An E cient Approach for Approximating Multi - dimensional RangeQueries and Nearest Neighbor Classi cation in Large

We propose a locally adaptive technique to address the problem of setting the bandwidth parameters optimally for kernel density estimation. Our technique is eecient and can be performed in only two dataset passes. We also show how to apply our technique to eeciently solve range query approximation, classiication and clustering problems for very large datasets. We validate the eeciency and accuracy of our technique by presenting experimental results on a variety of both synthetic and real datasets.