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In addition to the standard observational assessment for autism spectrum disorder (ASD), recent advancements in neuroimaging and machine learning (ML) suggest a rapid and objective alternative using brain imaging. This work presents a pipelined framework, using functional magnetic resonance imaging (fMRI) that allows not only an accurate ASD diagnosis but also the identification of the brain regions contributing to the diagnosis decision. The proposed framework includes several processing stages: preprocessing, brain parcellation, feature representation, feature selection, and ML classification. For feature representation, the proposed framework uses both a conventional feature representation and a novel dynamic connectivity representation to assist in the accurate classification of an autistic individual. Based on a large publicly available dataset, this extensive research highlights different decisions along the proposed pipeline and their impact on diagnostic accuracy. A large publicly available dataset of 884 subjects from the Autism Brain Imaging Data Exchange I (ABIDE-I) initiative is used to validate our proposed framework, achieving a global balanced accuracy of 98.8% with five-fold cross-validation and proving the potential of the proposed feature representation. As a result of this comprehensive study, we achieve state-of-the-art accuracy, confirming the benefits of the proposed feature representation and feature engineering in extracting useful information as well as the potential benefits of utilizing ML and neuroimaging in the diagnosis and understanding of autism.