# Visual-Saliency-Based Abnormality Detection for MRI Brain Images--Alzheimer's Disease Analysis
## 2 Proposed Methodology
### Multiple-Kernel Learning (MKL)  
Multiple-kernel learning algorithms aim to discover the best combination of kernels to form the best classifier. Recently, different algorithms have been presented for forming two classes. The initial wrapper methods solve the MKL problem by handling a single SVM problem for a specific kernel weight. The second set of MKL algorithms uses optimization methods that reduce the number of computations. These methods use kernels that are larger than the wrapper methods. Basic multiple-kernel learning was discussed in [31] for simple classification problems. In the proposed method, a simple MKL and a simple and efficient MKL (SEMKL) [32] are used. The MKL method provides ordering for important features that are useful for classification tasks. Several studies have used MKL to classify genomic data and remote sensing data, and even though it is used for different classifications, it is an underestimated tool for Alzheimer's disease analysis. This study aims to use the MKL methodology by highlighting its unique benefits. The saliency maps contain information for classifying the AD and normal controls. Nevertheless, all parts do not have useful information for classification. Some regions have to be concentrated more for classification, whereas other regions are not highly concentrated. To analyze AD well, there is a mandate to reduce the size of the salient feature space. The Fisher discriminant ratio (FR) was used to characterize the classes. As it is a two-class classification problem, two means and two variances are obtained from the saliency map. \[FR=\frac{(m_{1}-m_{2})^{2}}{{v_{1}}^{2}+{v_{2}}^{2}} \tag{9}\]  
where \(m_{i}\) and \({v_{i}}^{2}\) are the mean and variance of the saliency maps, respectively. The \(FR\) value was calculated for each voxel of the volume. The \(FR\) value was taken as the threshold. If it is less than the threshold then more voxels can be selected. It also reduces the computational burden of voxel selection in the preliminary stage. It is used to select the most discriminative regions of the saliency map, which are used to segregate the disease images and normal control images. The classification performance was analyzed by varying the FR value. The simple MKL uses a sub-gradient descent to fetch the direction that has the most improvement. Subsequently, a line search was used to catch the finest set of weights. The  
Figure 4: Gabor filter with different orientations (\(0^{\circ}\), \(45^{\circ}\), \(90^{\circ}\), \(135^{\circ}\)) for MRI images. line search increases computational complexity; therefore, the SEMKL was used. The SEMKL dramatically decreases the number of computations by using a set of kernels derived from the Cauchy-Schwarz inequality. Prioritization of features and kernels is a prime consideration when choosing MKL algorithms. Kernel prioritization is important for overcoming the problems associated with MKL. The kernels can classify the data and provide boundaries [33]. The saliency maps provide a source of information on the location of the discriminative variations in the MRI images. They are the main source of differentiation between AD and normal diseases. In this method, multiple-kernel learning is used to classify the inputs [34]. The kernel matrices are of size \(M\times M\). A histogram intersection kernel is used to compute the similarity in the saliency maps. The kernel matrix is calculated between two saliency maps \(SM,SM^{\prime}\). \[KM(SM,SM^{\prime})=\sum_{i=1}^{m}\min\big{(}SM,SM^{\prime}\big{)} \tag{10}\]  
The multiple-kernel methods have higher classification accuracies than single-kernel methods [33]. Simple MKL adopts a gradient descent on the support vector machine objective value and updates the kernel weights iteratively. In addition, with multiple kernels, a single kernel was also calculated for each projection. All single kernels were summed using the weighted average method.