Electroencephalography (EEG) serves as an effective diagnostic tool for mental disorders and neurological abnormalities. Enhanced analysis and classification of EEG signals can help improve performance in classifying the disorders and abnormalities. A new approach is examined here for enhancing EEG classification performance using a novel model of data representation that leverages knowledge of spatial layout of EEG sensors. An investigation of the performance of the proposed data representation model provides evidence of consistently higher classification accuracy of the proposed model compared with a model that ignores the sensor layout. The performance is assessed for models that represent the information content of the EEG signals in two different ways: a one-dimensional concatenation of the channels of the frequency bands and a proposed image-like two-dimensional representation of the EEG channel locations. The models are used in conjunction with different machine learning techniques. Performance of these models is examined on two tasks: social anxiety disorder classification, and emotion recognition using a dataset, DEAP, for emotion analysis using physiological signals. We hypothesize that the proposed two-dimensional model will significantly outperform the one-dimensional model and this is validated in our results as this model consistently yields 5-8% higher accuracy in all machine learning algorithms investigated. Among the algorithms investigated, Convolutional Neural Networks provide the best performance, far exceeding that of Support Vector Machine and k-Nearest Neighbors algorithms.