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Evaluating the intrinsic dimension of evolving data streams

Data streams are fundamental in several data processing applications involving large amount of data generated continuously as a sequence of events. Frequently, such events are not stored, so the data is analyzed and queried as they arrive and discarded right away. In many applications these events are represented by a predetermined number of numerical attributes. Thus, without loss of generality, we can consider events as elements from a dimensional domain. A sequence of events in a data stream can be characterized by its intrinsic dimension, which in dimensional datasets is usually lower than the embedding dimensionality. As the intrinsic dimension can be used to improve the performance of algorithms handling dimensional data (specially query optimization) measuring it is relevant to improve data streams processing and analysis as well. Moreover, it can also be useful to forecast data behavior. Hence, we present an algorithm able to measure the intrinsic dimension of a data stream on the fly, following its continuously changing behavior. We also present experimental studies, using both real and synthetic data streams, showing that the results on well-understood datasets closely follow what is expected from the known behavior of the data.