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This paper introduces a new algorithm for clustering data in high-dimensional feature spaces, called GARDENHD. The algorithm is organized around the notion of data space reduction, i.e. the process of detecting dense areas (dense cells) in the space. It performs effective and efficient elimination of empty areas that characterize typical high-dimensional spaces and an efficient adjacency-connected agglomeration of dense cells into larger clusters. It produces a compact representation that can effectively capture the essence of data. GARDENHD is a hybrid of cell-based and density-based clustering. However, unlike typical clustering methods in its class, it applies a recursive partition of sparse regions in the space using a new space-partitioning strategy. The properties of this partitioning strategy greatly facilitate data space reduction. The experiments on synthetic and real data sets reveal that GARDENHD and its data space reduction are effective, efficient, and scalable.