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Clustering high-dimensional data has been a major challenge due to the inherent sparsity of the points. Most existing clustering algorithms become substantially inefficient if the required similarity measure is computed between data points in the full-dimensional space. To address this problem, a number of projected clustering algorithms have been proposed. However, most of them encounter difficulties when clusters hide in subspaces with very low dimensionality. These challenges motivate our effort to propose a robust partitional distance-based projected clustering algorithm. The algorithm consists of three phases. The first phase performs attribute relevance analysis by detecting dense and sparse regions and their location in each attribute. Starting from the results of the first phase, the goal of the second phase is to eliminate outliers, while the third phase aims to discover clusters in different subspaces. The clustering process is based on the k-means algorithm, with the computation of distance restricted to subsets of attributes where object values are dense. Our algorithm is capable of detecting projected clusters of low dimensionality embedded in a high-dimensional space and avoids the computation of the distance in the full-dimensional space. The suitability of our proposal has been demonstrated through an empirical study using synthetic and real datasets.