Kernel Methods for Functional Neuroimaging Analysis

We propose an approach to analyzing functional neuroimages in which: (1) regions of neuronal activation are described by a superposition of spatial kernel functions, the parameters of which are estimated from the data; and (2) the presence of activation is detected by means of a generalized likelihood ratio test (GLRT). In an on-off design we model the spatial activation pattern as a sum of an unknown number of kernel functions of unknown location, amplitude and/or size. We employ two Bayesian methods of estimating the kernel functions. The first is a maximum a posteriori (MAP) estimation method based on a reversible-jump Markov-chain Monte-Carlo (RJMCMC) algorithm that searches for both the appropriate model complexity and parameter values. The second is a relevance vector machine (RVM), a kernel machine that is known to be effective in controlling model complexity (and thus discouraging overfitting).