Abstract In the Multiple Data Streams (MDS) environment, dat a sources generate data with no end in sight. Because of the difference of data sources, transaction numbers of MDS are not always equal to each other during a sam e period. Preprocessing MDS to obtain same number of samples for each stream is an essential step for lots of mining tasks. All existing preprocessing methods assume that data arrive simul taneously. However, this assumption may not be true in many real environments due to multiple data sources and diffe rent ways of data generating. This asynchronous iss ue is explored in this paper, by introducing the differential geometry as a trick. First, we establish a novel stream model called POLAR. The POLAR is an intrinsic surface spanned by time, probabilit y and value. And then, we propose a preprocessing a pproach, called COPOLAR, to obtain same number of samples for each stream of MDS. COPOLAR first projects original observations onto POLAR; and then merges points with shortest geodesi c distances along a geodesic on surface into mid6point on the same geodesic iteratively and incrementally until the nu mber of points which we hope to obtain is met. Expe rimental results on synthetic and real data show that COPOLAR is effect ive in terms of maintaining characteristics of both statistics and vector.

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