Analysis of functional neuroimaging data in the studies of human brain has become very critical in understanding neuro-degenerative diseases such as Alzheimer's disease (AD). The most common approach in AD neuroimaging studies has been of univariate nature, where individual brain regions/voxels are analyzed separately. In many cases these techniques prove to be effective. However, they could not shed light on inter brain region connectivity associated with the brain function or disease of interest. Indeed, human brain is a very complex organ anatomically and the functional interactions between its regions are even more. As a result, there is a need to understand this interdependency or inter-connection of brain regions. There are several existing techniques to address this issue. They include principal component analysis (PCA), PCA based scaled subprofile modeling (SSM), Bayesian network approach and independent component analysis (ICA). In this study, we propose a machine learning technique called "Sparse Inverse Covariance Analysis" to learn the brain region interactivity, with minimal computational cost and appropriate degree of sparsity. Under Gaussian assumption, each element of the inverse covariance matrix represents conditional dependence between the constituent pair of variables, given all other variables. By introducing sparsity constraint, unnecessary/noisy functional dependencies are eliminated by setting the constituent element to zero, resulting into conditional independence between the variable pairs. Using functional FDG-PET data acquired from 49 AD and 67 normal subjects from the Alzheimer's disease neuroimaging initiative (ADNI) project, we evaluate this technique in terms of distinct brain region connectivity pattern in patients with AD compared to that in normal control subjects. It was found that the patients with AD had disconnections that are not present in the normal controls. This different connectivity pattern is potentially usable for clinical diagnosis and for establishing sensitive markers for the disease progression and treatment evaluation.