Feature extraction for activity recognition in context-aware ubiquitous computing applications is usually a heuristic process, informed by underlying domain knowledge. Relying on such explicit knowledge is problematic when aiming to generalize across different application domains. We investigate the potential of recent machine learning methods for discovering universal features for context-aware applications of activity recognition. We also describe an alternative data representation based on the empirical cumulative distribution function of the raw data, which effectively abstracts from absolute values. Experiments on accelerometer data from four publicly available activity recognition datasets demonstrate the significant potential of our approach to address both contemporary activity recognition tasks and next generation problems such as skill assessment and the detection of novel activities.