Finding atrophy patterns of grey matter through orthonormal non-negative factorization

We used orthonormal projective non-negative matrix factorization (OPNMF) to identify distinct spatial components of voxel-wise volume loss in the brains of patients with Alzheimer's disease relative to age-matched normal controls. Non-negative matrix factorization (NMF) is a dimension reduction approach which can be used to extract spatially localized components of volume loss from 3D T1-weighted MR images. OPNMF is a variant of NMF with a potential for providing more biologically meaningful components to help better assess the patterns of brain atrophy. Once components have been defined, non-negative coefficients representing each component's contribution to volume loss can be defined in subjects not included in the group used for component discovery. These coefficients are subject-specific quantitative attributes of atrophy, and we studied their partial dependence network using a Gaussian copula graphical model. We also verified their ability to distinguish diagnosis groups. We performed a clustering approach to investigate possible imaging subtypes of Alzheimer's Disease patients. Our results are the first attempt to apply OPNMF to Alzheimer's Disease and we detect different subtypes based on components of gray matter atrophy which correlate with previous work.