Group learning using contrast NMF : Application to functional and structural MRI of schizophrenia

Non-negative matrix factorization (NMF) has increasingly been used as a tool in signal processing in the last couple of years. NMF, like independent component analysis (ICA) is useful for decomposing high dimensional data sets into a lower dimensional space. Here, we use NMF to learn the features of both structural and functional magnetic resonance imaging (sMRI/fMRI) data. NMF can be applied to perform group analysis of imaging data and we apply it to learn the spatial patterns which linearly covary among subjects for both sMRI and fMRI. We add an additional contrast term to NMF (called co-NMF) to identify features distinctive between two groups. We apply our approach to a dataset consisting of schizophrenia patients and healthy controls. The results from co-NMF make sense in light of expectations and are improved compared to the NMF results. Our method is general and may prove to be a useful tool for identifying differences between multiple groups.