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Data reduction can improve the storage, transfer time, and processing requirements of very large data sets. One of the challenges of designing effective data reduction techniques is to be able to preserve the ability to use the reduced format directly for a wide range of database and data mining applications. We propose the novel idea of hierarchical subspace sampling in order to create a reduced representation of the data. The method is naturally able to estimate the local implicit dimensionalities of each point very effectively and, thereby, create a variable dimensionality reduced representation of the data. Such a technique is very adaptive about adjusting its representation depending upon the behavior of the immediate locality of a data point. An important property of the subspace sampling technique is that the overall efficiency of compression improves with increasing database size. Because of its sampling approach, the procedure is extremely fast and scales linearly both with data set size and dimensionality. We propose new and effective solutions to problems such as selectivity estimation and approximate nearest-neighbor search. These are achieved by utilizing the locality specific subspace characteristics of the data which are revealed by the subspace sampling technique.