Poor alertness experienced by individuals may lead to serious accidents that impact on people’s health and safety. To prevent such accidents, an efficient automatic alertness states identification is required. Sparse representation-based classification has recently gained a lot of popularity. A classifier from this class typically comprises three stages: dictionary learning, sparse coding and class assignment. Gini index, a recently proposed method, was shown to possess a number of properties that make it a better sparsity measure than the widely used l0- and l1-norms. This paper investigates whether these properties also lead to a better classifier. The proposed classifier, unlike the existing sparsity-based ones, embeds the Gini index in all stages of the classification process. To assess its performance, the new classifier was used to automatically identify three alertness levels, namely awake, drowsy, and sleep using EEG signal. The obtained results show that the new classifier outperforms those based on l0- and l1-norms.