Error-space representations for multi-dimensional data streams with temporal dependence

In many application scenarios, data points are not only temporally dependent, but also expected in the form of a fast-moving stream. A broad selection of efficient learning algorithms exists which may be applied to data streams, but they typically do not take into account the temporal nature of the data. We motivate and design a method which creates an efficient representation of a data stream, where temporal information is embedded into each instance via the error space of forecasting models. Unlike many other methods in the literature, our approach can be rapidly initialized and does not require iterations over the full data sequence, thus it is suitable for a streaming scenario. This allows the application of off-the-shelf data-stream methods, depending on the application domain. In this paper, we investigate classification. We compare to a large variety of methods (auto-encoders, HMMs, basis functions, clustering methodologies, and PCA) and find that our proposed methods perform very competitively, and offers much promise for future work.