Heuristically mining the top-k high-utility itemsets with cross-entropy optimization

Mining high-utility itemsets (HUIs) is one of the most important research topics in data mining because HUIs consider non-binary frequency values of items in transactions and different profit values for each item. However, setting appropriate minimum utility thresholds by trial and error is a tedious process for users. Thus, mining the top-k HUIs without setting a utility threshold is becoming an alternative to determine all the HUIs. In this paper, we propose two algorithms, called the top-k high-utility itemset mining based on cross-entropy method (TKU-CE) and TKU-CE+, for mining the top-k HUIs heuristically. The TKU-CE algorithm is based on cross-entropy, and implements top-k HUI mining using combinatorial optimization. The main idea of TKU-CE is to generate the top-k HUIs by gradually updating the probabilities of itemsets with high-utility values. TKU-CE+ optimizes TKU-CE in three respects. First, unpromising items are filtered by critical utility value, to reduce the computational burden in the initial stage. Second, a sample refinement strategy is used in each iteration, to reduce the computational burden in the iterative stage. Finally, smoothing mutation is proposed, to randomly generate some new itemsets in addition to those from previous iterations. Consequently, diversity of samples is improved, so that more actual top-k HUIs can be discovered with fewer iterations. Compared with state-of-the-art algorithms, TKU-CE and TKU-CE+ are easy to implement and avoid the computational costs that would be incurred by additional data structures and threshold-raising strategies. Extensive experimental results show that both algorithms are efficient, memory-saving, scalable, and can discover the most actual top-k HUIs.