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An algorithm is proposed to cluster high dimensional data named as Clustering Algorithm Based On Sparse Feature Vector for Categorical Attributes (CABOSFV_C). It compresses data effectively by using `Sparse Feature Vector of a Set for Categorical Data' without losing the information necessary for making clustering decisions, and can get the clustering result with once data scan by defining `Sparse Feature Dissimilarity of a Set for Categorical Data' as distance measure. Because of the data reduction and once data scan strategy the algorithm has almost linear computation complexity and handles noise effectively. In addition, CABOSFV_C is suitable not only for sparse data but also for complete data, which is illustrated by two numeric examples at the end of the paper as well as other salient features of the algorithm.