One side lattice memory reduced ordering function allows discrimination in resting state fMRI

Currently there is a lot effort to define neurological biomarkers from resting state fMRI data for different neurological diseases. fMRI voxels are high dimensional vectors, so that dimensional reduction, to scalar values if possible, is highly desirable. At the same time, biomarkers are to be provided as brain localizations which may have an anatomical interpretation. A general procedure consists in the reduction of fMRI data to scalar values, which are then entered in a feature selection process to obtain the desired localizations of discriminant voxel sites in the brain. These voxel sites may be interpreted as biomarkers. Classification is performed on the feature vectors extracted from the selected brain voxel sites. In this paper, we follow an approach born from Multivariant Mathematical Morphology in order to obtain meaningful orderings on multivariate data. We define a supervised /i-ordering defined on the fMRI time series by the response of Lattice Auto-associative Memories (LAAM) built from specific fMRI voxels. Instead of performing morphological processing based on the induced ordering, we use the LAAM supervised /i-function map for feature selection and feature extraction. We perform a classification experiment on a set of resting state fMRI images of schizophrenia patients with and without a history of auditive hallucinations obtaining high accuracy with one side LAAM /i-function.