however, be more accurately differentiated through one-class SVMs. SVM hyperplanes may also be difficult to interpret since they may be very high-dimensional. SVMs also do not output any probabilistic information related to the classification label because they are intrinsically binary classifiers. Classification tasks with more than two labels necessitate training multiple binary classifiers for each pair of cases. SVMs are highly effective in high-dimensional  
Figure 5: Visualization of the decision boundary for sequential minimal SVM on FDG-PET images of AD patients and healthy controls. Images scaled according to mean z-score and standard deviation of whole images for the purposes of visualization. Reprinted/adapted with permission from Ref. [85]. Copyrights under Creative Commons Attribution 4.0 International License ([[http://creativecommons.org/licenses/by/4.0/](http://creativecommons.org/licenses/by/4.0/)]([http://creativecommons.org/licenses/by/4.0/](http://creativecommons.org/licenses/by/4.0/)), accessed on 1 October 2022). spaces and perform optimally on linearly separable data. The optimization algorithms are also quite mature and highly efficient in their use of computational resources [124]. After determining the optimal hyperplane separating each group, an FDG-PET image may be vectorized (AKA flattened) and fed into an SVM for classification. This remains a very common way of using SVMs on image-based data because this method is extremely amenable to feature selection/engineering practices and to the concatenation of additional features along this voxel-vector (data fusion). Using two different forms of SVM-based classifiers (the iterative single-data algorithm and sequential minimal optimization), [PERSON] et al., were able to test two forms of SVM for classifying different patient groups. In classifying AD vs. HC, they achieved the best performance with the iterative single-data algorithm SVM (AUC = 0.945, sensitivity = 0.840, specificity = 0.955), whereas for classifying sMCI vs. pMCI, they reported a combined performance (sensitivity \(\times\) specificity) of 0.590 on a privately curated dataset [85]. [PERSON] et al., were able to classify AD vs. HC patients using a SVM classifier and PCA-based data preprocessing that performed with sensitivity = 88.64%, sensitivity = 87.70%, and accuracy = 88.24% [125]. [PERSON] et al., were able to achieve 90.38% accuracy on the same task using raw image data (voxels as features) [126]. [PERSON] et al., were able to introduce a feature selection algorithm that used 21 regions from FDG-PET images to achieve 95.07% accuracy on AD vs. HC classification using SVM [127]. [PERSON] et al., developed an SVM-based classifier that used \({}^{18}\)F-flortaucipir tau-PET data and SSM-PCA [128]. They showed that their classifier and tracer were able to differentiate between amyloid-positive and amyloid-negative, typical and atypical AD patients, and FTD. Their classifier was also able to predict amyloid positivity with an AUC = 0.952 [128]. [PERSON] et al., used the colocalization of amyloid and tau burden in a cohort of amyloid-positive patients for an SVM classifier.