Towards mining closed frequent itemsets over a sliding window using limited memory space, a synopsis data structure to monitor transactions in the sliding window so that one can output the current closed frequent itemsets at any time. Due to time and memory constraints, the synopsis data structure cannot monitor all possible itemsets, but monitoring only frequent itemsets makes it difficult to detect new itemsets when they become frequent. Herein, there is introduced a compact data structure, the closed enumeration tree (CET), to maintain a dynamically selected set of itemsets over a sliding-window. The selected itemsets include a boundary between closed frequent itemsets and the rest of the itemsets Because the boundary is relatively stable, the cost of mining closed frequent itemsets over a sliding window is dramatically reduced to that of mining transactions that can possibly cause boundary movements in the CET.