Abstract
The underlying optimization problem for the maximal margin classifier is only feasible if the two classes of pattern vectors are linearly separable. However, most of the real life classification problems are not linearly separable. Nevertheless, the maximal margin classifier encompasses the fundamental methods used in standard SVM classifiers. The solution to the optimization problem in the maximal margin classifier minimizes the bound on the generalization error (Vapnik, 1998). The basic premise of this method lies in the minimization of a convex optimization problem with linear inequality constraints, which can be solved efficiently by many alternative methods (Bennett & Campbell, 2000).
Key Terms in this Chapter
MRS: Magnetic resonance spectroscopy, also known as MRSI (MRS Imaging) and volume selective NMR spectroscopy, is a technique which combines the spatially-addressable nature of MRI with the spectroscopically-rich information obtainable from NMR. MR spectroscopy provides a wealth of chemical information on a region.
EEG: Electroencephalography is the measurement of the electrical activity of the brain from electrodes placed on the scalp or, in special cases, subdurally or in the cerebral cortex. The resulting traces are known as an electroencephalogram (EEG) and represent a summation of post-synaptic potentials from a large number of neurons.
MRI: Magnetic resonance imaging, formerly referred to as magnetic resonance tomography (MRT), is a noninvasive method using nuclear magnetic resonance to render images of the inside of an object. It is primarily used in medical imaging to demonstrate pathological or other physiological alterations of living tissues. MRI also has uses outside of the medical field, such as detecting rock permeability to hydrocarbons and as a non-destructive testing method to characterize the quality of products such as produce and timber.
SPECT: Single photon emission computed tomography is a nuclear medicine tomographic imaging technique using gamma rays. It is very similar to conventional nuclear medicine planar imaging using a gamma camera. However, it is able to provide true 3D information. This information is typically presented as cross-sectional slices through the patient, but can be freely reformatted or manipulated as required.
SVM: Support vector machine is a set of related supervised learning methods used for classification and regression. SVMs belong to a family of generalized linear classifiers. They can also be considered a special case of Tikhonov regularization. A special property of SVMs is that they simultaneously minimize the empirical classification error and maximize the geometric margin; hence they are also known as maximum margin classifiers.
TCD: Transcranial doppler is a test that measures the velocity of blood flow through the brain’s blood vessels. It is used to help in the diagnosis of emboli, stenosis, vasospasm from a subarachnoid hemorrhage (bleeding from a ruptured aneurysm), and other problems. It is often used in conjunction with other tests such as MRI, MRA, carotid duplex ultrasound, and CT scans.
fMRI: Functional magnetic resonance imaging is the use of MRI to measure the haemodynamic response related to neural activity in the brain or spinal cord of humans or other animals. It is one of the most recently developed forms of neuroimaging.