Brain interictal epileptiform discharges (IEDs), as the fundamental indicators of seizure, are transient events occurring between two or before seizure onsets, captured using electroencephalogram (EEG). For epilepsy diagnosis and localization of seizure sources, both interictal and ictal recordings are extremely informative. Accurate detection of IEDs from over the scalp helps faster diagnosis of epilepsy. The scalp EEG (sEEG) suffers from a low signal-to-noise ratio and high attenuation of IEDs due to the high skull electrical impedance. On the other hand, the intracranial EEG (iEEG) recorded using implanted electrodes enjoys high temporal-spatial resolution and enables capturing most IEDs. Therefore, in this thesis, the focus is on the identification of IEDs from the concurrent scalp and intracranial EEGs. Multi-way analysis provides an opportunity to jointly analyse the data in different domains. IEDs may share some features within and between the segments. We have developed methods based on multi-way analysis and tensor factorization to detect the IEDs from the concurrent sEEG in both segmented and real-time approaches. The diversities in IED morphology, strength, and source location within the brain cause a great deal of uncertainty in their labeling by clinicians. We have exploited and incorporated this uncertainty (the probability of the waveform being an IED) in an IED detection system. Furthermore, IEDs are naturally sparse. We have benefited from the sparsity of IED waveforms in developing an algorithm to exploit sparse common features among the IED segments, referred to as sparse common feature analysis. By mapping sEEG to iEEG, the sEEG quality is improved. In this thesis, the proposed tensor factorization maps the time-frequency features of sEEG to those of iEEG to detect the IEDs from over the scalp with high sensitivity. We have concatenated time, frequency, and channel modes of iEEG recordings into a tensor. After decomposing the tensor into temporal, spectral, and spatial components, the EEG time-frequency features have been extracted and projected onto the temporal components. Furthermore, we have developed two novel algorithms based on generative adversarial networks to map the raw sEEG to iEEG. As a result of this work, the visibility of IEDs from sEEG has over 4-fold improvement. Additionally, the outcome paves the path for future research in epilepsy prediction, seizure source localisation, and modeling the brain seizure pathways.