The study of the functional organization of the human brain using resting-state functional MRI (rsfMRI) has been of significant interest in cognitive neuroscience for over two decades. The functional organization is characterized by patterns that are believed to be hierarchical in nature. From a clinical context, studying these patterns has become important for understanding various disorders such as Major Depressive Disorder, Autism, Schizophrenia, etc. However, extraction of these interpretable patterns might face challenges in multi-site rsfMRI studies due to variability introduced due to confounding variability introduced by different sites and scanners. This can reduce the predictive power and reproducibility of the patterns, affecting the confidence in using these patterns as biomarkers for assessing and predicting disease. In this thesis, we focus on the problem of robustly extracting hierarchical patterns that can be used as biomarkers for diseases. We propose a matrix factorization based method to extract interpretable hierarchical decomposition of the rsfRMI data. We couple the method with adversarial learning to improve inter-site robustness in multi-site studies, removing non-biological variability that can result in less interpretable and discriminative biomarkers. Finally, a generative-discriminative model is built on top of the proposed framework to extract robust patterns/biomarkers characterizing Major Depressive Disorder. Results on large multi-site rsfMRI studies show the effectiveness of our method in uncovering reproducible connectivity patterns across individuals with high predictive power while maintaining clinical interpretability. Our framework robustly identifies brain patterns characterizing MDD and provides an understanding of the manifestation of the disorder from a functional networks perspective which can be crucial for effective diagnosis, treatment and prevention. The results demonstrate the method's utility and facilitate a broader understanding of the human brain from a functional perspective.