Accounting for Voxel Neighbourhood Relationship in the SVM

Methods The standard primal SVM includes a 2-norm constraint on the weight vector w. If we consider classifying brain scans with a linear kernel this encodes the expectation that the total activity across the whole brain is constrained. What it fails to capture is the expectation that activity levels form a smooth function across the brain. This is indirectly implemented by the smoothing in the preprocessing stage. An alternative approach is to put an appropriate prior over the weight vector that makes the machine learning biased towards weight vectors that are smooth. A natural way to define a prior is through a Gaussian Process (GP), that defines a multivariate Gaussian distribution P (w) over weight vectors w. Inclusion of log (P (w)) in the SVM objective will then bias the learner to pick more probable weights that are smoother. This will put larger values for pairs of variables that we expect to have similar values. Results …