Neuroimaging is an interdisciplinary field involving physicists, engineers, computer scientists and statisticians to help analyze and quantify any information gleaned from the captured images. Brain images are captured as 1D signals (via electro-encephalography (EEG)), 2D/3D images and 4D volumes (via computer tomography and magnetic resonance imaging). However, the pathogenesis of each neurological disorder is different and requires different approaches to analyze them. The overall goal of this dissertation is focused on developing novel computational algorithms to address challenging problems in 1D, 2D/3D and 4D neuroimaging. This dissertation makes contributions to the above tasks by proposing: (1) A novel machine learning algorithm to classify 1D Electrocorticographic channels for language localization; (2) A multi-domain deep learning framework to improve the channel localization task in 1D data; (3) A novel multi-modal ML algorithm to analyze fMRI and MRI data; (4) A capsule encoder model to learn stronger representations of high-dimensional data.