For a training set X = {x 1 , x 2 , ..., x m } of m samples and a test set Y = {y 1 , y 2 , ..., y n } of n samples, such that X ∩ Y = ∅, each component in the full kernel matrix is defined as follows (step S2 in Figure 2): where z i and z j are samples from the set We then normalize the kernel matrix by dividing each component by the square root of the product of the two corresponding diagonal components: We transform the normalized kernel matrix into a radial basis function (RBF) kernel matrix as follows: As the kernel matrix is already normalized, we can choose σ 2 = 0.5 for simplicity.
equation (4) becomes: each row in the RBF kernel matrixK is now interpreted as a feature vector, going from step S2 to step S3 in Figure 2.