Distance Exponent: A New Concept for Selectivity Estimation in Metric Trees

A fast and effective method to find correlations among attributes in databases

“…The algorithm is based on the box-counting approach (Schroeder 1991), a practical way to estimate the D 2 () of a point dataset. Theoretically, it should give a close approximation of the intrinsic dimension, and our experiments have shown that it does indeed do so (Traina et al 1999. The box-counting method is described as follows.…”

“…Furthermore, as pointed out in Traina et al (1999) and Schroeder (1991), the majority of real datasets are fractals, and we can use their correlation fractal dimension D 2 () as their intrinsic It is worth noting that the correlation fractal dimension is not affected by outliers.…”

An empirical evaluation of intrinsic dimension estimators

“…We chose various synthetic and real-life metric spaces and four indexing methods that are representatives of the major families of indices: two based on pivots and two based on compact partitions. Our comparison between real and estimated search difficulty yields that Distance Exponent [12,13] and Correlation [14] are currently the best predictors in practice, however all the estimators behave relatively well.…”

“…Traina et al [12,13] discuss the problem of the selectivity estimation for range queries in real-world metric spaces, including spatial or multidimensional datasets as special cases. It plays an important role when analyzing real metric spaces.…”

“…Building the distance plot requires Oðn 2 Þ distance computations. To reduce this cost, nbðrÞ is estimated using an index [12], in particular the M-tree [5]. That is, a way to estimate the distance exponent D of a dataset stored in a metric index is by means of the very same index.…”