Searching in metric spaces with user-defined and approximate distances
ACM Transactions on Database Systems (TODS)
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ACM SIGMOD Record
Estimating the selectivity of tf-idf based cosine similarity predicates
ACM SIGMOD Record
Time-Aware Similarity Search: A Metric-Temporal Representation for Complex Data
SSTD '09 Proceedings of the 11th International Symposium on Advances in Spatial and Temporal Databases
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This paper discusses the problem of selectivity estimation for range queries in metric datasets, which include vector, or dimensional, datasets as a special case. The main contribution of this paper is that, surprisingly, many different real datasets follow a "power law". From this observation we derive an analysis for the distance distribution of metric datasets. This is the first analysis of distance distributions for real metric datasets.We called the exponent of our power law as "distance exponent". We show that it plays a relevant role for the analysis of real, metric datasets. Specifically, we show (a) how to exploit the distance exponent to derive formulas for selectivity estimation of range queries and (b) how to compute it quickly from a metric index tree.We performed several experiments on many real datasets (road intersections of U.S. counties, vectors characteristics extracted from face matching systems, sets of words, distance matrixes) and synthetic datasets (Sierpinsky triangle, a 2-dimensional uniform distribution and a 2-dimensional line). Our selectivity estimation formulas are accurate, within relative error from 4% to 17%, and always within one standard deviation from the analytical results. Moreover, we present also a quick algorithm to estimate the "distance exponent", which gives good accuracy and saves orders of magnitude in computation time.