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Incorporating constraints into frequent itemset mining not only improves data mining efficiency, but also leads to concise and meaningful results. In this paper, a framework for closed constrained gradient itemset mining in retail databases is proposed by introducing the concept of gradient constraint into closed itemset mining. A tailored version of CLOSET+, LCLOSET, is first briefly introduced, which is designed for efficient closed itemset mining from sparse databases. Then, a newly proposed weaker but antimonotone measure, top-X average measure, is proposed and can be adopted to prune search space effectively. Experiments show that a combination of LCLOSET and the top-X average pruning provides an efficient approach to mining frequent closed gradient itemsets. [ABSTRACT FROM AUTHOR]