\input zb-basic \input zb-ioport \iteman{io-port 05109813} \itemau{Wang, Jianyong; Han, Jiawei; Pei, Jian} \itemti{Closed Constrained Gradient Mining in Retail Databases.} \itemso{IEEE Transactions on Knowledge and Data Engineering 18, No.06, 764-769 (2006).} \itemab Summary: 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, {\rm{top}}{\hbox{-}}X average measure, is proposed and can be adopted to prune search space effectively. Experiments show that a combination of LCLOSET and the {\rm{top}}{\hbox{-}}X average pruning provides an efficient approach to mining frequent closed gradient itemsets. \itemrv{~} \itemcc{} \itemut{gradient pattern.} \itemli{doi:10.1109/TKDE.2006.88} \end