In this paper we compare three linear methods, independent component analysis (ICA), common spatial patterns (CSP), and linear discrimination (LD) for recovering task relevant neural activity from high spatial density electroencephalography (EEG). Each linear method uses a different objective function to recover underlying source components by exploiting statistical structure across a large number of sensors. We test these methods using a dual-task event-related paradigm. While engaged in a primary task, subjects must detect infrequent changes in the visual display, which would be expected to evoke several well-known event-related potentials (ERPs), including the N2 and P3. We find that though each method utilizes a different objective function, they in fact yield similar components. We note that one advantage of the LD approach is that the recovered component is easily interpretable, namely it represents the component within a given time window which is most discriminating for the task, given a spatial integration of the sensors. Both ICA and CSP return multiple components, of which the most discriminating component may not be the first. Thus, for these methods, visual inspection or additional processing is required to determine the significance of these components for the task.