Sampling Streaming Data Along Geodesic

This paper proposes an approach to sample data stream based on differential geometry. Our aim is to take advantage of information of discarded data and support stream to generate different number of transactions during different periods. To this end, we establish a novel data stream model represented by a surface, within which time is quantified and probability, value and time, viewed as one united body, could be calculated simultaneously. We project data stream onto a surface of the model and replace points which have the shortest geodesic distance with their mid-point. To the best of our knowledge, this is the first work on introducing differential geometry as a sampling trick. Experimental results show that our approach is effective.