The study of healthy brain development helps to better understand the brain transformation and brain connectivity patterns which happen during childhood to adulthood. This study presents a sparse machine learning solution across whole-brain functional connectivity (FC) measures of three sets of data, derived from resting state functional magnetic resonance imaging (rs-fMRI) and task fMRI data, including a working memory n-back task (nb-fMRI) and an emotion identification task (em-fMRI). These multi-modal image data are collected on a sample of adolescents from the Philadelphia Neurodevelopmental Cohort (PNC) for the prediction of brain ages. Due to extremely large variable-to-instance ratio of PNC data, a high dimensional matrix with several irrelevant and highly correlated features is generated and hence a pattern learning approach is necessary to extract significant features. We propose a sparse learner based on the residual errors along the estimation of an inverse problem for the extreme learning machine (ELM) neural network. The purpose of the approach is to overcome the overlearning problem through pruning of several redundant features and their corresponding output weights. The proposed multimodal sparse ELM classifier based on residual errors (RES-ELM) is highly competitive in terms of the classification accuracy compared to its counterparts such as conventional ELM, and sparse Bayesian learning ELM.