A novel methodology is proposed for identifying epileptiform discharges associated with individuals exhibiting Infantile Spasms (ISS) also known as West Syndrome, which is characterized by electroencephalogram (EEG) recordings exhibiting hypsarrythmia (HYPS). The approach to identify these discharges consists of three stages: first - construct the time-frequency domain (TFD) of the EEG recording using matching pursuit TFD (MP-TFD), second - decompose the TFD matrix into two submatrices (W, H) using non-negative matrix factorization (NMF), and third - use the decomposed spectral and temporal vectors to locate the epileptiform discharges, referred to as spikes, during intervals of HYPS. The method was applied to an EEG dataset of five individuals and the identification of spike locations was compared with those which were visually identified by the epileptologists and those obtained using commercially available clinical analysis software. The MP-TFD method resulted in average true positive and false negative percentages of 86% and 14%, respectively, which represents a significant improvement over the clinical software, which achieved average true positive and false negative percentages of 4% and 96%, respectively.