DiffNodesets: An Efficient Structure for Fast Mining Frequent Itemsets

Mining frequent itemsets is an essential problem in data mining and plays an important role in many data mining applications. In recent years, some itemset representations based on node sets have been proposed, which have shown to be very efficient for mining frequent itemsets. In this paper, we propose DiffNodeset, a novel and more efficient itemset representation, for mining frequent itemsets. Based on the DiffNodeset structure, we present an efficient algorithm, named dFIN, to mining frequent itemsets. To achieve high efficiency, dFIN finds frequent itemsets using a set-enumeration tree with a hybrid search strategy and directly enumerates frequent itemsets without candidate generation under some case. For evaluating the performance of dFIN, we have conduct extensive experiments to compare it against with existing leading algorithms on a variety of real and synthetic datasets. The experimental results show that dFIN is significantly faster than these leading algorithms.Comment: 22 pages, 13 figure

Clique percolation in random graphs

As a generation of the classical percolation, clique percolation focuses on the connection of cliques in a graph, where the connection of two $k$-cliques means that they share at least $l<k$ vertices. In this paper, we develop a theoretical approach to study clique percolation in Erd\H{o}s-R\'{e}nyi graphs, which gives not only the exact solutions of the critical point, but also the corresponding order parameter. Based on this, we prove theoretically that the fraction $\psi$ of cliques in the giant clique cluster always makes a continuous phase transition as the classical percolation. However, the fraction $\phi$ of vertices in the giant clique cluster for $l>1$ makes a step-function-like discontinuous phase transition in the thermodynamic limit and a continuous phase transition for $l=1$. More interesting, our analysis shows that at the critical point, the order parameter $\phi_c$ for $l>1$ is neither $0$ nor $1$, but a constant depending on $k$ and $l$. All these theoretical findings are in agreement with the simulation results, which give theoretical support and clarification for previous simulation studies of clique percolation.Comment: 6 pages, 5 figure