To address the problems of high global query sensitivity and low utility of mining results in the existing works, a Lattice-Trajectory Pattern Mining (LTPM) algorithm based on prefix sequence lattice and trajectory truncation was proposed for mining sequential patterns with differential privacy. An adaptive method was employed to obtain the optimal truncation length, and a dynamic programming strategy was used to truncate the original database. Based on the truncated database, the equivalent relation was used to construct the prefix sequence lattice for mining trajectory patterns. Theoretical analysis shows that LTPM satisfies ε-differential privacy. The experimental results show that the True Postive Rate (TPR) and Average Relative Error (ARE) of LTPM are better than those of N-gram and Prefix algorithms, which verifies that LTPM can effectively improve the utility of the mining results.

Focusing on the drawback that Discovering Maximum Frequent Itemsets Algorithm (DMFIA) has to generate lots of maximum frequent candidate itemsets in each dimension when given datasets with many candidate items and each maximum frequent itemset is not long, an improved Algorithm for mining Maximum Frequent Itemsets based of Frequent-Pattern tree (FP-MFIA) for mining maximum frequent itemsets based on FP-tree was proposed. According to Htable of FP-tree, this algorithm used bottom-up searches to mine maximum frequent itemsets, thus accelerated the count of candidates. Producing infrequent itemsets with lower dimension according to conditional pattern base of every layer when mining, cutting and reducing dimensions of candidate itemsets can largely reduce the amount of candidate itemsets. At the same time taking full advantage of properties of maximum frequent itemsets will reduce the search space. The time efficiency of FP-MFIA is at least two times as much as the algorithm of DMFIA and BDRFI (algorithm for mining frequent itemsets based on dimensionality reduction of frequent itemset) according to computational time contrast based on different supports. It shows that FP-MFIA has a clear advantage when candidate itemsets are with high dimension.