document: Robust space transformations for distance-based operations For many KDD operations , such as nearest neighbor search , distance-based clustering , and outlier detection , there is an underlying & kgr ;-D data space in which each tuple\/object is represented as a point in the space . In the presence of differing scales , variability , correlation , and\/or outliers , we may get unintuitive results if an inappropriate space is used . The fundamental question that this paper addresses is : `` What then is an appropriate space ? '' We propose using a robust space transformation called the Donoho-Stahel estimator . In the first half of the paper , we show the key properties of the estimator . Of particular importance to KDD applications involving databases is the stability property , which says that in spite of frequent updates , the estimator does not : ( a ) change much , ( b ) lose its usefulness , or ( c ) require re-computation . In the second half , we focus on the computation of the estimator for high-dimensional databases . We develop randomized algorithms and evaluate how well they perform empirically . The novel algorithm we develop called the Hybrid-random algorithm is , in most cases , at least an order of magnitude faster than the Fixed-angle and Subsampling algorithms .
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