In comparison to other biomedical signals, electroencephalography (EEG) signals are quite complex in nature, so it requires a versatile model for feature extraction and classification. The structural information that prevails in the originally featured matrix is usually lost when dealing with standard feature extraction and conventional classification techniques. The main intention of this work is to propose a very novel and versatile approach for EEG signal modeling and classification. In this work, a sparse representation model along with the analysis of sparseness measures is done initially for the EEG signals and then a novel convergence of utilizing these sparse representation measures with Swarm Intelligence (SI) techniques based Hidden Markov Model (HMM) is utilized for the classification. The SI techniques utilized to compute the hidden states of the HMM are Particle Swarm Optimization (PSO), Differential Evolution (DE), Whale Optimization Algorithm (WOA), and Backtracking Search Algorithm (BSA), thereby making the HMM more pliable. Later, a deep learning methodology with the help of Convolutional Neural Network (CNN) was also developed with it and the results are compared to the standard pattern recognition classifiers. To validate the efficacy of the proposed methodology, a comprehensive experimental analysis is done over publicly available EEG datasets. The method is supported by strong statistical tests and theoretical analysis and results show that when sparse representation is implemented with deep learning, the highest classification accuracy of 98.94% is obtained and when sparse representation is implemented with SI-based HMM method, a high classification accuracy of 95.70% is obtained.